Synchronized manual with one of Justin

Updated source was located at
located at https://bitbucket.org/jrsteven/phys251_manual/src/master/

19 files changed, 523 insertions, 442 deletions

diff --git a/blackbody.tex b/blackbody.tex
index 4ead1fc..912d204 100644
--- a/blackbody.tex
+++ b/blackbody.tex
@@ -8,6 +8,10 @@
  \textbf{Experiment objectives}: explore radiation from objects at certain temperatures,
     commonly known as ``blackbody radiation''; make measurements testing the Stefan-Boltzmann
     law in high- and low-temperature ranges; measure the inverse-square law for thermal radiation.
+\vspace{0.25in}
+\hrule
+\textbf{A brief writeup}: Your instructor may tell you to do a brief writeup of this experiment. If so you will take data as instructed in the pages that follow. However when it comes time to do the analysis and write the report you will follow the {\it Instructions for a brief writeup} on page~\pageref{pag:briefwriteup}.
+\hrule
 
 \section*{Theory}
 
@@ -240,15 +244,17 @@ Lamp, Power supply.
 1.00&&&&&\\\hline \dots &&&&&\\\hline&&&&&\\\hline
 \end{tabular}
 \caption{
-	Sample table for experimental data recording
+	Sample table for recording your data. 
 	\label{tbl:sampla_data_table} % spaces are big no-no withing labels
 }
 \end{center}
 \end{table}
 
-In the lab report plot the reading from the radiation sensor (convert to $W/m^2$) versus $T^4$. According to the Stefan-Boltzmann Law, the data should fall along a straight line. Do a fit and report the value of the slope that you obtain. How does it compare to the accepted value of Stefan's constant?
+In the lab report plot the reading from the radiation sensor (convert to $W/m^2$) (on the y axis) versus the temperature $T$ on the x axis. According to the Stefan-Boltzmann Law, the data should show a $S\propto T^4$ behavior. Do a fit to $S=C T^n$ where $C$ and $n$ are free parameters. Report the value of each parameter and its uncertainty. Does $n=4$, within uncertainty? How does it compare to the accepted value of Stefan's constant?  
+
+Examine the fit.  How many points are within 1 uncertainty ($\sigma$) of the line?  How many are between 1 and 2 $\sigma$? For a good fit, about 2/3 of the points should be within $1\sigma$ of the line, and the other 1/3 between 1-$2\sigma$, with perhaps one point between 2 and $3\sigma$, if we have about 20 points. That latter number scales up with the number of points. Unless you have a few 100 datapoints, a good fit should not have any points further than $3\sigma$. Based on this criteria, was is your fit good?  Do the points seem to systematically differ from the fit line in a particular region?  Can you think of a reason why that would be?
 
-Don't be alarmed if the value of slope is way off from Stefan's constant. The Stefan-Boltzmann Law, as stated in Eq.(\ref{SBl}), is only true for ideal black bodies. For other objects, a more general law is: $S=A\sigma T^4$, where A is the absorptivity. $A=1$ for a perfect blackbody. $A<1$ means the object does not absorb (or emit) all the radiation incident on it (this object only radiates a fraction of the radiation of a true blackbody). The material lampblack has $A=0.95$ while tungsten wire has $A=0.032$ (at $30^{\circ} C$) to 0.35 (at $3300^{\circ}C$). Comparing your value of slope to Stefan's constant, and assuming that the Stefan-Boltzmann Law is still valid, what do you obtain for $A$? Is it consistent with tungsten? What else could be affecting this measurement?
+The parameter $C$ is equal to $A\sigma$. For an ideal black body $A=1$, but in your case it will be very different. $A<1$ means the object does not absorb (or emit) all the radiation incident on it (this object only radiates a fraction of the radiation of a true blackbody). The material lampblack has $A=0.95$ while tungsten wire has $A=0.032$ (at $30^{\circ} C$) to 0.35 (at $3300^{\circ}C$). Using the result of your fit, and assuming we know the Stephan-Boltzman constant $\sigma$ by some other means, what is $A$ and what is the uncertainty on it?  Is it consistent with tungsten? What else could be affecting this measurement?
 
 
 \section*{Test of the inverse-square law}
@@ -274,11 +280,61 @@ is true for a lamp.
 	at constant intervals the optimal approach? At what distances would you expect
 	the sensor reading change more rapidly?}
 
- \item  Make a plot of the corrected radiation measured from the lamp versus the inverse square of the distance from the lamp to the sensor $(1/x^2)$ and do a linear fit to the data.  How good is the fit? Is this data linear over the entire range of distances? Comment on any discrepancies. What is the uncertainty on the slope?  What intercept do you expect? Comment on these values and their uncertainties.
+ \item  Make a plot of the corrected radiation measured from the lamp versus the distance from the lamp to the sensor $x$.  Fit the data to $S= B + C x^n$ where $B$, $C$ and $n$ are free parameters. Based on the criteria in the previous section, how good is the fit? 
+
+
+\item What are the values of $B$, $C$ and $n$ (and, of course, their uncertainties)?  How do they agree with what you expect from the inverse square law?
+
+\item  Can the lamp be considered a point source? If not, how could this affect your measurements?
+
+\end{enumerate}
+
+\hrule
+
+{\huge Your instructor may have told you to do a ``brief writeup'' of this experiment. If so, please see the instructions starting on the next page (page~\pageref{pag:briefwriteupBB}).}
+
+\hrule
+
+\newpage
+
+\section*{Instructions for a brief writeup}\label{pag:briefwriteupBB}
+
+This lab is reasonably straightforward. There is much data to take and several fits, but describing the setup and providing an introduction seems less necessary than for some of the others. Therefore, just answer the following questions/bullet points in your report. {\bf Please restate each one so it's easy for us to follow along.} {\it Refer the the relevant section earlier in the manual for additional discussion. This is just a bullet point summary of the deliverables.}
 
-\item  Does radiation from the lamp follow the inverse square law? Can the lamp be considered a point source? If not, how could this affect your measurements?
+\subsection*{Thermal radiation rates from different surfaces}
+First, tabulate your data and include it (with label and caption).  Then use your data to address the following questions:
+\begin{enumerate}
+\item Is it true that good absorbers of radiation are good emitters? \textit{Hint:} use what you know about absorption of visible light for these surfaces
+\item Is emission from the black and white surfaces similar?
+\item Do objects at the same temperature emit different amounts of radiation?
+\item Is glass effective in blocking thermal radiation? What about other objects that you tried? 
+\end{enumerate}
+
+\subsection*{Tests of the Stephan-Boltzmann Law}
+
+
+\begin{enumerate}
+\item Tabulate your data as in Tab 4.1 and include it.
+\item Estimate and report uncertainties on the voltage, current, and radiation sensor.
+\item Plot the readings from the radiation sensor (y-axis) vs $T$ (x-axis) with uncertainties and fit to $S=C T^n$. Include the plot in your report.
+\item Is it a good fit? 
+\item Does the Stephan-Boltzman equation seem to hold? Does $n=4$, within uncertainties?
+\item What value (and uncertainty) do your data imply for $A$? Is it consistent with tungsten? What else could be affecting your measurement? 
 
+
+\end{enumerate}
+
+\subsection*{Test of the inverse square law}
+
+\begin{enumerate}
+\item Tabulate your data and include it in the report. Be sure to include the lamp-off data, used to correct the lamp-on data for ambient radiation.
+\item Estimate and report uncertainties on the distance between the sensor and lamp,  and on the readings from the radiation sensor.
+\item Make a plot of the corrected radiation (y-axis, with uncertainty) vs distance (x-axis) and fit it to $S= B + C x^n$. Include it in your report. 
+\item How good is the fit?
+\item Does $n=-2$ within uncertainty? Do the data confirm the inverse square law?
+\item What are $B$ and $C$?  What did you expect?  Comment on any discrepancies. 
 \end{enumerate}
+
 %
 %\item The Blackbody Spectrum Equipment: Spectrometer, computer, high
 %temperature source.
diff --git a/ediffract.tex b/ediffract.tex
index e1da926..8ace7bf 100644
--- a/ediffract.tex
+++ b/ediffract.tex
@@ -35,7 +35,7 @@
 
 \begin{figure}[h]
 \centering
-\includegraphics[width=\textwidth]{./pdf_figs/ed1} \caption{\label{ed1}Electron
+\includegraphics[width=\textwidth]{./pdf_figs/ed1_new} \caption{\label{ed1}Electron
 Diffraction from atomic layers in a crystal.}
 \end{figure}
 \section*{Theory}
@@ -48,7 +48,7 @@ Fabry-Perot or Michelson interferometers. The de Broglie wavelength for the
 electron is given by $\lambda=h/p$, where $p$ can be calculated by knowing the
 energy of the electrons when they leave the ``electron gun'':
 \begin{equation}\label{Va}
-\frac{p^2}{2m}=eV_a,
+\frac{1}{2}mv^2=\frac{p^2}{2m}=eV_a,
 \end{equation}
  where $V_a$ is the accelerating potential.  The condition for constructive
 interference is that the path length difference for the two waves
@@ -77,7 +77,7 @@ electron's mass, and $V_a$ is the accelerating voltage.
 
 \section*{Experimental Procedure}
 
-\textbf{Equipment needed}: Electron diffraction apparatus and power supply, tape, ruler.
+\textbf{Equipment needed}: Electron diffraction apparatus and power supply, ruler and thin receipt paper or masking tape.
 
 \subsection*{Safety}
 You will be working with high voltage. The power supply will be connected for you,
@@ -127,8 +127,8 @@ Anode Current & $I_A$& 0.15 mA at 4000 V ( 0.20 mA max.)
 Slowly change the voltage and determine the highest achievable accelerating
 voltage, and the lowest voltage when the rings are visible.
 \item  Measure the diffraction angle $\theta$ for both inner and outer rings for 5-10 voltages from that range,
-using the same masking tape (see procedure below). Each lab partner should
-repeat these measurements (using an individual length of the masking tape).
+using the same thin receipt paper (see procedure below). Each lab partner should
+repeat these measurements (using an individual length of the thin paper).
 \item Calculate the average value of $\theta$ from the individual measurements for each
 voltage $V_a$. Calculate the uncertainties for each $\theta$.
 \end{enumerate}
@@ -137,7 +137,7 @@ voltage $V_a$. Calculate the uncertainties for each $\theta$.
 
 To determine the crystalline structure of the target, one needs to carefully
 measure the diffraction angle $\theta$. It is easy to see (for example, from
-Fig.~\ref{ed1} ) that the diffraction angle $\theta$ is 1/2 of the angle
+Fig.~\ref{ed1}) that the diffraction angle $\theta$ is 1/2 of the angle
 between the beam incident on the target and the diffracted beam to a ring,
 hence the $2\theta$ appearing in Fig.~\ref{ed4}. You are going to determine
 the diffraction angle $\theta$ for a given accelerated voltage from the
@@ -147,13 +147,13 @@ L\sin{2\theta} = R\sin\phi,
 \end{equation}
 where the distance between the target and the screen $L = 0.130$~m is controlled during the production process to have an accuracy better than 2\%. {\it Note, this means that the electron tubes are not quite spherical.}
 
-The ratio between the arc length and the distance between the target and the
-radius of the curvature of the screen $R = 0.066$~m gives the angle $\phi$ in
-radian:  $\phi = s/2R$. To measure $\phi$ carefully place a piece of
-masking tape on the tube so that it crosses the ring along the diameter.
+The ratio between the arc length $s$ and the
+radius of the curvature for the screen $R = 0.066$~m gives the angle $\phi$ in
+radians:  $\phi = s/2R$. To measure $\phi$ carefully place a piece of
+thin receipt paper on the tube so that it crosses the ring along the diameter.
 Mark the position of the ring for each accelerating voltage, and then
-remove the masking tape and measure the arc length $s$ corresponding to
-each ring. You can also make these markings by using the thin paper on which cash register receipts are printed.
+remove the paper and measure the arc length $s$ corresponding to
+each ring. You can also make these markings on masking tape placed gently on the tube.
 
 
 \begin{figure}
@@ -170,10 +170,10 @@ is proportional to $d$, one needs to substitute the expression for the
 electron's velocity  Eq.(\ref{Va}) into the diffraction condition given by
 Eq.(\ref{bragg}):
 \begin{equation}\label{bragg.analysis}
-2d\sin\theta=\lambda=\frac{h}{\sqrt{2m_ee}}\frac{1}{\sqrt{V_a}}
+\sin\theta=\frac{h}{2\sqrt{2m_ee}}\frac{1}{d}\frac{1}{\sqrt{V_a}}
 \end{equation}
 
-Make a plot of $1/\sqrt{V_a}$ versus $\sin\theta$ for the inner and outer rings
+Make a plot of $\sin\theta$ (y-axis, with uncertainty) vs $1/\sqrt{V_a}$ (x-axis) for the inner and outer rings
 (both curves can be on the same graph). Fit the linear dependence and measure
 the slope for both lines. From the values of the slopes find the distances
 between atomic layers $d_{inner}$ and $d_{outer}$.
@@ -181,7 +181,7 @@ between atomic layers $d_{inner}$ and $d_{outer}$.
 Compare your measurements to the accepted values: $d_{inner}=d_{10} = .213$~nm
 and $d_{outer}=d_{11}=0.123$~nm.
 
-\section*{Looking with Electrons}
+\section*{Seeing with Electrons}
 	
 The resolution of ordinary optical microscopes
 is limited (the diffraction limit) by the wavelength of light ($\approx$ 400
diff --git a/emratio.tex b/emratio.tex
index 42d6630..af4df4b 100644
--- a/emratio.tex
+++ b/emratio.tex
@@ -123,7 +123,6 @@ between the cathode and the anode. The grid is held positive with respect to
 the cathode and negative with respect to the anode. It helps to focus the
 electron beam.
 
-
 The Helmholtz coils of the $e/m$ apparatus have a radius and separation of
 $a=15$~cm. Each coil has $N=130$~turns. The magnetic field ($B$) produced by
 the coils is proportional to the current through the coils ($I_{hc}$) times
@@ -135,6 +134,15 @@ scale, you can measure the radius of the beam path without parallax error. The
 cloth hood can be placed over the top of the $e/m$ apparatus so the experiment
 can be performed in a lighted room.
 
+\subsection*{Pasco High Voltage Power Supply}
+
+The Pasco High Voltage Power Supply in Fig.~\ref{hv_power.fig} provides up to 500 V DC accelerating voltage to the electrodes in the e/m tube, which is measured on the voltmeter shown in Fig.~\ref{emfig3}.  The electron gun heater is also powered by this supply using the right panel, which should be set to a maximum of 6 V AC using the dial on the supply.
+
+\begin{figure}[h]
+\centering
+\includegraphics[width=0.7\columnwidth]{./pdf_figs/eoverm_powersupply.jpeg}
+\caption{\label{hv_power.fig} Pasco High Voltage Power Supply.}
+\end{figure}
 
 \subsection*{Safety}
 You will be working with high voltage. Make all connections when power is off.
@@ -180,7 +188,7 @@ For each measurement record:
 \item[Accelerating voltage $V_a$]
 \item[Current through the Helmholtz coils $I_{hc}$]
 \end{description}
-Look through the tube at the electron beam. To avoid parallax errors, move your head to align one side the electron beam ring with its reflection that you can see on the mirrored scale. Measure the radius of the beam as you see it, then repeat the measurement on the other side, then average the results. Each lab partner should repeat this measurement, and estimate the uncertainty. Do this silently and tabulate results. After each set of measurements (e.g., many values of $I_{hc}$ at one value of $V_a$) compare your results. This sort of procedure helps reduce group-think, can get at some sources of systematic errors, and is a way of implementing experimental skepticism. 
+Look through the tube at the electron beam. To avoid parallax errors, move your head to align one side of the electron beam ring with its reflection that you can see on the mirrored scale. Measure the radius of the beam as you see it, then repeat the measurement on the other side, then average the results. Each lab partner should repeat this measurement, and estimate the uncertainty. Do this silently and tabulate results. After each set of measurements (e.g., many values of $I_{hc}$ at one value of $V_a$) compare your results. This sort of procedure helps reduce group-think, can get at some sources of systematic errors, and is a way of implementing experimental skepticism. 
 
 \item Repeat the radius measurements for at least 4 values of $V_a$ and for each $V_a$ for 5-6 different values of the magnetic field.
 
@@ -214,21 +222,16 @@ cause the radius to be measured as smaller than it should be.
 
 \subsection*{Calculations and Analysis:}
 \begin{enumerate}
- \item Calculate $e/m$ for each of the
-readings using Eq. \ref{emeq7}.    NOTE: Use MKS units for
-calculations.
+ \item Calculate $e/m$ for each of the readings using Eq. \ref{emeq7} and determine the uncertainty on $e/m$ based on your uncertainty estimates for those readings.  NOTE: Use MKS units for calculations.
 \item  For each of the four $V_a$ settings calculate the mean
-$<e/m>$, the standard deviation $\sigma$ and {\bf the standard error in the
-mean $\sigma_m$.}
+$<e/m>$ and the standard deviation $\sigma$.
 Are these means consistent with one another sufficiently that you can
-combine them ?  [Put quantitatively, are they within $2 \sigma$ of each
-  other ?]
-\item Calculate the {\bf grand mean} for all $e/m$ readings, its
-standard deviation $\sigma$  {\bf and the standard error in the grand mean
-$\sigma_m$}.
-\item Specify how this grand mean compares to the accepted value, i.e., how many $\sigma_m$'s is it from the accepted value ?
+combine them?  [Put quantitatively, are they within $2 \sigma$ of each
+  other?]
+%\item Calculate the {\bf grand mean} for all $e/m$ readings and its standard deviation $\sigma$.  
+%\item Specify how this grand mean compares to the accepted value, i.e., how many $\sigma$'s is it from the accepted value ?
 
-\item  Finally, plot the data in the following way which should, ( according to Eq. \ref{emeq7}), reveal a linear relationship: plot  $V_a$ on the abscissa [x-axis] versus  $r^2 B^2/2$ on the ordinate [y-axis]. The uncertainty in $r^2 B^2/2$ should come from the standard deviation of the different measurements made by your group at the fixed $V_a$. The optimal slope of this configuration of data should be $<m/e>$. Determine the slope from your plot and its error by doing a linear fit. What is the value of the intercept? What should you expect it to be?
+\item Finally, plot the data in the following way which should, ( according to Eq. \ref{emeq7}), reveal a linear relationship: plot  $V_a$ on the abscissa [x-axis] versus  $r^2 B^2/2$ on the ordinate [y-axis]. The uncertainty in $r^2 B^2/2$ should come from the standard deviation of the different measurements made by your group at the fixed $V_a$. The optimal slope of this configuration of data should be $<m/e>$. Determine the slope from your plot and its error by doing a linear fit, and compare the slope parameter to the accepted value for $<m/e>$. What is the value of the intercept? What should you expect it to be?
 
 \item Comment on which procedure gives a better value of $<e/m>$ (averaging or linear plot).
 \end{enumerate}
@@ -250,7 +253,7 @@ where $\mu_0$ is the magnetic permeability constant, $I$ is the total electric c
 This configuration provides very uniform magnetic field along the common axis of the pair, as shown in Fig.~\ref{emfig4}. The correction to the constant value given by Eq.(\ref{emeq_apx}) is proportional to $(x/a)^4$ where $x$ is the distance from the center of the pair. However, this is true only in the case of precise alignment of the pair: the coils must be parallel to each other!
 \begin{figure}[h]
 \centering
-\includegraphics[width=0.6\columnwidth]{./pdf_figs/emratioFig4}
+\includegraphics[width=0.7\columnwidth]{./pdf_figs/emratioFig4}
 \caption{\label{emfig4}Dependence of the magnetic field produced by a Helmholtz
 coil pair $B$ of the distance from the center (on-axis) $x/a$. The magnetic
 field is normalized to the value $B_0$ in the center.}
diff --git a/evmik_manual.sty b/evmik_manual.sty
index e4af124..fc8784a 100644
--- a/evmik_manual.sty
+++ b/evmik_manual.sty
@@ -1,8 +1,10 @@
 % -*- latex -*-
 \usepackage{subfiles}
 \usepackage{tabularx,boxedminipage,amsmath,fullpage,units}
+\usepackage{framed}
 \usepackage{graphicx}
-\usepackage{subcaption}
+%\usepackage[compatibility=false]{subcaption}
+%\captionsetup{compatibility=false}
 \usepackage[pdftex,final]{hyperref}
 \hypersetup{
 	colorlinks=true,       % false: boxed links; true: colored links
diff --git a/faraday_rotation.tex b/faraday_rotation.tex
index 23cab82..9745b78 100644
--- a/faraday_rotation.tex
+++ b/faraday_rotation.tex
@@ -55,7 +55,7 @@ We'll see the Faraday effect by observing changes in the intensity of light as w
 The phase-locking technique works in the following way. We'll vary the
 magnetic field periodically with time as a sine wave, and then observe the
 signal from the photodiode as a function of time.  The signal will look
-like a large constant with a small wobble on it, along with some random
+like a large constant with a small sine wave "wobble" on it, along with some random
 noise with a similar magnitude to the wobble. However, we can subtract off
 the non time-varying portion of the signal, using a high pass filter. Then,
 since we know the period and phase of the magnetic field, we can time our
@@ -106,7 +106,7 @@ The experimental setup is shown in Fig.~\ref{fig:setup}.
 
 \begin{description}
 \item[Choice of $\theta$] You need to pick an angle $\theta$, which may seem arbitrary. There is a best choice. Examine Eq.~\ref{eq:Ifinal}.  Pick $\theta$ and be sure to tighten the thumbscrew.
-\item[Faraday rotation] Plug the photodiode output into the scope, set the scope so its channel is DC coupled, and make sure that the ``probe'' setting is at 1x. Turn the amplifier dial about halfway to the maximum setting you found. Observe the photodiode trace on the scope, perhaps changing the volts/div setting so you can see the trace more clearly. What is the voltage? Record it.  The changing magnetic field should be causing a change in the polarization angle of the laser light, which should cause a wobble to the photodiode signal.   Can you see any wobble? 
+\item[Faraday rotation] Plug the photodiode output into the scope, set the scope so its channel is DC coupled, and make sure that the ``probe'' setting is at 1x. Turn the amplifier dial about halfway to the maximum setting you found. Observe the photodiode trace on the scope, perhaps changing the volts/div setting so you can see the trace more clearly. What is the voltage? Record it.  The changing magnetic field should be causing a change in the polarization angle of the laser light, which should cause a sinusoidal time dependence to the photodiode signal, referred to as the "wobble."   Can you see any wobble? 
 \item[AC coupling] The wobble is riding atop a large constant (DC) signal.
 	The scope can remove the DC signal by ``AC coupling'' the
 	photodiode channel. This essentially directs the scope input
diff --git a/interferometry.tex b/interferometry.tex
index 62487ae..e573a91 100644
--- a/interferometry.tex
+++ b/interferometry.tex
@@ -9,27 +9,27 @@ interferometers, calibrate them using a laser of known wavelength, and then use
 
 \section*{Introduction}
 
-Optical interferometers are the instruments that rely on interference of two or more superimposed reflections of the input laser beam. These are one of the most common optical tools, and are used for precision measurements, surface diagnostics, astrophysics, seismology, quantum information, etc. There are many configurations of optical interferometers, and in this lab you will become familiar with two of the more common setups.
+Optical interferometers are the instruments that rely on the interference of two or more superimposed reflections of the input laser beam. These are one of the most common optical tools, and are used for precision measurements, surface diagnostics, astrophysics, seismology, quantum information, etc. There are many configurations of optical interferometers, and in this lab you will become familiar with two of the more common setups.
 
 The \textbf{Michelson interferometer}, shown in Fig.~\ref{fig1mich.fig}, is based on the interference of two beams: the initial light is split into two arms on a beam splitter, and then these resulting beams are reflected and recombined on the same beamsplitter again. The difference in optical paths in the two arms leads to a changing relative phase of two beams, so when overlapped the two light fields will interfere constructively or destructively.
 \begin{figure}[h]
 \centering
-\includegraphics[width=0.8\linewidth]{./pdf_figs/fig1} \caption{\label{fig1mich.fig}A Michelson Interferometer setup.}
+\includegraphics[width=0.65\linewidth]{./pdf_figs/michelson.png} \caption{\label{fig1mich.fig}A Michelson Interferometer setup.}
 \end{figure}
-Such an interferometer was first used by Michelson and Morley in 1887 to determine that electromagnetic waves propagate in vacuum, giving the first strong evidence against the theory of a \textit{luminiferous aether} (a fictitious medium for light wave propagation) and providing insight into the true nature of electromagnetic radiation. Michelson interferometers are widely used in many areas of physics and engineering. At the end of this writeup we describe LIGO, the world's largest Michelson interferometer, designed to measure the gravitational waves and thus test general relativity.
+Such an interferometer was first used by Michelson and Morley in 1887 to determine that electromagnetic waves propagate in vacuum, giving the first strong evidence against the theory of a \textit{luminiferous aether} (a fictitious medium for light wave propagation) and providing insight into the true nature of electromagnetic radiation. Michelson interferometers are widely used in many areas of physics and engineering, including the recent discovery of gravitational waves at the LIGO facility (see Sect.~\ref{LIGO} at the end of this lab for more information).
 
 Figure~\ref{fig1mich.fig} shows the traditional setting for a Michelson
 interferometer. A beamsplitter (a glass plate which is partially
 silver-coated on the front surface and angled at 45 degrees) splits the
 laser beam into two parts of equal amplitude. One beam (that was initially
-transmitted by the beamsplitter) travels to a fixed mirror $M_1$ and back
+transmitted by the beamsplitter) travels to a moveable mirror $M_1$ and back
 again. One-half of this amplitude is then reflected from the
 partially-silvered surface and directed at 90 degrees toward the observer
 (you will use a viewing screen). At the same time the second beam
-(reflected by the beamsplitter) travels at 90 degrees toward mirror $M_2$
-and back. Since this beam never travels through the glass beamsplitter
-plate, its optical path length is shorter than for the first beam. To
-compensate for that, it passes twice through a clear glass plate called the compensator plate, that has the same thickness. At the beamsplitter one-half of this light is transmitted to an observer, overlapping with the first beam, and the total amplitude of the light at the screen is a combination of amplitude of  the two beams:
+(reflected by the beamsplitter) travels at 90 degrees toward an adjustable mirror $M_2$
+and back. Since this beam travels through the glass beamsplitter
+plate 3 times, its optical path length is longer than the first beam which only passes through the beamsplitter 1 time.  To
+compensate for that, the first beam passes twice through a clear glass plate called the compensator plate, that has the same thickness.  At the beamsplitter one-half of this light is transmitted to an observer, overlapping with the beam reflected by $M_2$, and the total amplitude of the light at the screen is a combination of amplitude of  the two beams:
 \begin{equation}
 \mathbf{E}_{total} =  \mathbf{E}_1 + \mathbf{E}_2 = \frac12 \mathbf{E}_0 + \frac12 \mathbf{E}_0\cos(k\Delta l)
 \end{equation}
@@ -37,7 +37,7 @@ Here $k\Delta l$ is a phase shift (``optical delay'') between the two wavefronts
 optical path lengths  for the two beams $\Delta l$ , $k=2\pi n/\lambda$ is the wave number, $\lambda$ is the
 wavelength of light in vacuum, and $n$ is the refractive index of the optical medium (in our case - air).
 
-Mirror $M_2$ is mounted on a precision traveling platform. Imagine that we adjust its position (by turning the micrometer screw)  such that the distance traversed on both arms is exactly identical. Because the thickness of the compensator plate and the beamsplitter are the same, both wavefronts pass through the same amount of glass and air, so the path length of the light beams in both interferometer arms will be exactly the same. Therefore, the two fields will arrive in phase to the observer, and their amplitudes will add up constructively, producing a bright spot on the viewing screen. If now you turn the micrometer to offset the length of one arm by a half of light wavelength, $\Delta l = \lambda/2$, they will acquire a relative phase of $\pi$, and total destructive interference will occur:
+Mirror $M_1$ is mounted on a precision traveling platform. Imagine that we adjust its position (by turning the micrometer screw)  such that the distance traversed on both arms is exactly identical. Because the thickness of the compensator plate and the beamsplitter are the same, both wavefronts pass through the same amount of glass and air, so the path length of the light beams in both interferometer arms will be exactly the same. Therefore, the two fields will arrive in phase to the observer, and their amplitudes will add up constructively, producing a bright spot on the viewing screen. If now you turn the micrometer to offset the length of one arm by a half of light wavelength, $\Delta l = \lambda/2$, they will acquire a relative phase of $\pi$, and total destructive interference will occur:
 \begin{displaymath}
 \mathbf{E}_1 +\mathbf{E}_2=0\;\;\mathrm{or} \;\;\mathbf{E}_1 = -\mathbf{E}_2.
 %\end{displaymath}
@@ -47,7 +47,7 @@ Mirror $M_2$ is mounted on a precision traveling platform. Imagine that we adjus
 It is easy to see that constructive interference happens when the difference between path lengths in the two interferometer arms is equal to the integer number of wavelengths $\Delta l = m\lambda$, and destructive interference corresponds to a half-integer number of wavelengths $\Delta l = (m + 1/2) \lambda$ (here $m$ is an integer number). Since the wavelength of light is small ($600-700$~nm for a red laser), Michelson interferometers are able to measure distance variation with very good precision.
 
 
-In \textbf{Fabry-Perot configuration} the input light field bounces between two closely spaced partially reflecting surfaces, creating a large number of reflections. Interference of these multiple beams produces sharp spikes in the transmission for certain light frequencies. Thanks to the large number of interfering rays, this type of interferometer has extremely high resolution, much better than a Michelson interferometer. For that reason Fabry-Perot interferometers are widely used in telecommunications, lasers and spectroscopy to control and measure the wavelengths of light. In this experiment we will take advantage of the high spectral resolution of the Fabry-Perot interferometer to resolve two very closely-spaces emission lines in Na spectra by observing changes in overlapping interference fringes from the two lines.
+In \textbf{Fabry-Perot configuration} the input light field bounces between two closely spaced partially reflecting surfaces, creating a large number of reflections. Interference of these multiple beams produces sharp spikes in the transmission for certain light frequencies. Thanks to the large number of interfering rays, this type of interferometer has extremely high resolution, much better than a Michelson interferometer. For that reason Fabry-Perot interferometers are widely used in telecommunications, lasers and spectroscopy to control and measure the wavelengths of light. In this experiment we will take advantage of the high spectral resolution of the Fabry-Perot interferometer to resolve two very closely-spaced emission lines in Na spectra by observing changes in the overlapping interference fringes from the two lines.
 \begin{figure}[h]
 \centering
 \includegraphics[width=0.8\linewidth]{./pdf_figs/fpfig1} \caption{\label{fpfig1}Sequence of Reflection and Transmission for a ray arriving at the treated inner surfaces $P_1 \& P_2$.}
@@ -107,44 +107,54 @@ simply that the mirrors are not parallel, and additional alignment of the interf
 
 \begin{figure}
 \centering
-\includegraphics[width=0.8\linewidth]{./pdf_figs/fig2} \caption{\label{fig2mich.fig}Explanation of circular fringes. Notice that to simplify the figure we have ``unfold'' the interferometer by neglecting the reflections on the beamsplitter.}
+\includegraphics[width=0.8\linewidth]{./pdf_figs/fig2} \caption{\label{fig2mich.fig}Explanation the interference pattern. Notice that to simplify the figure we have ``unfold'' the interferometer by neglecting the reflections on the beamsplitter.}
 \end{figure}
 
-When the path length difference $\Delta l$ is varied by moving one of the mirrors using the micrometer, the fringes appear to ``move''. As the micrometer is turned, the condition for constructive and destructive interference is alternately satisfied at any given angle.  If we fix our eyes on one particular spot and count, for example, how many bright fringes pass that spot as we move mirror $M_2$ by a known distance, we can determine the wavelength of light in the media using the condition for constructive interference, $\Delta l = 2d\cos
-\theta = m\lambda$.
+When the path length difference is varied, by using the micrometer to move one of the mirrors a distance $\Delta l$ along the horizontal axis of Figure~\ref{fig2mich.fig}, the fringes appear to ``move''. As the micrometer is turned, the condition for constructive and destructive interference is alternately satisfied at any given angle.  If we fix our eyes on one particular spot and count how many bright fringes pass that spot as we move mirror $M_1$ by a known distance, we can determine the wavelength of light in the media using the condition for constructive interference
+
+\begin{equation}
+\label{eqn:constructive}
+2\Delta l \cos\theta = m\lambda.
+\end{equation}
+
+The factor of two comes from from the fact that if I move the mirror $\Delta l$ light has to go an additional distance $\Delta l \cos\theta$ to get to it and then the same distance return from it.  For simplicity, we might concentrate on the center of the fringe bull's eye at $\theta = 0$.  Equation~\ref{eqn:constructive} for constructive interference then reduces to $2 \Delta l = m\lambda$ (m = integer). If $X_1$ is the initial position of the mirror $M_1$ (as measured on the micrometer) and $X_2$ is the final position after a number of fringes $\Delta m$ has been counted, we have $2\Delta l = 2(X_2-X_1) = \lambda\Delta m$.   Then the laser wavelength $\lambda$ is then given as:
 
-For simplicity, we might concentrate on the center of the fringe bull's eye at $\theta = 0$. The equation above
-for constructive interference then reduces to $2\Delta l = m\lambda$ (m = integer). If $X_1$ is the initial
-position of the mirror $M_2$ (as measured on the micrometer) and $X_2$ is the final position after a number of
-fringes $\delta m$ has been counted, we have $2(X_2-X_1) = \lambda\Delta m$.   Then the laser wavelength,
-$\lambda$, is then given as:
 \begin{equation}\label{old3}
 \lambda = 2(X_2-X_1)/\Delta m.
 \end{equation}
 
 Set up the interferometer as shown in Figure~\ref{fig1mich.fig} using
-components from the PASCO interferometry kit. The mirrors $M_{1,2}$ are, correspondingly, a movable and an adjustable mirror from the kit. Align the interferometer with a laser beam. Adjust the beam so that it is impinging on the beamsplitter and on the viewing screen. Try to make the beams to hit near the center of all the optics, including both mirrors, the compensator plate and beam splitter. The interferometer has leveling legs which can be adjusted. Align the beams such that they overlap on the viewing screen, and so that the reflected beam is directed back into the laser.  This can be tricky to get right the first time. Be patient, make small changes, think about what you are doing, and get some help from the instructor and TA. 
+components from the PASCO interferometry kit. The mirrors $M_{1,2}$ are, correspondingly, a movable and an adjustable mirror from the kit. Alignment is not too difficult:
+
+\begin{enumerate}
+\item Begin by installing the movable mirror, adjustable mirror, component holder with viewing screen (magnetically attaches), and the lens holder. Do not install the lens yet. Make sure screws are firmly tightened as we don't want components to move around.
+\item Level the table by adjusting its legs and/or adjust the laser height, location and direction to get the beam spot at the center of the movable mirror.  It is a good idea to tape your laser down at this point, or make sure it's securely mounted in the optical breadboard (if your station has one). 
+\item Tweak the laser direction using the two knobs on its back so that the beam reflects back into its aperture.
+\item Install the beam splitter, orient it to center the new beam spot on the adjustable mirror.
+\item Tweak the adjustable mirror using the two knobs on its back. You want to make the two sets of dots visible on the viewing screen come into alignment. When they are properly aligned you should see interference fringes appear in the dot.
+\item It is possible to see interference without the compensator (ask yourself why). But, it can potentially make the pattern better and more distinct. Try inserting it and aligning to improve the pattern.
+\item Install the lens to blow up the pattern.
+\item Further tweak the adjustable mirror to bring the bullseye on screen. You will find it's very sensitive and a little tweaking goes a long way.
+\end{enumerate}
 
-Once the interferometer is aligned, insert a convex lens ($f=\unit[18]{mm}$
-works well) after the laser to spread out the beam (ideally the laser beam
-should be pass through the center of the lens to preserve alignment).
-Adjust the adjustable mirror slightly until you see the interference
-fringes in the screen. Continue to make small adjustments until you see a clear bull's eye circular pattern. \emph{A word of caution: sometimes dust on a mirror or imperfections on optical surfaces may produce similar intensity patterns. True interference disappears if you block one arm of the interferometer. Try it!}
+ Be patient, make small changes, think about what you are doing, and get some help from the instructor and TA.  It helps to start the alignment procedure with the micrometer and the movable mirror near the center of their ranges. Also, the alignment knobs on the laser and adjustable mirror should be at the middle of their ranges, so that the plane of each is perpendicular to the table. 
+
+\emph{A word of caution: sometimes dust on a mirror or imperfections on optical surfaces may produce similar intensity patterns. True interference disappears if you block one arm of the interferometer. Try it!}
 
 \textbf{Note}: before starting the measurements, make sure you understand how to read the micrometer properly!
 \begin{figure}[h]
 \centering
 %\includegraphics[width=0.7\columnwidth]{./pdf_figs/fig3}
-\subcaptionbox{Reading = 211~$\mu$m} {
+%\subcaptionbox{Reading = 211~$\mu$m} {
 \includegraphics[height=1.3in]{./pdf_figs/micrometer1}
-}
-\subcaptionbox{Reading = 345~$\mu$m} {
+%}
+%\subcaptionbox{Reading = 345~$\mu$m} {
 \includegraphics[height=1.3in]{./pdf_figs/micrometer2}
-}
-\subcaptionbox{Reading = 166~$\mu$m} {
+%}
+%\subcaptionbox{Reading = 166~$\mu$m} {
 \includegraphics[height=1.3in]{./pdf_figs/micrometer3}
-}
-\caption{\label{fig3mich.fig}Micrometer readings. The coarse division equals to 100~$\mu$m, and smallest division on the rotary dial is 1~$\mu$m (same as 1 micron). The final measurements is the sum of two. }
+%}
+\caption{\label{fig3mich.fig}Micrometer readings. The coarse division equals to 100~$\mu$m, and smallest division on the rotary dial is 1~$\mu$m (same as 1 micron). The final measurements is the sum of two. So, from left to right, the figures above show 211~$\mu$m, 345~$\mu$m, and 166~$\mu$m.}
 \end{figure}
 
 \section*{Wavelength measurements using Michelson interferometer}
@@ -153,7 +163,7 @@ fringes in the screen. Continue to make small adjustments until you see a clear
 
 Record the initial reading on the micrometer. Focus on the central fringe and begin turning the micrometer. You will see that the fringes move. For example, the central spot will change from bright to dark to bright again, that is counted as one fringe. A good method: pick out a reference line on the screen and then softly count fringes as they pass the point.  Count a total of about $\Delta m = 50$ fringes and record the new reading on the micrometer.
 
-Each lab partner should make at least two independent measurements, starting from different initial positions of the micrometer. For each trial, approximately 50 fringes should be accurately counted and tabulated with the initial $X_1$ and final $X_2$ micrometer settings. Do this at least five times (e.g., $5\times 50$ fringes). Consider moving the mirror both forward and backward. Make sure that the difference $X_2-X_1$ is consistent between all the measurements. Calculate the average value of the micrometer readings $<X_2-X_1>$. 
+Each lab partner should make at least two independent measurements, starting from different initial positions of the micrometer. For each trial, approximately 50 fringes should be accurately counted and tabulated with the initial $X_1$ and final $X_2$ micrometer settings. Do this at least five times (e.g., $5\times 50$ fringes). Consider moving the mirror both forward and backward. Make sure that the difference $X_2-X_1$ is consistent between all the measurements. Calculate the average value and standard deviation of the micrometer readings $<X_2-X_1>$.  What value do you obtain for the laser wavelength, and what are your uncertainties on that measurement?  Does this match what you expect for a red laser?
 
 %When your measurements are done, ask the instructor how to measure the wavelength of the laser using a commercial wavemeter. Using this measurement and Equation~\ref{old3} calculate the true distance traveled by the mirror $\Delta l$, and calibrate the micrometer (i.e. figure out precisely what displacement corresponds to one division of the micrometer screw dial).
 
@@ -187,22 +197,23 @@ energy physics were aligned using a similar technique. An experimenter
 would close his eyes and then put his head in a collimated particle beam.
 Cerenkov radiation caused by particles traversing the experimenter's
 eyeball is visible as a blue glow or flashes. This is dangerous but various
-people claim to have done it... when a radiation safety officer isn't
+people claim to have seen it done... when a radiation safety officer wasn't
 around.}.  However, your eyes will get tired quickly! Placing a diffuser plate in front of the lamp will make the observations easier. Since the interferometer is already aligned, you should see the interference picture. Make small adjustments to the adjustable mirror to make sure you see the center of the bull's eye.
 
 Repeat the same measurements as in the previous part by moving the mirror and counting the number of fringes. Each lab partner should make at least two independent measurements, recording initial and final position of the micrometer, and you should do at least five trials. Calculate the wavelength of the Na light for each trial. Then calculate the average value and its experimental uncertainty. Compare with the expected value of \unit[589]{nm}.
 
 In reality, the Na discharge lamp produces a doublet - two spectral lines that are very close to each other: \unit[589]{nm} and \unit[589.59]{nm}. Do you think your Michelson interferometer can resolve this small difference? Hint: the answer is no - we will use a Fabry-Perot interferometer for that task.
 
+\clearpage
+
 \section*{Alignment of the Fabry-Perot interferometer}
 
 \begin{figure}
 \centering
-\includegraphics[width=0.8\linewidth]{./pdf_figs/fpfig3} \caption{\label{fpfig3.fig}The Fabry-Perot Interferometer. For initial alignment the laser and the convex lens are used instead of the Na lamp.}
+\includegraphics[width=0.8\linewidth]{./pdf_figs/fpfig3} \caption{\label{fpfig3.fig}The Fabry-Perot Interferometer.  \textbf{For initial alignment the laser and the convex lens are used instead of the Na lamp.}}
 \end{figure}
 Disassemble the Michelson Interferometer, and assemble the Fabry-Perot interferometer as shown in
-Figure~\ref{fpfig3.fig}. First, place the viewing screen behind the two
-partially-reflecting mirrors ($P1$ and $P2$), and adjust the mirrors such
+Figure~\ref{fpfig3.fig}, initially using the laser for alignment instead of the sodium lamp. First, place the viewing screen behind the two partially-reflecting mirrors ($P1$ and $P2$), and adjust the mirrors such
 that the multiple reflections on the screen overlap. Then place a convex
 lens after the laser to spread out the beam, and make small adjustments
 until you see the concentric circles. Is there any difference between the
@@ -269,7 +280,7 @@ valid the approximation that $\lambda_1\lambda_2\approx \lambda^2$
 \boxed{\Delta\lambda \approx \frac{\lambda^2}{2(d_2-d_1)}}
 \end{equation}
 
-Use this equation and your experimental measurements to calculate average value of Na doublet splitting and its standard deviation. Compare your result with the established value of $\Delta \lambda_{Na}=0.598$~nm.
+Use this equation and your experimental measurements to calculate average value of Na doublet splitting and its standard deviation, as well as any experimental uncertainties. Compare your result with the established value of $\Delta \lambda_{Na}=0.598$~nm.
 
 \begin{figure}[h]
 \centering
@@ -277,25 +288,25 @@ Use this equation and your experimental measurements to calculate average value
 \end{figure}
 
 \newpage
-\section*{Detection of Gravitational Waves}
-
-\textbf{A Michelson interferometer can help to test the theory of relativity!} 
+\section*{Observation of Gravitational Waves (LIGO)}
+\label{LIGO}
+\textbf{A Michelson interferometer can help to test the theory of general relativity!} 
 %
 Gravity waves, predicted by the theory of relativity, are ripples in the fabric
 of space and time produced by violent events in the distant universe, such as
 the collision of two black holes. Gravitational waves are emitted by
 accelerating masses much as electromagnetic waves are produced by accelerating
-charges, and often travel to Earth. The only indirect evidence for these  waves
-has been in the observation of the rotation of a binary pulsar  (for which the
-1993 Nobel Prize was awarded).
-%
+charges, and often travel to Earth. Until recently the only indirect evidence for these waves
+was the observation of the rotation of a binary pulsar  (for which the 1993 Nobel Prize was awarded).
+
+
 \begin{figure}[h]
 \centering
 \includegraphics{./pdf_figs/LIGO} \caption{\label{LIGO.fig}For more details see http://www.ligo.caltech.edu/}
 \end{figure}
-Laser Interferometry Gravitational-wave Observatory (LIGO) sets the ambitious
-goal of the direct detection of a gravitational wave. The measuring tool in this
-project is a giant Michelson interferometer. Two mirrors hang $2.5$~mi apart,
+
+The Laser Interferometry Gravitational-wave Observatory (LIGO) Michelson interferometer
+built with the goal of directly detecting gravitational wave. Two mirrors hang $2.5$~mi apart,
 forming one ``arm'' of the interferometer, and two more mirrors make a second arm
 perpendicular to the first. Laser light enters the arms through a beam splitter
 located at the corner of the L, dividing the light between the arms. The light
@@ -306,18 +317,14 @@ light back toward the laser. But if there is any difference between the lengths
 of the two arms, some light will travel to where it can be recorded by a
 photodetector.
 
-The space-time ripples cause the distance measured by a light beam to change as the gravitational wave passes by. These changes are minute: just $10^{-16}$ centimeters, or one-hundred-millionth the diameter of a hydrogen atom over the $2.5$ mile length of the arm. Yet, they are enough to change the amount of light falling on the photodetector, which produces a signal defining how the light falling on changes over time. LlGO requires at least two widely separated detectors, operated in unison, to rule out false signals and confirm that a gravitational wave has passed through the earth. Three interferometers were built for LlGO -- two near Richland, Washington, and the other near Baton Rouge, Louisiana.
-%
-%\begin{figure}
-%\centering
-%\includegraphics{LISA.eps} \caption{\label{LISA.fig}For more details see http://lisa.nasa.gov/}
-%\end{figure}
+The space-time ripples cause the distance measured by a light beam to change as the gravitational wave passes by. These changes are minute: just $10^{-16}$ centimeters, or one-hundred-millionth the diameter of a hydrogen atom over the $2.5$ mile length of the arm. Yet, they are enough to change the amount of light falling on the photodetector, which produces a signal defining how the light falling on the photodetector changes over time. LlGO requires at least two widely separated detectors, operated in unison, to rule out false signals and confirm that a gravitational wave has passed through the earth. Three interferometers were built for LlGO -- two near Richland, Washington, and the other near Baton Rouge, Louisiana, shown in Fig.~\ref{LIGO.fig}.
 
-%\emph{
-%
-%LIGO is the family of the largest existing Michelson interferometers, but just wait for a few years until LISA (Laser Interferometer Space Antenna) - the first space gravitational wave detector - is launched. LISA is essentially a space-based Michelson interferometer: three spacecrafts will be arranged in an approximately equilateral triangle. Light from the central spacecraft will be sent out to the other two spacecraft. Each spacecraft will contain freely floating test masses that will act as mirrors and reflect the light back to the source spacecraft where it will hit a detector causing an interference pattern of alternating bright and dark lines. The spacecrafts will be positioned approximately 5 million kilometers from each other; yet it will be possible to detect any change in the distance between two test masses down to 10 picometers (about 1/10th the size of an atom)!
-%
-%}
+\begin{figure}[h]
+\centering
+\includegraphics[width=0.6\linewidth]{./pdf_figs/LIGO_data.png} \caption{\label{LIGO_data.fig} Data from LIGO's two sites from the first detection of gravitational waves caused by the collision of two black holes (from \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102}{Physical Review Letters \textbf{116}, 061102).}}
+\end{figure}
+
+In 2015, LIGO observed the first direct detection of gravitational waves from the collision of two black holes.  Figure~\ref{LIGO_data.fig} shows data from the black hole merger event where the `strain' reflects the observed change in distance in the interferometer arm due to the passing gravitation wave, which oscillates as a function of time.  For a more information you can browse the \href{http://www.ligo.caltech.edu/}{LIGO webpage} and view a \href{https://www.ligo.caltech.edu/video/ligo20170601v2}{simulation of a black hole merger}.
 
 \end{document}
 
diff --git a/manual.tex b/manual.tex
index 21ac688..6772e14 100644
--- a/manual.tex
+++ b/manual.tex
@@ -11,9 +11,9 @@
 %\include{chapters/intro}
 
 \subfile{./interferometry}
-\subfile{./emratio}
-\subfile{./ediffract}
 \subfile{./blackbody}
+\subfile{./ediffract}
+\subfile{./emratio}
 \subfile{./pe-effect}
 \subfile{./single-photon-interference}
 \subfile{./faraday_rotation}
diff --git a/pdf_figs/LIGO_data.png b/pdf_figs/LIGO_data.png
new file mode 100644
index 0000000..21cf4e9
--- /dev/null
+++ b/pdf_figs/LIGO_data.png
diff --git a/pdf_figs/bnc_and_banana.jpg b/pdf_figs/bnc_and_banana.jpg
new file mode 100644
index 0000000..75eeae4
--- /dev/null
+++ b/pdf_figs/bnc_and_banana.jpg
diff --git a/pdf_figs/eoverm_powersupply.jpeg b/pdf_figs/eoverm_powersupply.jpeg
new file mode 100644
index 0000000..95c101e
--- /dev/null
+++ b/pdf_figs/eoverm_powersupply.jpeg
diff --git a/pdf_figs/michelson.png b/pdf_figs/michelson.png
new file mode 100644
index 0000000..62d7ff0
--- /dev/null
+++ b/pdf_figs/michelson.png
diff --git a/pdf_figs/shutter_up_down.png b/pdf_figs/shutter_up_down.png
new file mode 100644
index 0000000..2768787
--- /dev/null
+++ b/pdf_figs/shutter_up_down.png
diff --git a/pdf_figs/young1.png b/pdf_figs/young1.png
new file mode 100644
index 0000000..fa97d41
--- /dev/null
+++ b/pdf_figs/young1.png
diff --git a/pdf_figs/young2.png b/pdf_figs/young2.png
new file mode 100644
index 0000000..f9c38fa
--- /dev/null
+++ b/pdf_figs/young2.png
diff --git a/pe-effect.tex b/pe-effect.tex
index 976511a..aaf1adc 100644
--- a/pe-effect.tex
+++ b/pe-effect.tex
@@ -138,11 +138,7 @@ the $h/e$ apparatus.
 \end{itemize}
 
 \item Go back to the original spectral line.
-\item Place the variable transmission filter in front of the white
-	reflective mask (and over the colored filter, if one is used) so
-	that the light passes through the section marked 100\% and reaches
-	the photodiode. Record the DVM voltage reading and  time to
-	recharge after the discharge button has been pressed and released.
+\item Place the variable transmission filter in front of the white reflective mask (and over the colored filter, if one is used) so that the light passes through the section marked 100\% and reaches the photodiode. Record the DVM voltage reading and time to recharge after the discharge button has been pressed and released.
 \item Do the above measurements for all sections of the variable transmission filter. 
 
 \end{enumerate}
@@ -153,46 +149,45 @@ the $h/e$ apparatus.
 The mercury lamp visible diffraction spectrum.}
 \end{figure}
 
-\section*{Part B: The dependence of the stopping potential on the frequency
-    of light}
+\section*{Part B: The dependence of the stopping potential on the frequency of light}
+
+In this section you'll measure the stopping power for the five different emission lines of Mercury to demonstrate that the stopping power depends on, and is a measurement of, the wavelength (and frequency).  Your measurements will consist of the stopping power for each of the five Mercury lines, measured for both first and second orders.  This is a total of 10 data points.  You'll then analyze the data by fitting stopping power vs frequency to extract Planck's constant and the work function. That procedure is described in more detail in the next section. 
+
+There is a particular issue with the yellow and green lines that, if left unaddressed, can corrupt your measurements. The procedure below walks you through the measurements of those two lines lines, highlighting a few a few places that systematic problems can creep in if we are not careful.  In particular, you will be using yellow and green filters to mitigate one source of systematic bias.  
+
 \begin{enumerate}
-\item You can easily see the five brightest colors in the mercury light spectrum. Adjust the $h/e$ apparatus so that the 1st order yellow colored band falls upon the opening of the mask of the photodiode. Take a quick measurement with the lights on and no yellow filter and record the DVM voltage. Do the same for the green line and one of the blue ones. 
 
-\item Repeat the measurements with the lights out and record them (this will require coordinating with other groups and the instructor).  Are the two sets of measurements the same?  Form a hypothesis for why or why not.
-\item Now, with the lights on, repeat the yellow and green measurements with the yellow and green filters attached to the h/e detector. What do you see now?  Can you explain it? (Hint: hold one of the filters close to the diffraction grating and look at the screen).
-\item Repeat the process for each color using the second order lines.  Be sure to use the green and yellow filters when you are using the green and yellow spectral lines.
+
+\item Adjust the $h/e$ apparatus so that the 1st order yellow colored band falls upon the opening of the mask of the photodiode. Take a quick measurement with the lights on and record the DVM voltage. Do the same for the green and blue lines. 
+
+\item Now, with the lights still on, repeat the yellow and green measurements with the yellow and green filters attached to the h/e detector. What do you see now?  In order to explain your observations try holding the filters just in front of the diffraction grating and look at the pattern on the screen.
+
+\item Now turn the lights off.  This will require coordinating with other groups and the instructor. Repeat the measurements with and without the filters. Are the two sets of measurements the same?  Form a hypothesis for why or why not.
+
+\item Now, you need to decide on the best procedure for collecting the data. Lights on or lights off? Filters or no filters? Discuss amongst your group and with the instructor or TA.   You will need to measure both the first and second order lines. This is all five colors, for a total of 10 data points.
+
+Note: When collecting the data in the steps above, be sure to estimate uncertainties on the stopping power. These come in part from the digital voltmeter, but also from the repeatability of your measurements, how well lines are centered on the slit (perhaps off-center could be better?) and so on.
 
 \end{enumerate}
 
 \section*{Analysis}
 \section*{Classical vs. Quantum model of light}
 \begin{enumerate}
-\item Describe the effect that passing different amounts of the same
-colored light through the Variable Transmission Filter has on the stopping
-potential and thus the maximum energy of the photoelectrons, as well as the
-charging time after pressing the discharge button.
-\item Describe the effect that different colors of light had on the stopping
-potential and thus the maximum energy of the photoelectrons.
-\item Defend whether this experiment supports a classical wave or a
-quantum model of light based on your lab results.
+\item Describe the effect that passing different amounts of the same colored light through the Variable Transmission Filter has on the stopping potential and thus the maximum energy of the photoelectrons, as well as the charging time after pressing the discharge button.
+
+\item Describe the effect that different colors of light had on the stopping potential and thus the maximum energy of the photoelectrons.
+
+\item Defend whether this experiment supports a classical wave or a quantum model of light based on your lab results.
 \end{enumerate}
-Read the theory of the detector operation in the Appendix, and explain why
-there is a slight drop in the measured stopping potential as the light
-intensity is reduced. \\{\bf NOTE:} While the impedance of the unity gain
-amplifier is very high ($10^{13}~\Omega$), it is not infinite and some charge
-leaks off. 
+
+Read the theory of the detector operation in the Appendix, and explain why there is a slight drop in the measured stopping potential as the light intensity is reduced. 
 
 \section*{The relationship between Energy, Wavelength and Frequency}
 
 \begin{enumerate}
-\item
-Use  the table in Fig.~\ref{fig:mercury_spectrum} to find the exact frequencies and wavelengths of the spectral lines you used and plot the measured stopping potential values versus light frequency for measurements of the first and second order lines (can be on same graph).
+\item Use the table in Fig.~\ref{fig:mercury_spectrum} to find the exact frequencies and wavelengths of the spectral lines you used and plot the measured stopping potential values versus light frequency for measurements of the first and second order lines.
 
-\item Fit the plots according to $eV_0 = h\nu-\phi$, extracting values for
-	slopes and intercepts. Find the average value for slope and its
-	uncertainty. From the slope, determine  $h$ counting
-	$e=1.6\cdot10^{-19}$~C. Do your measured values agree with the
-	accepted value of  $h=6.62606957(29) \times 10^{-34}$J$\cdot$s within experimental uncertainty?
+\item Fit your data according to $eV_0 = h\nu-\phi$, extracting values for the slope and intercept. {\it Note, this fitting step takes the measurement uncertainties on the stopping power and propagates them to the slope and intercept.} It's important to do this step with Igor, Matlab, or some other tool which can compute a $\chi^2$, minimize it with respect to the fit parameters, and then report the parameter uncertainties.  From the slope, determine  $h$ using $e=1.6\cdot10^{-19}$~C. Find the average value and uncertainty on the average. Does your value agree with the accepted value of  $h=6.62606957(29) \times 10^{-34}$J$\cdot$s within uncertainty?
 
 \item From the intercepts, find the average value and uncertainty of the work function $\phi$. Look up some values of work functions for typical metals. Is it likely that the detector material is a simple metal?
 
@@ -201,6 +196,7 @@ Use  the table in Fig.~\ref{fig:mercury_spectrum} to find the exact frequencies
 \section*{Appendix: Operation principle of the stopping potential detector}
 
 The schematic of the apparatus used to measure the stopping potential is shown in Fig.~\ref{pefig5}. Monochromatic light falls on the cathode plate of a vacuum photodiode tube that has a low work function $\phi$. Photoelectrons ejected from the cathode collect on the anode. The photodiode tube and its associated electronics have a small capacitance which becomes charged by the photoelectric current. When the potential on this capacitance reaches the stopping potential of the photoelectrons, the current decreases to zero, and the anode-to-cathode voltage stabilizes. This final voltage between the anode and cathode is therefore the stopping potential of the photoelectrons.
+
 \begin{figure}[h]
 \centering \includegraphics[width=0.7\linewidth]{./pdf_figs/pe_det}
 \caption{\label{pefig5} The electronic schematic diagram of the $h/e$
@@ -214,12 +210,13 @@ front panel of the apparatus. This high impedance, unity gain ($V_{out}/V_{in}
 = 1$) amplifier lets you measure the stopping potential with a digital
 voltmeter.
 
-Due to the ultra high input impedance, once the capacitor has been charged from
-the photodiode current, it takes a long time to discharge this potential through
-some leakage. Therefore a shorting switch labeled ``PUSH TO Zero'' enables the
-user to quickly bleed off the charge.
+Due to the ultra high input impedance, once the capacitor has been charged from the photodiode current, it takes a long time to discharge this potential through some leakage. Therefore a shorting switch labeled ``PUSH TO Zero'' enables the user to quickly bleed off the charge. While the impedance of the unity gain amplifier is very high ($10^{13}~\Omega$), it is not infinite and some charge gradually leaks off. This effect can bias the measured stopping power for low intensity light sources.
+
 \newpage
 \section*{Sample data tables:}
+
+\subsection*{Part A}
+
 {\large
 %\begin{tabular}{|p{27mm}|p{27mm}|p{27mm}|p{27mm}|}
 \begin{tabular}{|c|c|c|c|}
@@ -233,45 +230,22 @@ Approx. Charge Time \\
 &40&&\\ \hline
 &20&&\\ \hline
 \hline
- Color & \%Transmission & Stopping Potential &
-Approx. Charge Time \\
-\hline
-&100&&\\\hline
-&80&&\\ \hline
-&60&&\\ \hline
-&40&&\\ \hline
-&20&&\\ \hline
 \end{tabular}
 }
-\vskip .1in
-%
-%
-%{\large
-%\begin{tabular}{|p{27mm}|p{27mm}|}
-%\hline
-% Light Color  & Stopping Potential \\\hline
-%Yellow&\\\hline
-%Green&\\ \hline
-%Blue&\\ \hline
-%Violet&\\ \hline
-%Ultraviolet&\\ \hline
-%\end{tabular}
-%}
+
+\subsection*{Part B}
 
 {\large
 \begin{tabular}{|c|c|c|c|}
 \hline
- 1st Order Color&$\lambda$ (nm) &$\nu$  ($10^{14}Hz$) &
+Color&$\lambda$ (nm) &$\nu$  ($10^{14}Hz$) &
 Stopping Potential (V) \\
 \hline Yellow&&&\\\hline Green&&&\\ \hline Blue&&&\\ \hline Violet&&&\\
-\hline Ultraviolet&&&\\ \hline \hline
-2nd Order Color&$\lambda$ (nm) &$\nu$  ($10^{14}Hz$) &
-Stopping Potential (V) \\
-\hline Yellow&&&\\\hline Green&&&\\ \hline Blue&&&\\ \hline Violet&&&\\
-\hline Ultraviolet&&&\\ \hline \hline
-
+\hline Ultraviolet&&&\\ \hline 
 \end{tabular}
 }
 
+You'll either want different tables for different orders, or perhaps add additional stopping power columns to the one above.
+
 \end{document}
 
diff --git a/single-photon-interference.tex b/single-photon-interference.tex
index 1b20598..350d5aa 100644
--- a/single-photon-interference.tex
+++ b/single-photon-interference.tex
@@ -5,23 +5,43 @@
 
 \noindent
  \textbf{Experiment objectives}: Study wave-particle duality for photons by measuring
- interference patterns in the Young double-slit experiment using a conventional light source (laser) and a
+ interference patterns in the double-slit experiment using a conventional light source (laser) and a
  single-photon source (strongly attenuated lamp).
 
 
 
 \section*{History}
 
-There is a rich historical background behind the experiment you are about to perform.  Isaac Newton first
-separated white light into its colors, and, in the 1680's, hypothesized that light was composed of `corpuscles',
-supposed to possess some properties of particles.  This view reigned until the 1800's, when Thomas Young first
-performed the two-slit experiment now known by his name.  In this experiment he discovered a property of
-destructive interference, which seemed impossible to explain in terms of
-corpuscles, but was very naturally
-explained in terms of waves.  His experiment not only suggested that such `light waves' existed; it also
-provided a result that could be used to determine the wavelength of light, measured in familiar units. Light
-waves became even more acceptable with dynamical theories of light, such as Fresnel's and Maxwell's, in the 19th
-century, until it seemed that the wave theory of light was incontrovertible.
+There is a rich historical background behind the experiment you are about to perform.  Isaac Newton first separated white light into its colors, and, in the 1680's, hypothesized that light was composed of `corpuscles', supposed to possess some properties of particles.  This view reigned until the 1800's, when Thomas Young first performed the two-slit experiment now known by his name.  Young directed light through a single aperture (slit) followed by a pair of double apertures, and then observed the result on a viewing screen (see Fig.~\ref{young.fig}).
+
+
+\begin{figure}[h!]
+\centering
+\includegraphics[width=0.8\linewidth]{./pdf_figs/young2.png} \\
+\includegraphics[width=0.8\linewidth]{./pdf_figs/young1.png}
+
+ \caption{\label{young.fig} Young's double slit experiment. Top: The experimental setup.  Bottom: Young's interpretation of the result as interference, analogous to the corresponding phenomenon in water waves. The figure was drawn by Young himself.  {\it Images from Wikimedia.} }
+\end{figure}
+
+Young discovered that the light appeared as light and dark fringes on the screen, a fact that seemed impossible to explain in terms of corpuscles, but was very naturally explained in terms of waves, much like the interference observed in water and sound waves.  In particular, wave theory predicts that the intensity of light $I(x)$ from double slit interference should be distributed as:
+
+\begin{equation} \label{2slit_wDif}
+I(x)= 4 I_0 \cos^2\left(\frac{\pi d}{\lambda}\frac{x}{\ell} \right)\left[\frac{\sin (\frac{\pi
+a}{\lambda}\frac{x}{\ell})}{\frac{\pi a}{\lambda}\frac{x}{\ell}} \right]^2
+\end{equation}
+
+Here, $x$ is the position on the viewing screen, with $x=0$ corresponding to the center of the interference pattern. The light wavelength is $\lambda$, the slits have a width of $a$, and they are separated by a distance $d$. The distance between the double slit and the viewing screen is $\ell$.
+
+Interference can also occur if there is only one slit. In this case the intensity distribution is described by Fraunhofer diffraction (see Fig.~\ref{interference.fig} and the derivations in the Appendix):
+\begin{equation} \label{1slit}
+I(x) = I_0 \frac{(\sin (\frac{\pi a}{\lambda}\frac{x}{\ell}))^2}{(\frac{\pi
+a}{\lambda}\frac{x}{\ell})^2}
+\end{equation}
+
+
+Young's experiment not only suggested that such `light waves' existed but was also able to determine the wavelength of light.  You should spend some time thinking about the latter point. How would the interference pattern change if we change $\lambda$? Given a particular interference pattern how might we determine $\lambda$? % refer to the calculation later in the lab
+
+
 
 
 \begin{figure}[h]
@@ -29,13 +49,7 @@ century, until it seemed that the wave theory of light was incontrovertible.
 \includegraphics[width=0.4\linewidth]{./pdf_figs/ambigram} \caption{\label{ambigram.fig} ``Light is a Particle / Light is a Wave'' oscillation ambigram (from \emph{For the Love of Line and Pattern}, p. 30).}
 \end{figure}
 
-And yet the discovery of the photoelectric effect, and its explanation in terms of light quanta by Einstein,
-threw the matter into dispute again.  The explanations of blackbody radiation, of the photoelectric effect, and
-of the Compton effect seemed to point to the existence of `photons', quanta of light that possessed definite and
-indivisible amounts of energy and momentum.  These are very satisfactory explanations so far as they go, but
-they throw into question the destructive-interference explanation of Young's experiment.  Does light have a dual
-nature, of waves and of particles?  And if experiments force us to suppose that it does, how does the light know
-when to behave according to each of its natures?
+ Light waves became even more acceptable with dynamical theories of light, such as Fresnel's and Maxwell's, in the 19th century, until it seemed that the wave theory of light was incontrovertible. And yet the discovery of the photoelectric effect, and its explanation in terms of light quanta by Einstein, threw the matter into dispute again.  The explanations of blackbody radiation, of the photoelectric effect, and of the Compton effect seemed to point to the existence of `photons', quanta of light that possessed definite and indivisible amounts of energy and momentum.  These are very satisfactory explanations so far as they go, but they throw into question the destructive-interference explanation of Young's experiment.  Does light have a dual nature, of waves and of particles?  And if experiments force us to suppose that it does, how does the light know when to behave according to each of its natures?
 
 It is the purpose of this experimental apparatus to make the phenomenon of light interference as concrete as
 possible, and to give you the hands-on familiarity that will allow you to confront wave-particle duality in a
@@ -44,270 +58,295 @@ Feynman asserts that nobody really does -- but you will certainly have
 direct experience with the actual phenomena
 that motivates all this discussion.
 
-\section*{Experimental setup} \textbf{Equipment needed}: Teachspin ``Two-slit interference'' apparatus,
-oscilloscope, digital multimeter, counter.
+\newpage
+
+\section*{Experimental setup} 
+
+\subsection*{Equipment needed}
+
+You will need the Teachspin ``Two-slit interference'' apparatus, an oscilloscope, a digital multimeter, two $\sim$1m RG58 coaxial cables with BNC connectors, a BNC to banana plug adapter, and a frequency counter (such as the BK Precision 1823A).
+
+\subsection*{Inspecting the apparatus}
+
+\begin{framed}
+{\center{\large \bf \textcolor{red}{Important equipment safety information}\\} }
+ The double slit apparatus has a very sensitive and somewhat fragile sensor called a photomultiplier tube (PMT) that you will use to observe individual photons. The tube is inside the detector box at the right end of the apparatus as shown in Fig~\ref{tsifig1.fig}. The PMT works by being supplied a DC high voltage (500-800V) by circuitry in the same box.  The PMT should never be exposed to room light, especially with the HV on.  Before taking the top off of the long and narrow interference channel you need to verify that:
+\begin{enumerate}
+\renewcommand{\theenumi}{\Alph{enumi}}
+\item the shutter rod is down
+\item the high voltage switch on the detector box is also off
+\item  the high voltage dial on the detector box is turned all the way to zero.
+\end{enumerate}
+ As long as the top is off the rod must remain down and the HV must remain off. Finally, when the HV is on the laser/off/bulb switch at the far left end of the interference channel must be on bulb mode, or off. The laser is far too intense for the PMT. Make sure you have read this, understood, and got sign-off from the instructor before proceeding.
+\end{framed}
 
 \begin{figure}
 \centering
 \includegraphics[width=0.8\linewidth]{./pdf_figs/tsisetup} \caption{\label{tsifig1.fig}The double-slit interference apparatus.}
 \end{figure}
 
-\textbf{Important}: before plugging anything in or turning anything on,  confirm that the shutter (which
-protects the amazingly sensitive single-photon detector) is \textbf{closed}.  Locate the detector box at the
-right end of the apparatus, and find the rod which projects out of the top of its interface with the long
-assembly. Be sure that this rod is pushed all the way down: take this opportunity to try pulling it vertically
-upward by about $2$~cm, but then ensure that it's returned to its fully down position.  Also take this occasion
-to confirm, on the detector box, that the toggle switch in the HIGH-VOLTAGE section is turned off, and that the
-10-turn dial near it is set to $0.00$, fully counter-clockwise.
-
-To inspect the inside of the apparatus, open the cover by turning the four latches that hold it closed. The details
-of the experimental apparatus are shown in Fig.~\ref{tsifig1.fig}. Take time to locate all the important
-components of the experiment:
+\begin{figure}
+\centering
+\includegraphics[width=0.8\linewidth]{./pdf_figs/bnc_and_banana_annotated} \caption{\label{bnc.fig} RG58 coaxial cable with a BNC connector and a BNC$\leftrightarrow$banana connector.}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[width=0.8\linewidth]{./pdf_figs/shutter_up_down} \caption{\label{shutter.fig} The apparatus's shutter. When down it protects the PMT and exposes the photodiode to light in the interference channel. When up, the PMT is exposed to the light. The shutter must be kept down when the box is open.}
+\end{figure}
+
+
+To inspect the inside of the apparatus, open the cover by turning the four latches that hold it closed. The details of the experimental apparatus are shown in Fig.~\ref{tsifig1.fig}. Take time to locate all the important components of the experiment:
+
 \begin{itemize}
-\item Two distinct light sources at the left end: one a red \emph{laser} and the other a green-filtered \emph{light
-bulb}. A toggle switch on the front panel of the light source control box switches power from one source to the
-other.
-
-\item Various \emph{slit holders} along the length of the long box: one to
-	hold a two-slit mask, one for the slit blocker,
-and one for a detector slit. Make sure you locate the \emph{slits} (they may be installed already) and two
-\emph{micrometer drives}, which allow you to make mechanical adjustments to the two-slit apparatus. \textbf{Make
-sure you figure out how to read the micrometer dials!} On the barrel there are two scales with division of
-$1$~mm, shifted with respect to each other by 0.5~mm; every fifth mark is labeled with an integer 0, 5, 10 and
-so on: these are at 5-mm spacing. The complete revolution of the drum is $0.5$~mm, and the smallest division on
-the rotary scale is $0.01$~mm.
-
-\item Two distinct light detectors at the right-hand end of the apparatus: a \emph{photodiode}
-and a \emph{photomultiplier tube} (PMT for short). The photodiode is used with the much brighter laser light;
-it's mounted on the light shutter in such a way that it's in position to use when the shutter is closed (pushed
-down). The photomultiplier tube is an extremely sensitive detector able to detect individual photons (with energy
-of the order of $10^{-19}$~J), and it is used with the much dimmer light-bulb source. Too much light can easily
-damage it, so \textbf{the PMT is safe to use only when the cover of the apparatus is in place, and only when the
-light bulb is in use}. It is exposed to light only when the shutter is in its up position.
+\item There are two distinct light sources at the left end: one a red \emph{laser} and the other a green-filtered \emph{light bulb}. A toggle switch on the front panel of the light source control box switches power from one source to the other.
+
+\item There are two distinct light detectors at the right-hand end of the apparatus: a {\em photodiode} and the aforementioned {\em PMT}. The photodiode is used with the much brighter laser light; it's mounted on the bottom of the light shutter rod so that it's in position to use when the shutter is closed (pushed down, See Fig.~\ref{shutter.fig}). The photomultiplier tube is an extremely sensitive detector able to detect individual photons (with energy of the order of $10^{-19}$~J); it is used with the much dimmer light-bulb source. 
+
+\item There are various \emph{slit holders} along the length of the long box. From left to right in Fig.~\ref{tsifig1.fig} these are: a single slit to establish the point source of light diagrammed in Fig.~\ref{young.fig}; a double slit to create the interference pattern; a slit blocker just downstream of the double slit; and finally the detector slit, which sits in front of the photodetectors, allowing only a portion of the interference pattern to reach them.  The distance $\ell$ between the double slit and detector slit is important. Be sure to measure it!
+
+\item There are two \emph{micrometer drives}, which allow you to make mechanical adjustments to the two-slit apparatus.  The right-hand dial controls the position of the detector slit. The dial near the center of the apparatus controls the position of the slit blocker. \textbf{Make sure you figure out how to read these micrometer dials!} One unit on the dial corresponds to $10~\mu$m\footnote{Yes, this is confusing!  We have an unfortunate language overlap, where ``micrometer'' refers to both the device and the unit of distance -- $\mu$m.  There is not much we can do about it. If it helps, you can refer to $1~\mu$m as a ``micron''.}  so turning from 100 to 200 on the dial moves the detector slit by $100\times 10~\mu\mathrm{m} = 1000~\mu\mathrm{m} = 1~\mathrm{mm}$.
+
+
 \end{itemize}
 
 
 \section*{Experimental procedure}
 
 The experiment consists of three steps:
+\begin{description}
+\item[Observing interference and finding dial settings]  You will first identify single and double slit interference patterns directly with the top off of the apparatus. You'll do this by looking at interference fringes on a bit of paper you'll insert into the long box, to the right of the double slit in Fig.~\ref{tsifig1.fig}.  You will record the slit blocker position corresponding to single and double slit interference in your lab book so you can switch between the two when the top is on.
+
+\item[Measuring interference with an intense source] Using the photodiode and laser you will measure the intensity of the single- and double-slit interference patterns as a function of $x$, the position transverse to the laser beam. Your analysis will consist of fitting the data with equations \ref{1slit} and \ref{2slit_wDif}. A good fit demonstrates that the wave theory of light is correct and allows you to determine the slit width and slit separation. This is a recreation of Young's original experiment.
+
+\item[Measuring interference with a weak source] Then, using a very weak light source, you will record the intensity of the single- and double-slit interference pattern by counting the number of photons as a function of $x$. This measurement will introduce you to the technology we use to observe single-photons detection technology and will also demonstrate that interference occurs even if we only have one photon going through the apparatus at a time. This is the very essence of wave/particle duality!
+
+\end{description}
+
+
+\subsection*{Observing interference and finding dial settings}
+\begin{framed}
+{\center{\large \bf \textcolor{red}{Important personal safety information}\\} }
+The apparatus has a 5-mW diode laser with an output wavelength of $670 \pm 5$~nm. It could potentially harm your eyes if you are not careful. Don't observe the beam directly (i.e., by staring into it) and be careful of reflections off of reflective surfaces.
+\end{framed}
+
+
+
+For this mode of operation, you will be working with the cover of the apparatus open. 
+
 \begin{enumerate}
-\item  You will first observe two-slit interference directly by observing the intensity
-distribution of a laser beam on a viewing screen.
-\item Using the photodiode you will accurately measure the intensity distribution after single- and two-slit interference patterns,
-which can be compared to predictions of wave theories of light. \\
-These two steps recreate Young's original experiment.
-\item Then, using a very weak light source, you will record the two-slit interference pattern one photon at a time.
-While this measurement will introduce you to single-photon detection technology, it will also show you that
-however two-slit interference is to be explained, it must be explained in terms that can apply to single
-photons.
+\item  Switch on the laser.
+
+\item Make a viewing screen by cutting a bit of white paper to the dimensions of the interference channel. Insert your screen just to the right of the double slit and slit blocker.  
+
+\item Adjust the position and angle of laser so that it impinges on the single slit, then the double slit, and travels all the way to the detector slit. You may need to make sure, by visual inspection, that the slit blocker is not blocking one or both of the double slits.
+
+\item Move your screen along the beam path toward the detector slit to see the interference pattern forming. By the time your viewing card reaches the right-hand end of the apparatus, you'll see that the two overlapping ribbons of light combine to form a pattern of illumination displaying the celebrated ``fringes'' named after Thomas Young.
+
 \end{enumerate}
 
-\subsection*{Visual observation of a single- and two-slit interference}
-
-For this mode of operation, you will be working with the cover of the apparatus open. Switch the red diode laser
-on using the switch in the light source control panel, and move the laser
-to the center of its magnetic pedestal
-so that the red beam goes all the way to the detector slit. The diode laser manufacturer asserts that its output
-wavelength is $670 \pm 5$~nm, and its output power is about 5~mW. \emph{\textbf{As long as you don't allow the
-full beam to fall directly into your eye, it presents no safety hazard.}} Place a double-slit mask on the holder
-in the center of the apparatus, and then put your viewing card just after the mask to observe the two ribbons of
-light, just a third of a millimeter apart, which emerge from the two slits.
-Move your viewing card along the beam
-path to see the interference pattern forming. By the time your viewing card reaches the right-hand end of the
-apparatus, you'll see that the two overlapping ribbons of light combine to form a pattern of illumination
-displaying the celebrated ``fringes'' named after Thomas Young.
-
-Position a viewing card at the far-right end of the apparatus so you can refer to it for a view of the fringes.
-Now it is the time to master the control of the slit-blocker. By adjusting the multi-turn micrometer screw, make
-sure you find and record the ranges of micrometer reading where you observe the following five situations:
+You are going to take data with the box closed and will want to be able to move the blocking slit to go from double slit mode to single slit mode without opening it. We'll also want to be able to completely block the light from both slits in order to measure the background signal from the photodiode and the PMT. Adjust the position of the blocking slit using the micrometer to find the following situations:
+
 \begin{enumerate}
-\item both slits are blocked;
-\item light emerges only from one of the two slits;
-\item both slits are open;
-\item light emerges only from the other slit;
+\item both slits are open
+\item light emerges only from a single slit
 \item the light from both slits is blocked.
 \end{enumerate}
-It is essential that you are confident enough in your ability to read, and
-to set, these five positions and that
-you are able to do so even when the box cover is closed. In your lab book describe what you see at the viewing
-card at the far-right end of the apparatus for each of the five settings.
-
-\textbf{One slit is open:} According to the wave theory of light, the intensity distribution of light on the
-screen after passing a single-slit is described by Fraunhofer diffraction (see Fig.~\ref{interference.fig} and
-the derivations in the Appendix):
-\begin{equation} \label{1slit}
-I(x) = I_0 \frac{(\sin (\frac{\pi a}{\lambda}\frac{x}{\ell}))^2}{(\frac{\pi
-a}{\lambda}\frac{x}{\ell})^2},
-\end{equation}
-where $I$ is the measured intensity in the point $x$ in the screen, $I_0$ is the intensity in the brightest
-maximum, $a$ is the width of the slit, and $\ell$ is the distance between the slit and the screen (\emph{don't
-forget to measure and record this distance in the lab journal!})
-
-In your apparatus move the slit blocker to let the light go through only one slit and inspect the
-light pattern in the viewing screen. Does it look like the intensity distribution you expect from
-the wave theory? Take a minute to discuss how this picture would change if the slit was much wider or
-much narrower.
-
-\textbf{Two slits are open:} Now move the slit blocker to the position that opens both slits to observe Young's
-two-slit interference fringes. Again, compare what you see on the screen with the interference picture predicted
-by wave theory:
-\begin{equation} \label{2slit_wDif}
-I(x)= 4 I_0 \cos^2\left(\frac{\pi d}{\lambda}\frac{x}{\ell} \right)\left[\frac{\sin (\frac{\pi
-a}{\lambda}\frac{x}{\ell})}{\frac{\pi a}{\lambda}\frac{x}{\ell}} \right]^2,
-\end{equation}
-where an additional parameter $d$ is the distance between the centers of the two slits. Discuss how this picture
-would change if you were to vary the width or the separation of the two
-slits or the wavelength of the laser. Make a
-note of your predictions in the lab book.
-
-\subsection*{Quantitative characterization of interference patterns using laser light}
-
-At this stage you will use a photodiode to measure the intensity distribution of the interference pattern by
-varying the position of the detector slit. You will continue using the red laser. While you may conduct these
-measurements with the box cover open, room light will inevitably add some varying background to your signals, so
-it is a good idea to dim the room lights or (even better!) to close up the cover of the apparatus. For
-convenience, have the slit-blocker set to that previously determined setting which allows light from both slits
-to emerge and interfere.
-
-The shutter of the detector box will still be in its closed, or down, position: this blocks any light from
-reaching the PMT, and correctly positions  a 1-cm$^{2}$ photodiode, which acts just like a solar cell in actively
-generating electric current when it's illuminated. The output current is proportional to total power
-illuminating the detector area, so it is important to use a narrow slit to allow only a selected part of the
-interference pattern to be measured. Make sure that a detector slit mask (with a single narrow slit) on a
-movable slit holder at the right-hand side of the apparatus is in place. By adjusting the micrometer screw of the
-detector slit, you can move the slit over the interference pattern, eventually mapping out its intensity
-distribution quantitatively.  For now, ensure that the detector slit is located somewhere near the middle of the
-two-slit interference pattern, and have the slit-blocker set to the setting which allows light from both slits
-to emerge and interfere.
-
-The electric \emph{current} from the photodiode, proportional to the \emph{light intensity}, is conducted by a
-thin coaxial cable to the INPUT BNC connector of the photodiode-amplifier section of the detector box, and
-converted to \emph{voltage} signal at the OUTPUT BNC connector adjacent to it. Connect to this output a digital
-multimeter set to 2 or 20-Volt sensitivity; you should see a stable positive reading. Turn off the laser first
-to record the ``zero offset'' - the reading of the multimeter with no light. You will need to subtract this reading
-from all of the other readings you make with this photodiode, amplifier, and voltmeter
-combination.
-
-Turn your laser source back on, and watch the photodiode's voltage-output signal as you vary the setting of the
-detector-slit micrometer. If all is well, you will see a systematic variation of the signal as you scan over the
-interference pattern. Check that the maximum signal you see is about 3-8 Volts; if it is much less than this,
-the apparatus is out of alignment, and insufficient light is reaching the detector.
-
-\textbf{Initial tests of the wave theory of light:} If we assume that the light
-beam is a stream of particles, we
-would naively expect that closing one of two identical slits should reduce the measured intensity of light at
-any point on the screen by half, while the wave theory predicts much more dramatic variations in the different
-points in the screen. Which theory provides a more accurate description of what you see?
 
-\begin{itemize}
-\item Find the highest of the maxima --- this is the ``central fringe'' or
-	the ``zeroth-order fringe'' that the  theory
-predicts ---  and record the photodiode reading. Then adjust the position of the slit-blocker to let the light
-to pass through only one of the slits, and measure the change in the photodiode signal.
+Record the dial setting for each. Make sure that you are fully in the single and double-slit conditions as it is possible to be halfway, with the top of the pattern different than the bottom due.  It is essential that you are confident enough in your ability to read, and to set, these three positions and that you are able to do so even when the box cover is closed. In your lab book describe and sketch what you see on the viewing card at the far-right end of the apparatus for each of the three settings.
 
-\item To see another and even more dramatic manifestation of the wave nature of light, set the slit-blocker again
-to permit light from both slits to pass along the apparatus, and now place the detector slit at either of the
-minima immediately adjacent to the central maximum; take some care to find the very bottom of this minimum.
-Record what happens when you use the slit-blocker to block the light from one, or the other, of the two slits.
 
-\item Check your experimental results against the theoretical predictions using Eqs.~(\ref{1slit}) and (\ref{2slit_wDif}).
-Do your observations confirm or contradict wave theory?
 
-\end{itemize}
+\subsection*{Measuring interference with an intense source}
 
-Once you have performed these spot-checks, and have understood the
-motivation for them and the obtained results, you are ready to conduct
-systematic measurements of intensity distribution (the photodiode
-voltage-output signal) as a function of detector slit position. You will
-make such {\bf measurements in two slit-blocker positions: when both slits
-are open, and when only one slit is open}. You will need to take enough data points to reproduce the intensity distribution in each case. Taking points systematically every 0.05 or \unit[0.1]{mm} on the tick lines will produce a very high quality dataset. One person should turn the dial and the other should record readings directly to paper or a spreadsheet (if you do this, print it out and tape into your logbook). Estimate your uncertainties from the dial and the voltmeter. Cycle through multiple maxima and minima on both sides of the central maximum. It is a good idea to plot the data points immediately along with the data taking -- nothing beats an emerging graph for teaching you what is going on, and your graph will be pretty impressive. \emph{Note: due to large number of points you don't need to include the tables with these measurements in the lab report -- the plotted distributions should be sufficient. Be clear on your uncertainties though.}
-
-\textbf{Slit separation calculations}: Once you have enough data points for each graph to clearly see the
-interference pattern, use your data to extract the information about the
-distance between the two slits $d$. To do
-that, find the positions of consecutive interference maxima or minima, and calculate average $d$ using
-Eq.~\ref{2slit_wDif}. Estimate the uncertainty in these parameters due to laser wavelength uncertainty. Check if
-your measured values are within experimental uncertainty from the manufacturer's specs: the center-to-center
-slit separation is 0.353 mm (or 0.406 or 0.457 mm, depending on which two-slit mask you have installed).
-
-Fit your data with Eqs.~(\ref{1slit}) and (\ref{2slit_wDif}). You will need to add these functions using ``Add new function'' option. Note that in this case you will have to provide a list of initial guesses for all the fitting parameters. A few tips:
-\begin{itemize}
-\item Make sure that units of all your measured values are self-consistent - the program will go crazy trying to combine measurements in meters and micrometers together!
-\item Try to plot your function for guesstimated values before doing a fit with it. This catches many silly errors.
-\item You will have to fit for a term to account for the overall normalization and also for the fact that the maximum is not set at $x=0$. In other words, substitute $x \rightarrow x-x_0$. Estimate both of these (for the normalization, look at what happens when $x-x_0 = 0$) but include them as free parameters in the fit.
-\item You need to add a parameter to account for the non-zero background you observed when the laser was off.
-\item Include the minimal number of parameters. If I have parameters $a$ and $b$ but they always appear as $ab$ in my function, then I am much better off including a term $c=ab$ when doing the fit. Otherwise the fit is underconstrained. Adjusting $a$ up has the same effect as adjusting $b$ down so it's impossible to converge on unique values for $a$ and $b$. Fitting algorithms really dislike this situation.
-\item If the program has problems fitting all the parameters, first hold the values of the parameters you know fairly well (such as the light wavelength, maximum peak intensity, background, etc.). Once you determine the approximate values for all other parameters, you can release the fixed ones, and let the program adjust everything to make the fit better.
+In this part of the experiment you will use a photodiode to measure the intensity distribution of the interference pattern by varying the position of the detector slit.  You will do this using the red laser with the shutter down.  
 
-\end{itemize}
+\subsubsection*{\textcolor{blue}{Orienting yourself with the laser and photodiode}}
 
-\subsection*{Single-photon interference}
-
-Before you start the measurements you have to convince yourself that the
-rate of photons emitted by the weak filtered light bulb is low enough to
-have, on average, less than one photon detected in the apparatus at any
-time. Roughly estimate the number of photons per second arriving to the
-detector. First, calculate the number of photons emitted by the light bulb
-in a 10~nm spectral window of the green filter (between $541$ and
-$551$~nm), if it runs at 6V and 0.2A. Note that only 5\% of its electric
-energy turns into light, and this optical energy is evenly distributed in
-the spectral range between 500~nm and 1500~nm. These photons are emitted in
-all directions, but all of them are absorbed inside the box except for
-those passing through two slits with area approximately $0.1\times
-10~\mathrm{mm}^2$. Next, assuming that the beam of photons passing through
-the slits diffracts over a $1~\mathrm{cm}^2$ area by the time it reaches
-the detector slit, estimate the rate of photons reaching the detector.
-Finally, adjust the detected photon rate by taking into account that for
-PMT only 4\% of photons produce output electric pulse at the output. That's
-the rate of events you expect. Now estimate the time it takes a photon to
-travel through the apparatus, and estimate the average number of detectable
-photons inside at a given moment of time. \emph{You may do these
-calculations before or after the lab period, but make sure to include them in the lab report.}
-
-Now you need to change the apparatus to use the light bulb. Open the cover and slide the laser source to the side (do not remove the laser from the stand). Now set the 3-position toggle switch to the BULB position and dial the bulb adjustment up from 0 until you see the bulb light up. (\emph{The flashlight bulb you're using will live longest if you minimize the time you spend with it dialed above 6 on its scale, and if you toggle its power switch only when the dial is set to low values}). If the apparatus has been aligned, the bulb should now be in position to send light through the apparatus. Check that the green filter-holding structure is in place: the light-bulb should look green, since the green filter blocks nearly all the light emerging from the bulb, passing only wavelengths in the range 541 to 551 nm. The filtered light bulb is very dim, and you probably will not be able to see much light at the double-slit position even with room light turned off completely. No matter; plenty of green-light photons will still be reaching the double-slit structure -- in fact, you should now dim the bulb even more, by setting its intensity control down to about 3 on its dial.
-
-Now close and lock the cover - you are ready to start counting photons. But first a WARNING:  a photomultiplier tube is so sensitive a device that it should not be exposed even to moderate levels of light when turned off, and must not be exposed to anything but the dimmest of lights when turned on.  In this context, ordinary room light is intolerably bright even to a PMT turned off, and light as dim as moonlight is much too bright for a PMT turned on.
-
-\textbf{Direct observation of photomultiplier pulses} You will use a digital oscilloscope for first examination of the PMT output pulses, and a digital counter for counting the photon events. Set the oscilloscope level to about 50~mV/division vertically, and 250 - 500~ns/division horizontally, and set it to trigger on positive-going pulses or edges of perhaps $>20$~mV height. Now find the PHOTOMULTIPLIER OUTPUT of the detector box, and connect it via a BNC cable to the vertical input of the oscilloscope. Keeping the shutter closed, set the HIGH-VOLTAGE 10-turn dial to 0.00, and turn on the HIGH-VOLTAGE toggle switch. Start to increase the voltage while watching the scope display. \emph{If you see some sinusoidal modulation of a few mV amplitude, and of about 200 kHz frequency, in the baseline of the PMT signal, this is normal. If you see a continuing high rate ($>10$~kHz) of pulses from the PMT, this is not normal, and you should turn down, or off, the bias level and start fresh -- you may have a malfunction, or a light leak.} Somewhere around a setting of 4 or 5 turns of the dial, you should get occasional positive-going pulses on the scope, occurring at a modest rate of $1-10$ per second. If you see this low rate of pulses, you have discovered the ``dark rate'' of the PMT, its output pulse rate even in the total absence of light.  You also now have the PMT ready to look at photons from your two-slit apparatus, so finally you may open the shutter.  The oscilloscope should now show a much greater rate of pulses, perhaps of order $10^3$ per second, and that rate should vary systematically with the setting of the bulb intensity. \emph{You may find a small device called Cricket in your table. It allows you to ``hear'' the individual photon arrivals - ask your instructor to show you how it works.}
-
-To count the pulses using a counter you will use another PMT output -- the OUTPUT TTL -- that generates a single pulse, of fixed height and duration, each time the analog pulse exceeds an adjustable threshold. To adjust the TTL settings display  the OUTPUT TTL on the second oscilloscope channel and set it for 2 V/div vertically.  By simultaneously watching both analog and TTL-level pulses on the display, you should be able to find a discriminator setting, low on the dial, for which the scope shows one TTL pulse for each of, and for only, those analog pulses which reach (say) a $+50$~-mV level. If your analog pulses are mostly not this high, you can raise the PMT bias by half a turn (50 Volts) to gain more electron multiplication. If your TTL pulses come much more frequently than the analog pulses, set the discriminator dial lower on its scale.
-
-Now send the TTL pulses to a counter, arranged to display successive readings of the number of TTL pulses that occur in successive 1-second time intervals. To confirm that this is true, record a series of ``dark counts'' obtained with the light bulb dialed all the way down to 0 on its scale.  Now choose a setting that gives an adequate photon count rate (about $10^3$/second) and use the slit-blocker, according to your previously obtained settings, to block the light from both slits.  This should reduce the count rate to a background rate, probably somewhat higher than the dark rate.  Next, open up both slits, and try moving the detector slit to see if you can see interference fringes in the photon count rate.  You will need to pick a detector-slit location, wait for a second or more, then read the photon count in one or more 1-second intervals before trying a new detector-slit location.  If you can see maxima and minima, you are ready to take data. Finally, park the slit near the central maximum and choose the PMT bias at around $5$ turns of the dial and the bulb intensity setting to yield some
-convenient count rate ($10^3 - 10^4$ events/second) at the central maximum.
-
-%Before you begin the data collection you need to set the PMT bias voltage to a suitable range. \emph{This
-%procedure is \textbf{optional}, and necessary if the event rate you observe is too low and/or the dark rate
-%count is too high.} To do that you'll need to measure the dependence of dark count rate (PMT shutter closed) and
-%the count rate at the central maximum of the interference pattern (both slits open) on the PMT bias voltage over
-%the range 300 to 650 V. When you plot the two count rates on a semi-logarithmic graph, you should see the
-%``light rate'' reach a plateau, with the interpretation that you have reached a PMT bias which allow each
-%photoelectron to trigger the whole chain of electronics all the way to the TTL counter; you should also see the
-%(much lower) `dark rate' also rising with PMT bias.  Based on your graph choose the PMT bias setting at which
-%you are counting substantially all true photon events, but minimizing the number of ``dark events''.
-
-\textbf{Single-photon detection of the interference pattern}. Most likely the experimental results in the
-previous section have demonstrated good agreement with the wave description of light. However, the PMT detects
-individual photons, so one can expect that now one has to describe the light beam as a stream of particles, and
-the wave theory is not valid anymore. To check this assumption, you will repeat the measurements and take the
-same sort of data as in the previous section, except now characterizing the light intensity as photon count
-rate.
-\begin{itemize}
-\item Like previously, slowly change the position of the detection slit and record the average count rate in each
-point. Start with the two-slit interference. Plot the data and confirm that you see interference fringes.
+{\em The apparatus should be open for this part.}
+
+\begin{description}
+\item[The photodiode] When down, the shutter positions the $\sim 1 \times \unit[1]{cm^2}$ photodiode in the path of the interference pattern. The output voltage from the photodiode is proportional to the total amount of light hitting it.
+
+\item[Connecting to the photodiode] You need to connect a multimeter in DCV mode to the photodiode output on the detector box. To do this you will need a coaxial cable with BNC connectors on each end and a BNC $\leftrightarrow$ banana plug converter. These items are shown in Fig.~\ref{bnc.fig}.
+
+\item[The detector slit] The detector slit masks most of the photodiode, only allowing light through in a narrow window range along the horizontal ($x$) axis. By adjusting the micrometer screw of the detector slit, you can move the slit over the interference pattern, eventually mapping out its intensity distribution quantitatively.  
+
+\item[Getting in position] For now, ensure that the detector slit is located somewhere near the edge middle of the two-slit interference pattern, and have the slit-blocker set to give you double-slit interference.
+
+\item[Quick scan of the pattern] Now, turn the micrometer dial to move the detector slit. Observe how the voltage output of the photodiode changes as you translate the slit across light and dark fringes. To take good data you will do the same thing with the box closed, stopping at even intervals to record the photodiode output.
+
+\end{description}
 
-\item Repeat the measurement with one slit blocked and make the plot.
+\subsubsection*{\textcolor{blue}{Taking photodiode data}}
 
-\item Use the spacing of the interference maxima to check that the light source has a different wavelength than
-the red laser light you used previously. Using the previously determined value of the slit separation $d$,
-calculate the wavelength of the light, and check that it is consistent with the green filter specs
-($541-551$~nm).
+{\em Now, close the apparatus.} Be gentle when putting the top on!  \textcolor{red}{Note: you will have to follow the procedure below twice, once for double slit, and then again for single slit.}
 
+\begin{description}
+\item[Record the pedestal] Turn off the laser and observe that the photodiode produces an output even without light. This is the ``zero offset'' or ``pedestal'' reading. Record it in your lab book, along with an uncertainty. You will need this for your analysis.
+
+\item[Take a datapoint] Now you are ready to take data. Move the detector slit to one end of the interference pattern. Collect one datapoint by recording the detector slit position (by reading the micrometer) and the voltage from the photodiode. You will be taking a lot of datapoints and it is wise to plot them as you collect them. Therefore you should record the readings in a spreadsheet and do not need to put them in your lab book. 
+
+\item[Uncertainty -- Part 1] Estimate your uncertainty from the micrometer and multi-meter precision and stability. Record your uncertainty and any comments you have about it in your lab book. We will come back to this later.
+
+\item[Collect more points] Move the detector slit by some small interval, collecting additional datapoints. You want to map out the interference pattern with sufficient details that you can easily resolve the light and dark fringes. For double-slit interference, taking data every $\unit[100]{\mu m}$ should be OK.  The single slit pattern is less detailed and you need only take data every $\unit[200]{\mu m}$.
+
+\item[Plot the data] Plot your data as you take it to verify that you are seeing an interference pattern. Remake the plot every 20 steps or so. (This is easiest to do as a scatterplot in a spreadsheet).
+
+\item[The goal] The goal is to take about 70 points in double slit mode and 35 in single slit mode. This should allow you to see multiple maxima and minima in double slit, and the central maximum in single slit mode, along with (hopefully) a secondary maximum on at least one side. \textcolor{red}{Note: before moving from double to single-slit mode you should estimate your uncertainties by following the procedure described below.}
+\end{description}
+
+\subsubsection*{\textcolor{blue}{Uncertainties}}
+
+Are your uncertainties really just due to the measurement precision of the micrometer dial and DVM?  It is wise to test this by repeating some measurements in both single and double slit modes.. To do so:
+
+\begin{description}
+\item[Back to the beginning]
+ Move the detector slit all the way back to the starting point. Go a little past the point as you do so, then come back to it going in the direction that you took all the data. Record the old and new reading of that point in your lab book. 
+
+\item[Repeat points] Now, translate the detector slit and remeasure 8 representative points in your dataset. Recording the old and new values. 
+
+\item[And again] Do the same thing again, so that you have three repeated readings at each of the 8 points. 
+
+\item[Uncertainty -- Part 2] Use the standard deviation in each of the 8 measurements to estimate your uncertainty due to repeatability. Is it larger than that due to the precision? Talk this over with the instructor and how to generalize what you found to all the points. 
+\end{description}
+
+\subsection*{Measuring interference with a weak source}
+
+
+\subsubsection*{\textcolor{blue}{Orienting yourself with the bulb and PMT}}
+
+Now you need to change the apparatus to use the light bulb and PMT. Keep the shutter down for now. 
+
+\begin{description}
+\item[Open up] Open the cover and slide the laser source to the side (do not remove the laser from the stand). 
+
+\item[Bulb settings] Now set the 3-position toggle switch to the ``bulb'' position and dial its intensity to 8.  As long as you haven't touched anything else the apparatus is still aligned and light from the bulb will form interference patters that you can measure with the PMT.
+
+\item[Double slit mode] Use the dial to move the slit blocker into double slit mode.
+
+\item[Close it up] Now close and latch the cover. 
+
+\item[High voltage and PMT pulses] Have an instructor show you how to use the DVM to measure the voltage supplied to the PMT and how to observe the PMT output on an  oscilloscope. With the instructor, gradually turn on the HV to get up to a setting of around \unit[700]{V}. You should see pulses on the oscilloscope screen.
+
+% instructor: going for a darkrate of ~100Hz and a signal rate of at least 1kHz at the center of the pattern. May need to play with HV and discriminator settings. 
+
+\item[Counting Pulses]  The instructor will also show you how to look at the discriminator output on the scope and how to count pulses with a frequency counter. The counter should be set to count for 1 second. {\em Pause to document the setup procedure in your lab book. Sketch connections, record the HV rate, etc. You should document this well enough to repeat it in a year. }
+
+\item[Unstable Counter!] You've noticed that the counting rate isn't stable. This is because you are observing a random process. So, how do we assign an uncertainty?  Begin by recording 10 different readings $N_i$ from the frequency counter in your lab notebook.
+
+\item[Counting uncertainty] Compute the mean of the readings and their standard deviation and record those too. Compare the standard deviation to $\sqrt{N_i}$ for a couple of the points. Are the values similar?  It turns out that for a random counting process, if you count $N_i$ counts then the associated uncertainty is $\delta N_i = \sqrt{N_i}$. This is what you will use in your analysis\footnote{So, if you count $N=9$ counts in some period of time the uncertainty is apparently $\delta N = \sqrt{9} = 3$. But, what if you are sure it was 9 counts, not 8, not 10, etc?  You are really positive you didn't miss any. What then? You should discuss this with your instructor.}.
+
+% The issue is that the number of counts N is an exact number which itself has no uncertainty. However, we are trying to apply it to estimate the true (asymptotic) counting rate, which is just the underlining probability multiplied by some unimportant scale. In that case, the appropriate uncertainty is sqrt(N).  In fact, we should be doing a real Pearson-Chi2 fit in which the denominator in the Chi-2 is the value of the function (e.g. (delta fit-funct)^2) not a number from the data. But I think it's too far in the weeds and I don't know offhand how to do it in matlab. 
+
+\item[The dark rate] By the way, you have been observing counts even without light shining on the PMT, since the shutter is down. This is the so-called ``dark rate'' of the PMT. It is similar to the ``zero offset'' or ``pedestal'' that you saw for the photodiode. You should record it in your lab book. Ask your instructor what causes it and to explain how the PMT works. {\bf Then, finally, go ahead and raise the shutter before moving on to the next section.} 
+
+\end{description}
+
+\subsubsection*{\textcolor{blue}{Taking PMT data}}
+
+{\em The data taking must be done with the box closed and high voltage on. If for any reason you have to open the box you need to make sure the high voltage is off and the shutter is down.}
+
+You are now going to measure single and double slit interference just like you did with the laser and photodiode. In particular you should take about the same number of points with the same step size. Now, however you will be using the PMT counting rate as a measure of the light intensity, rather than the photodiode output, and you are observing a very dim light source. In fact the source is so dim that you can convince yourself with a ``back of the envelope'' computation that there is usually only one photon in the region downstream of the double slits at any given time.  That calculation is described in the data analysis section and it should appear in your report.  The ramification is that the interference pattern must be due to photons interfering with themselves! This experimentally establishes wave-particle duality.
+
+You don't need to repeat datapoints to establish an uncertainty. The dominant contribution is just due to the statistical noise  in the counting rate ($\delta N_i = \sqrt{N_i}$). In Matlab, if you have your $N_i$ in an array {\tt N} then the $\delta N_i$ can just be computed as {\tt dN=sqrt(N)}, or similar in Python {\tt dN=np.sqrt(N)}. You can then plot the data and uncertainties with the {\tt errorbar} function in either Matlab or Python
+
+You should be careful not to wait to record ``round numbers'' or other aesthetically pleasing readings from the counter. The best way of doing this is to establish a routine. For example, turn the micrometer dial and then look at the counter. Record the second reading that you see since the first might be corrupted by the move. You need only record the rate as an integer (i.e., you can neglect any numbers after the decimal place).
+
+\subsubsection*{Qualitative observations}
+
+In both the one and two slit cases make some qualitative observations. Do the patterns appear to agree with Equations.~\ref{2slit_wDif}-\ref{1slit}?  What would happen if we increased or decreased $d$, $a$, $\lambda$ and $\ell$.  Record your thoughts in your labbook, and use these insights in setting the initial parameters when fitting your data.
+
+%The plots of your experimental data are clear evidence of particle-wave duality for photons. You've made contact with the central question of quantum mechanics: how can light, which so clearly propagates as a wave that we can measure its wavelength, also be detected as individual photon events?  Or alternatively, how can individual photons in flight through this apparatus nevertheless `know' whether one, or both, slits are open, in the sense of giving photon arrival rates which decrease when a second slit is opened?  Discuss these issues in your lab report.
+
+\vspace{1cm}
+\hrule
+
+{\huge Your instructor may have told you to do a ``brief writeup'' of this experiment. If so, please see the instructions starting on the next page (page~\pageref{pag:briefwriteup}).}
+
+\hrule
+
+\newpage
+
+\section*{Instructions for a brief writeup}\label{pag:briefwriteup}
+
+In this lab you have collected 4 independent datasets (red laser and green bulb with single or double slit) and the analysis will require fits to these data.  Therefore, a formal lab report with abstract, introduction, conclusion, etc. is \textbf{not} required.  For this brief writeup: you only need to include the tables and figures requested below, as well as answering the questions listed in this section. {\bf Please restate each one so it's easy for us to follow along.} {\it Refer to the relevant section earlier in the manual or later in Appendices for additional discussion of the analysis procedure. This is just a bullet point summary of the deliverables.}
+
+%\subsection*{How does the interference patterns depend on  $d$, $a$, and $\lambda$?}
+%
+%What would happen if we increased or decreased $d$, $a$, and $\lambda$?  Explore this by finding the locations of the minima of Eqs.~(\ref{1slit}) and %(\ref{2slit_wDif}). Then look at what happens to those locations as you change $d$, $a$, and $\lambda$. Record the results in your lab book and report. Knowing how the pattern changes as you change the variables is useful as you pick starting values for those parameters to use in your fits.
+
+\subsection*{Data Tables and Uncertainties}
+
+\begin{itemize}
+\item Tabulate your data for each of the four interference patterns and include them (with labels and captions).
+\item Describe how uncertainties on position, photodiode voltage, and photon counting rate were determined, and report your estimated uncertainty values.
 \end{itemize}
 
-The plots of your experimental data are clear evidence of particle-wave duality for photons. You've made contact with the central question of quantum mechanics: how can light, which so clearly propagates as a wave that we can measure its wavelength, also be detected as individual photon events?  Or alternatively, how can individual photons in flight through this apparatus nevertheless `know' whether one, or both, slits are open, in the sense of giving photon arrival rates which decrease when a second slit is opened?  Discuss these issues in your lab report.
+\subsection*{Data Analysis and Fitting}
+
+For each of the four interference patterns, address the following points:
+
+\begin{enumerate}
+\item Plot the measurements for the photodiode voltage or photon counting rate (y-axis) vs position (x-axis) with uncertainties and fit to Eqs.~(\ref{2slit_wDif}) and (\ref{1slit}) for Double and Single Slit, respectively.  Include a figure with the plot of your data and the resulting fit in your report (with labels and captions).
+\item Is it a good fit: in terms of the observed $\chi^2$ and number of degrees of freedom?
+\item What are the best fit parameters and uncertainties?
+\item Is B consistent with what you expect from the background (\textit{i.e.} pedestal or dark rate) measurements you collected during lab?  Comment on any discrepancies. 
+\end{enumerate}
+
+\noindent Finally, quantitatively compare your measurements of $a$ and $d$ between the four datasets.  Are they consistent?
+
+\subsection*{Did we really see single photon interference?}
+
+To conclude that photons interfere with themselves, rather than with other nearby photons, we have to be sure that the rate of photons is low enough that only one of them is in the vicinity of the double slit at any given time.  You need to work through the steps in the Appendix ``Computing the photon rate" below, writing numbers in your lab book. In this brief writeup summarize the results in a paragraph or two, including the numbers you calculate at each stage.  Write a nice bit of narrative text, not just a bunch of bullets with numbers.
+
+\newpage 
+\section*{Appendix: Computing the photon rate}
 
+{\em This is a so-called back of the envelope calculation.}
+
+\begin{enumerate}
+
+%\item Begin by roughly estimating the number of photons per second arriving to the detector. 
+\item Begin by computing the amount of electrical power that is converted to light by the light bulb. Assume we operate the bulb at \unit[6]{VDC} and it draws \unit[0.2]{A} of current.  From this you can get the power drawn by the bulb. % Ans: 1.2W
+
+\item Most of the power goes into heating the bulb. Assume 5\% of it is converted to light evenly distributed from 500-1500~nm. 
+ 
+\item The bulb has a green filter that blocks the light outside the range 541-551~nm.  From this you can get the amount of power radiated as green light. %1.2W*0.05*10nm/1500nm = 6e-4W
+
+\item You can convert the power (energy/time) into a rate of photons using the fact that $E = \frac{hc}{\lambda}$.  From this you can find the rate of green photons emitted from the bulb+filter.  % One 546nm photon has E=6.626e-34 J sec * 3e8 m/sec / 546e-9m  = 3.64e-19 J 
+% (6e-4 J/sec) / (3.64e-19 J/photon) = 1.65e15 photons/sec
+
+\item The photons emitted by the bulb get diluted by the apertures in the interference channel.  The first is a single slit about $R=\unit[10]{cm}$ from the bulb with a width of \unit[0.1]{mm} and a height of \unit[1]{cm}.  Assuming that the bulb radiates evenly onto a spherical surface of radius $R$, compute the fraction of the light that would pass through the slit. % slit area/4 pi R^2=7.96e-6
+% rate passing slit is 7.96e-6 * 1.65e15 photons/sec = 1.31e10 photons/sec
+
+\item After the single slit the beam is diffracted into a single slit interference pattern and impinges on the double slit. If you had the apparatus in front of you, you could estimate the area that the interference pattern covers. A good guess is $\unit[1]{cm^2}$. Assume this and that the double slits have an area twice that of the single slit. You can compute the rate of photons passing through the double slits. % 1.31e10 photons/sec * 2 * 7.96e-6 = 2.1e5 photons/sec
+
+\item We know that a photon travels at a speed $c=\unit[3\times 10^8]{m/sec}$. Divide that by the number of photons per second that pass through the double slits. This gives you the typical space between photons in meters/photon. % 1428 m/photon
+
+\item Invert the number from the previous bullet point and multiply by the 0.5~m between the double slit and detector slit to determine how many photons are in the setup on average.  Is it a number much less than one?  If so, there is a good reason to believe that the photons must be interfering with themselves to form the light and dark fringes you see.  % 3.5e-4 photons in the half meter downstream of the double slit
+
+\end{enumerate}
+
+\newpage 
+\section*{Appendix: Fitting the interference data}
+
+You need to fit your data with Eqs.~(\ref{2slit_wDif}) and (\ref{1slit}).  A detailed example is provided in ``Help on the double slit analysis'' in the Matlab folder on Blackboard or ``Fitting Help: Single and Double Slit" in the Python folder on Blackboard. {\em Please utilize this, it will save you a lot of time!}
+
+A few fitting tips and notes:
+
+\begin{itemize}
+\item Make sure that units of all your measured values are self-consistent - the program will go crazy if you mix meters and micrometers together!
+\item Try to plot your function using estimated values of the parameters before doing a fit with it. This catches many silly errors.
+\item The fitting function has a term to account for the overall normalization and also for the fact that the maximum is not set at $x=0$. In other words, we substitute $x \rightarrow x-x_0$ when coding the fit function. Estimate both of these (for the normalization, look at what happens when $x-x_0 = 0$) but include them as free parameters in the fit.
+\item The fitting function has a term to account for the ``pedestal'' (for the photodiode) or ``dark rate'' (for the PMT) you observed when the lights were off. The estimated value should be changed to agree with what you observed. 
+\item Just a note: fitting functions should include the minimal number of parameters. If I have parameters $a$ and $b$ but they always appear as $ab$ in my function, then I am much better off including a term $c=ab$ when doing the fit. Otherwise the fit is underconstrained. Adjusting $a$ up has the same effect as adjusting $b$ down so it's impossible to converge on unique values for $a$ and $b$. Fitting algorithms really dislike this situation.
+\item If the program has trouble fitting all the parameters, first hold the values of the parameters you know fairly well (such as the light wavelength, maximum peak intensity, background, etc.). Once you determine the approximate values for all other parameters, you can release the fixed ones, and let the program adjust everything to make the fit better.
+\end{itemize}
 
-\section*{\emph{Two-Slit interference with atoms}\footnote{Special thanks to Prof. Seth Aubin for providing the materials for this section}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Appendices %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newpage 
+\section*{Appendix: Two-Slit interference with atoms\footnote{Special thanks to Prof. Seth Aubin for providing the materials for this section}}
 
 \emph{According to quantum mechanics, the wave-particle duality must be applied not only to light, but to any
 ``real'' particles as well. That means that under the right circumstance, atoms should behave as waves with
diff --git a/spectr.tex b/spectr.tex
index 98d518c..d867b46 100644
--- a/spectr.tex
+++ b/spectr.tex
@@ -300,7 +300,7 @@ where $m$ is the diffraction order, and $d$ is the distance between the lines in
     the collimator slit, swing the rotating telescope slowly
     through 90 degrees both on the left \& right sides of the forward
     direction.  You should observe diffraction maxima for most
-    spectral wavelength, $\lambda$, in 1st, 2nd, and 3rd order.  If these
+    spectral wavelength, $\lambda$, in 1st and 2nd order.  If these
     lines seem to climb uphill or drop downhill
     the grating has to be adjusted in its baseclamp to
     bring them all to the same elevation.
@@ -316,8 +316,7 @@ where $m$ is the diffraction order, and $d$ is the distance between the lines in
 \end{figure}
 Swing the rotating telescope slowly and determine which spectral lines from Balmer series you
 observe. You should be able to see three bright lines - Blue, Green and Red - in the first (m=1) and
-second (m=2) diffraction orders on both left \& right sides. In the third order (m=3) only the Blue,
-\& Green lines are visible, and you will not see the Red.
+second (m=2) diffraction orders on both left \& right sides. %In the third order (m=3) only the Blue, \& Green lines are visible, and you will not see the Red.
 
 One more line of the Balmer series is in the visible range - Violet, but its intensity is much lower
 than for the other three line. However, you will be able to find it in the first order if you look
@@ -337,7 +336,7 @@ spectrum resembling one shown in Fig.~\ref{fig:hydrogen_visible_spectrum}.
 %    You might not see the Violet line due to its low
 %    intensity. Red will not be seen in 3rd  order.
 
-After locating all the lines, measure  the angles at which each line occurs. The spectrometer reading for each line should be measured at least \emph{twice} by \textit{different} lab partners to avoid systematic errors. \textbf{Don't forget}: for every line you need to measure the angles to the right and to the left!
+After locating all the lines, measure  the angles at which each line occurs. The spectrometer reading for each of the first order lines should be measured at least \emph{twice} by \textit{different} lab partners to avoid systematic errors.  For the second order lines, you only need one measurement for your group.  \textbf{Don't forget}: for every line you need to measure the angles to the right and to the left!
 
 You should be able to determine the angle with accuracy of $1$ minute, but you should know how to
 read angles with high precision in the spectrometer: first use the bottom scale to get the rough
@@ -392,14 +391,10 @@ names are symbolic rather than descriptive!
 
 After that, carefully measure the left and right angles for as many
 spectral lines in the first and second orders
-as possible. The spectrometer reading for each line should be measured at least \emph{twice} by
-\textit{different} lab partners to avoid systematic errors.
-
-Determine  the wavelengths of all measured Na spectral lines using Eq. \ref{nlambda}. Compare these
-measured mean wavelengths to the accepted values given in Fig.~\ref{natrns}
-and in the table~\ref{tab:sodium}.
-Identify  at least seven of the lines with a particular transition, e.g. $\lambda = 4494.3${\AA}
-corresponds to $8d \rightarrow 3p$ transition.
+as possible. The spectrometer reading for each line should be measured at least \emph{once} by
+both lab partners to avoid systematic errors.
+
+Determine  the wavelengths of all measured Na spectral lines using Eq. \ref{nlambda}. Compare these measured mean wavelengths to the accepted values given in Fig.~\ref{natrns} and in Tab.~\ref{tab:sodium}. Identify  at least seven of the lines with a particular transition. The eight line in Tab.~\ref{tab:sodium} has a wavelength $\lambda = 4494.3${\AA}. It corresponds to the $8d \rightarrow 3p$ transition but isn't shown in Fig.~\ref{natrns}.
 
 \begin{table}
 
diff --git a/supcon.tex b/supcon.tex
index 4ce7d94..0d29f0a 100644
--- a/supcon.tex
+++ b/supcon.tex
@@ -154,28 +154,32 @@ near the critical temperature (6.4-4.5 mV). Make a plot of
 
 \end{enumerate}
 
-%\section*{Resistance of a ceramic resistor}
-%\begin{enumerate}
-%\item Attach a ceramic resistor to a multimeter reading resistance ($k\Omega$ range). Record the room temperature resistance.
 
-%\item Dunk the resistor in liquid nitrogen. Wait until it stops boiling. Record the resistance at this low temperature ($\approx$77 K).
-
-%\item Take the resistor out of the nitrogen and carefully set it down. Record the resistance as the temperature increases. Make a plot of the measured resustance vs temperature. Compare the plots for the superconductor and the normal resistor, and explain the differences.
-%\end{enumerate}
 
 \hskip-.8in\includegraphics[height=5in]{./pdf_figs/mvtok}
 
+\newpage
+
+\subsection*{Instructions for a brief writeup}
+
+The abstract, introduction and conclusion are not needed. Do the following analysis steps and/or answer the following questions. Make it clear which question you are addressing. For example:
+
+\noindent{\bf Thermocouple}\\
+Blah, blah, blah, blah...
+
+\subsubsection*{Address the following points}
+
+\begin{description}
+\item[Diagram] the experimental setup, including the current source, the superconductor and its wires, and the DMMs.
+\item[Thermocouple] Explain in your own words what a thermocouple is and how it works (i.e., the physics). No more than a paragraph is needed.
+\item[Resistance] In the Meissner effect demonstration, when moving the magnets around, did you feel resistance?  Why or why not? Explain in terms of physics concepts and principles that you learned in PHYS 102. 
+\item[Tabulate] your data, including columns for voltage, current, resistance, thermocouple voltage, and temperature.
+\item[Uncertainties] Estimate them and state them.
+\item[Temperature] Explain how you got the temperature from the thermocouple voltage. What was your procedure? No more than a couple of sentences are needed.
+\item[Plot] the resistance (y-axis) vs temperature (x-axis). Based on the plot, what is the critical temperature for YBCO?
+\item[Fit] the R vs T plot.  What function?  You tell me.  Based on the fitted function, can you estimate the critical temperature? Parameterizing a dataset and then using it to characterize the data, perhaps with a single number, is a common laboratory task. Get used to it!
+\end{description}
 
-%\begin{tabular}{|p{17mm}|p{17mm}|p{17mm}|p{35mm}|p{35mm}|}\hline
-% V (mV)& I (mA)& R ($\Omega$)& Thermocouple (mV)& Temperature (K)\\
-%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
-%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
-%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
-%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
-%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
-%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
-%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
-%\end{tabular}
 
 \end{document}
 
diff --git a/title_page.tex b/title_page.tex
index 1e3b640..85c96c5 100644
--- a/title_page.tex
+++ b/title_page.tex
@@ -2,7 +2,8 @@
 \author{
 	W. J. Kossler \and A. Reilly \and J. Kane (2006 edition)  \and
 	I. Novikova (2009 edition) 
-	\and M. Kordosky (2011-2012 editions)
+	\and M. Kordosky (2011-2012,2015-2017 editions)
 	\and E. E. Mikhailov (2013-2014 editions)
+	\and J. R. Stevens (2016-2018 edition)
 }
-\date{Fall 2014}
+\date{Fall 2018}