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+%\chapter*{Helium-Neon Laser}
+%\addcontentsline{toc}{chapter}{Helium-Neon Laser}
+
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+    \oddsidemargin  0.0in
+    \evensidemargin 0.0in
+    \textwidth      6.5in
+    \headheight     0.0in
+    \topmargin      0.0in
+    \textheight=9.0in
+
+\begin{document}
+\title{Helium-Neon Laser}
+\date {}
+\maketitle \noindent
+ \textbf{Experiment objectives}: assemble and align  a 3-mW HeNe laser from
+readily available optical components, record photographically the transverse mode structure of the
+laser output beam, and determine the linear polarization of the light produced by the HeNe laser.
+
+\subsection*{Basic operation of the laser}
+
+    The bright, highly collimated, red light beam ($\lambda = 6328 {\AA}$) from a helium-neon (HeNe)
+laser is a familiar sight in the scientific laboratory, in the industrial workplace, and even at the
+checkout counter in most supermarkets. HeNe lasers are manufactured in large quantities at low cost
+and can provide thousands of hours of useful service. Even though solid-state diode lasers can now
+provide red laser beams with intensities comparable to those obtained from HeNe lasers, the HeNe
+laser will likely remain a common component in scientific and technical instrumentation for the
+foreseeable future.
+%
+%In this experiment you will (a) assemble a 3-mW HeNe laser from readily available optical components,
+%(b) align a HeNe laser cavity using two different cavity mirror configurations, (c) record
+%photographically the transverse mode structure of the laser output beam, and (d) determine the linear
+%polarization of the light produced by the HeNe laser. The principal goal of this experiment is for
+%you to get hands-on experience with the various optical components of a working laser; however, to
+%help you appreciate fully the role played by each of the components, a brief overview of the
+%principles of HeNe laser operation is given here.
+
+\begin{figure}[h]
+\centerline{\epsfig{width=\textwidth, file=HeNesetup.eps}} \caption{\label{HeNesetup.fig}Diagram of
+optical and electrical components used in the HeNe laser experiment.}
+\end{figure}
+
+The principal goal of this experiment is for
+you to get hands-on experience with the various optical components of a working laser; however, to
+help you appreciate fully the role played by each of the components, a brief overview of the
+principles of HeNe laser operation is given here. The three principal elements of a laser are:
+(1) an energy pump, (2) an optical gain medium, and (3)
+an optical resonator. These three elements are described in detail below for the case of the HeNe
+laser used in this experiment.
+\begin{enumerate}
+\item \textbf{Energy pump}. A 1400-V DC power supply
+maintains a glow discharge or plasma in a glass tube containing an optimal mixture (typically 5:1 to
+7:1) of helium and neon gas, as shown in Fig.~\ref{HeNesetup.fig}. The discharge current is limited
+to about 5 mA by a 91-k$\Omega$ ballast resistor. Energetic electrons accelerating from the cathode
+to the anode collide with He and Ne atoms in the laser tube, producing a large number of neutral He
+and Ne atoms in excited states. He and Ne atoms in excited states can deexcite and return to their
+ground states by emitting light spontaneously. This light makes up the bright and diffuse pink-red
+glow of the plasma that is seen at even in the absence of laser action.
+
+The process of producing He and Ne in specific excited states is known as pumping, and in the HeNe
+laser this pumping process occurs through electron-atom collisions in the discharge. In other types
+of lasers, pumping is achieved by using light from a bright flashlamp or by using chemical reactions.
+Common to all lasers is a process for preparing large numbers of atoms, ions, or molecules in
+appropriate excited states so that a desired type of light emission can occur.
+
+\item \textbf{Optical gain medium}.
+To achieve laser action it is necessary to have more atoms in excited states than in ground states,
+and to establish what is called a \emph{population inversion}. To understand the significance of a
+population inversion to HeNe laser action, it is useful to consider the processes leading to
+excitation of He and Ne atoms in the discharge, using the simplified diagram of atomic He and Ne
+energy levels given in Fig.~\ref{HeNelevels.fig}. The rather complex excitation process necessary for
+lasing occurs
+in four steps. \\
+\emph{(a)} An energetic electron collisionally excites a He atom to the state labeled $2_1S^0$ in
+Fig.~\ref{HeNelevels.fig}. A He atom in this excited state is often written He*($2_1S^0$), where the
+asterisk is used
+to indicate that the He atom is in an excited state. \\
+
+\emph{(b)} The excited He*($2_1S^0$) atom collides with an unexcited Ne atom and the two atoms
+exchange internal energy, with an unexcited He atom and excited Ne atom, written Ne*(3$s_2$),
+resulting. This energy exchange process occurs with high probability because of the accidental near
+equality of the excitation energies of the two levels in these atoms.\\
+
+\emph{(c)} The 3$s_2$ level of Ne is an example of a metastable atomic state, meaning that it is only
+after a relatively long time -- on atomic that is -- that the Ne*(3$s_2$) atom deexcites to the
+2$p_4$ level by emitting a photon of wavelength 6328 $\AA$. It is this emission of 6328 $\AA$ light
+by Ne atoms that, in the presence of a suitable optical suitable optical configuration,
+leads to lasing action. \\
+
+\emph{(d)} The excited Ne*(2$p_4$) atom rapidly deexcites to the Ne ground state by emitting
+additional photons or by collisions with the plasma tube deexcitation process occurs rapidly, there
+are more Ne atoms in the 3$s_2$ state than there are in the 2$p_4$ state at any given moment in the
+HeNe plasma, and a population inversion is said to be established between these two levels. When a
+population inversion is established between the 3$s_2$ and 2$p_4$ levels of the excited Ne atoms, the
+discharge can act as an optical gain medium (a light light amplifier) for light of wavelength 6328
+$\AA$. This is because a photon incident on the gas will have a greater probability of being
+replicated in a 3$s_2\rightarrow 2p_4$ stimulated emission process (discussed below) than of being
+destroyed in the complementary $2p_4\rightarrow 3s_2$ absorption process.
+
+
+\begin{figure}[h]
+\centerline{\epsfig{width=0.8\textwidth, file=HeNelevels.eps}}
+\caption{\label{HeNelevels.fig}Simplified atomic energy level diagram showing excited states of
+atomic He and Ne that are relevant to the operation of the HeNe laser at 6328~$\AA$.}
+\end{figure}
+
+\item \textbf{Optical resonator}. As mentioned in 2(c) above, Ne atoms in the 3$s_2$ metastable
+state decay spontaneously to the 2$p_4$ level after a relatively long period of time under normal
+circumstances; however, a novel circumstance arises if, as shown in Fig.~\ref{HeNesetup.fig}, a HeNe
+discharge is placed between two highly reflecting mirrors that form an \emph{optical cavity} or
+\emph{resonator} along the axis of the discharge. When a resonator structure is in place, photons
+from the Ne* 3$s_2\rightarrow 2p_4$ transition that are emitted along the axis of the cavity can be
+reflected hundreds of times between the two high-reflectance end mirrors of the cavity. These
+reflecting photons can interact with other excited Ne*(3$s_2$) atoms and cause them to emit 6328
+$\AA$ light in a process known as \emph{stimulated} emission. The new photon produced in stimulated
+emission has the same wavelength and polarization as the stimulating photon, and it is emitted in the
+same direction. It is sometimes useful for purposes of analogy to think of the stimulated emission
+process as a "cloning" process for photons. The stimulated emission process should be contrasted with
+spontaneous emission processes that, because they are not caused by any preceding event, produce
+photons that are emitted isotropically, with random polarization, and over a broader range of
+wavelengths. As stimulated emission processes occur along the axis of the resonator, a situation
+develops in which essentially all Ne* 3$s_2\rightarrow 2p_4$ decays contribute deexcitation photons
+to the photon stream reflecting between the two mirrors. This photon multiplication (light
+amplification) process produces a very large number of photons of the same wavelength and
+polarization that travel back and forth between the two cavity mirrors. To extract a light beam from
+the resonator, it is only necessary that one of the two resonator mirrors, usually called \emph{the
+output coupler}, has a reflectivity of only 99\% so that 1\% of the photons incident on it travel out
+of the resonator to produce an external laser beam. The other mirror, called the high reflector,
+should be as reflective as possible. The diameter, bandwidth, and polarization of the HeNe laser beam
+are determined by the properties of the resonator mirrors and other optical components that lie along
+the axis of the optical resonator.
+
+\end{enumerate}
+
+
+\section*{Experimental Procedure}
+
+\textbf{Equipment needed}: Commercial HeNe laser, HeNe discharge tube connected to the power supply,
+two highly reflective mirrors, digital camera, polarizer, photodetector, digital multimeter.
+
+\subsection*{Safety}
+A few words of caution are important before you begin setting up your HeNe laser. \\
+First, \textbf{never} look directly into a laser beam, as severe eye damage could result. During alignment, you
+should observe the laser beam by placing a small, white index card at the appropriate point in the optical path.
+Resist the temptation to lower your head to the level of the laser beam in order to see where it is going. \\
+Second, \textbf{high voltage} ($\approx 1200$~V) is present at the HeNe discharge tube and you should avoid any
+possibility of contact with the bare electrodes of the HeNe plasma tube. \\ Finally, the optical cavity mirrors
+and the Brewster windows of the laser tube have \textbf{very delicate optical surfaces} that can be easily
+scratched or damaged with a single fingerprint. If these surfaces need cleaning, ask the instructor to
+demonstrate the proper method for cleaning them.
+
+
+
+\subsection*{Alignment of the laser}
+
+To assemble the HeNe laser and investigate its properties, proceed with the following steps.
+
+\begin{itemize}
+
+\item The discharge lamp has very small and angled windows, so first practice to align the beam of
+the commercial HeNe laser through the discharge tube. To do that turn on the commercial laser, place a white
+screen or a sheet of paper at some distance and mark the position of the laser spot. Now without turning the
+power, carefully place the discharge tube such that the laser beam passes through both angled windows without
+distortion, and hit the screen almost in the same point as without the tube. Repeat this step a few times until
+you are able to insert the tube inside the cavity without loosing the alignment. Then carefully slide the tube
+out of the beam and clamp it down.
+
+\item Set up a hemispherical resonator configuration using a flat, high reflectivity (R = 99.7\%)
+mirror, and a spherical mirror with a radius of curvature of r = 0.500 m and reflectivity R = 99\%.
+The focal length f of the spherical mirror is given by f = r/2 = 0.250 m. In the diagram of
+Fig.~\ref{HeNesetup.fig}, the flat, highly-reflective mirror will be serving as the right end of the
+cavity, and the spherical, less-reflective mirror will be serving as the left end of the cavity and
+is known as the output coupler. The high reflectivity of each mirror is due to a multilayer
+dielectric coating that is located on only one side of each mirror. Be sure to have the reflecting
+surfaces of both mirrors facing the interior of the optical cavity. Set the distance between the two
+mirrors to approximately d = 47 cm.
+
+\item To align the optical resonator of your HeNe laser it is easiest to use a beam of a working,
+commercial HeNe laser as a guide. Direct this alignment laser beam to the center of the high reflector mirror,
+with the output coupler and the HeNe discharge tube removed. With the room lights turned off, adjust the high
+reflector mirror so that its reflected beam returns directly into the output aperture of the alignment laser.
+Now insert and center the output coupler mirror, and also adjust it such that the reflected beam (from the back
+of the mirror) returns to the alignment laser. Now insert a small white card near the front of the output
+couplers very close to the laser beam but without blocking it, and locate the reflected beam from the high
+reflector mirror - it should be fairly close to the input beam.  Using fine adjustment screws in the high
+reflector mirror overlap these two beams as good as you can. In case of success you most likely will see some
+light passing through a high reflection mirror - fine-tune the position of the mirror some more to make this
+light as bright as possible.
+%and
+%aAdjust the output coupler mirror until you observe concentric interference rings on its intracavity
+%surface. It is likely that the interference rings will be converging or diverging slowly. It may be
+%necessary to adjust the spacing, d, between the two mirrors to achieve perfectly circular rings.
+
+\item Now reinsert the HeNe plasma tube between the two mirrors of the optical cavity and adjust the
+plasma tube position so that the alignment beam passes through the center of the Brewster windows of the plasma
+tube. Be careful not to touch the Brewster windows or mirror surfaces during this process. With the HeNe plasma
+tube in place, it should be possible to see a spot at the center of the high reflector mirror that brightens and
+dims slowly.  %at approximately the same rate as the diverging and converging circular interference rings
+%observed earlier.
+
+\item Turn on the high voltage power supply to the HeNe plasma tube and (with luck) you will observe
+the HeNe lasing. If lasing does not occur, make small adjustments to the plasma tube and the two
+mirrors. If lasing still does not occur, turn off the high voltage supply, remove the HeNe plasma
+tube, and readjust the resonator mirrors for optimal interference rings. If after several attempts
+you do not achieve proper lasing action, ask the instructor for help in cleaning the Brewster windows
+and resonator mirrors.
+
+\item Once lasing is achieved, record your alignment procedure in your laboratory notebook. %Describe
+%with a well-labeled sketch the nature of the concentric rings that you observed when aligning the
+%optical cavity. Determine the range of distances between the two mirrors for which lasing action can
+%be maintained in the confocal resonator configuration. Do this in small steps, by increasing or
+%decreasing the mirror separation distance d in small increments, and making small adjustments to the
+%two mirrors to maintain laser output.
+Turn off the alignment laser - you do not need it anymore.
+
+\end{itemize}
+
+\subsection*{Study of the mode structure of the laser output}
+
+Place a white screen at the output of your laser at some distance and inspect the shape of your beam.
+Although it is possible that your beam is one circular spot, most likely you will notice some
+structure as if the laser output consists of several beams. If you now slightly adjust the alignment
+of either mirror you will see that the mode structure changes as well.
+
+As you remember, the main purpose of the laser cavity is to make the light bounce back and forth
+repeating its path to enhance the lasing action of the gain medium. However, depending on the precise
+alignment of the mirrors it may take the light more than two bounces to close the loop: it is often
+possible for the beam to follow a rather complicated trajectory inside the resonator, resulting in
+complex transverse mode structure at the output.
+\begin{itemize}
+
+\item
+Take photographs of the transverse mode structure of the HeNe laser output beam. By making small
+adjustments to the mirrors and the position of the HeNe plasma tube it should be possible to obtain
+transverse mode patterns. Mount your photographs in your laboratory notebook.
+
+\item
+Adjust the mirrors such that the output mode has several maxima and minima in one direction. To
+double-check that this mode is due to complicated trajectory of a light inside the resonator, very
+carefully insert an edge of a white index card into the cavity, and move it slowly until the laser
+generation stops. Now mover the card back and force around this point while watching the generation
+appear and disappear, and pay close attention to the mode structure of the laser output. You may
+notice that the complicated transverse mode pattern collapses to simpler mode when the card blocks
+part of the original mode volume, forcing the generation in a different mode. Describe your
+observation in the lab journal.
+
+
+\end{itemize}
+
+\subsection*{Measure the polarization of the laser light}
+
+When a linearly polarized light beam of intensity $I_0$ passes through a linear polarizer that has
+its axis rotated by angle $\theta$ from the incident light beam polarization, the transmitted
+intensity $I$ is given by Malus's law:
+\begin{equation}
+I = I_0 cos^2\theta.
+\end{equation}
+
+In our experiment the laser generates linearly polarized light field. This is insured by the Brewster
+windows of the HeNe plasma tube: the angle of the windows is such that one light polarization
+propagates almost without reflection. This polarization direction is in the same plane as the
+incident beam and the surface normal (i.e. the plane of incidence). The light of the orthogonal
+polarization experiences reflection at every window, that makes the optical losses too high for such
+light.
+
+\begin{itemize}
+
+\item Visually inspect the discharge tube, note its orientation in the lab book. Make a rough prediction of
+the expected polarization of the generated beam.
+
+\item Determine the linear polarization of the HeNe laser output beam using the rotatable polarizer
+and photodiode detector.  Make detector readings at several values of angle $\theta$ (every
+$20^\circ$ or so) while rotating the polarizer in one full circle, and record them in a neat table in
+your laboratory notebook. Graph your data to demonstrate, fit with the expected $cos^2\theta$
+dependence, and from this graph determine the orientation of the laser polarization. Compare it with
+your predictions based on the Brewster windows orientation, and discuss the results in your lab
+report.
+
+\end{itemize}
+
+
+\section*{Acknowledgements}
+
+This lab would be impossible without help of Dr. Jeff Dunham from the Physics Department of the
+Middlebury College, who shared important information about experimental arrangements and supplies, as
+well as the lab procedure. This manual is based on the one used in Physics 321 course in Middlebury
+College.
+
+\end{document}
+\newpage
diff --git a/unused_chapters/appendices.tex b/unused_chapters/appendices.tex
new file mode 100644
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+\chapter*{Errors}
+
+\section*{Propagation of Random Errors}
+Suppose one measures basically the same quantity twice. This might be the 
+number of $\gamma$-rays detected in 10 minutes with a scintillation detector.
+Let $n_1$ be the number detected the first time and $n_2$ the number the
+second time. Assume that the average number for many such measurements is
+$\overline{n}$. We may then consider a variety of averages denoted by $<>$:
+\begin{eqnarray*}
+\overline{n}&=&<n>\\
+\overline{n_1}&=&<n>=\overline{n}\\
+<n_1-\overline{n}>&=&0\\
+\overline{n_2}&=&<n>\\
+\sigma_n&=&\sqrt{<(n-\overline{n})^2>}
+\end{eqnarray*}
+
+The root-mean-square(rms) deviation from the mean, ( $\sigma$) is what is 
+often called the 
+error in a measurement.
+We now determine  the ``variance'' ($\sigma^2$) expected for various combinations of 
+measurements. One only needs to take the square root of $\sigma^2$ to obtain
+the error. 
+\begin{eqnarray*}
+\sigma^2&=&<(n_1-\overline{n}+n_2-\overline{n})^2>\\
+&=&<(n_1-\overline{n})^2+(n_2-\overline{n})^2+2(n_1-\overline{n})(n_2-\overline{n})>\\
+&=&<(n_1-\overline{n})^2>+<(n_2-\overline{n})^2>+2<(n_1-\overline{n})(n_2-\overline{n})>\\
+&=&<(n_1-\overline{n})^2>+<(n_2-\overline{n})^2>+2<(n_1-\overline{n})><(n_2-\overline{n})>\\
+\sigma^2&=&\sigma_1^2+\sigma_2^2+0
+\end{eqnarray*}
+The average value of the last term is zero since the two measurements are
+independent and one can take the averages of each part separately.
+
+With this result it is easy to get the variance in a linear combination of
+$n_1$ and $n_2$. If
+
+\begin{displaymath}
+f=a\cdot n_1 +b\cdot n_2
+\end{displaymath}
+
+then:
+\begin{displaymath}
+\sigma_f^2=a^2\sigma_1^2+b^2\sigma_2^2
+\end{displaymath}
+
+If the errors are small  and $f$ is a function of $n_1$ and $n_2$: $f(n_1,n_2)$
+then:
+\begin{equation}\label{ssgen}
+\sigma_f^2=\left(\frac{\partial f}{\partial n_1}\right)^2\sigma_1^2+\left(\frac{\partial f}{\partial n_2}\right)^2\sigma_2^2
+\end{equation}
+It should be clear that one can extend Eq. \ref{ssgen} to arbitrary numbers of
+parameters.
+
+As an example of this latest form suppose $f=n_1\cdot n_2$ then:
+\begin{displaymath}
+\sigma_f^2=n_2^2\sigma_1^2+n_1^2\sigma_2^2
+\end{displaymath}
+or 
+\begin{displaymath}
+\frac{\sigma_f^2}{f^2}=\frac{\sigma_1^2}{n_1^2}+\frac{\sigma_2^2}{n_2^2}
+\end{displaymath}
+
+Thus in this case the fractionial variances  add.
+
+Note: the $\sigma_m$ the error in the mean of $n$ measurements of the
+same thing is: $\sigma_m=\sigma /\sqrt{n}$.
+\subsection*{Probability Distribution Functions}
+\subsubsection*{Binomial}
+If the probability of {\it success} in a trial is $p$ then
+the probability of  $n$ {\it successes}   in $N$ trials is:
+\begin{displaymath}
+P(n)=\frac{N!}{(N-n)!n!}p^n(1-p)^{N-n}
+\end{displaymath}
+This distribution has a mean $\mu=Np$ and variance $\sigma^2=Np(1-p)$.
+This is the starting point for figuring the odds in card games, for example.
+\subsubsection*{Poisson}
+The probability of $n$ events is:
+\begin{displaymath}
+P(n)=\frac{e^{-\mu}\mu^n}{n!}
+\end{displaymath}
+where is the $\mu$ is the mean value and the variance, $\sigma^2=\mu$.
+This is the distribution one gets, e.g., with the number of radioactive
+decays detected in a fixed finite amount of time. It can be derived from
+the binomial distribution in an appropriate limit.
+\subsubsection*{Normal or Gaussian Distribution}
+This is the first continuous probability distribution. 
+\begin{displaymath}
+P(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{\frac{-(x-\mu)^2}{2\sigma^2}}
+\end{displaymath}
+This function, as you might guess, has mean $\mu$ and variance $\sigma^2$.
+If one makes averages of almost anything one finds that the result is
+almost always well described by a Normal distribution. Both the binomial and
+Poisson distributions approach this distribution in  appropriate limits as
+does the $\chi^2$ described below.
+\subsubsection*{Chi-square distribution: $\chi^2$} 
+This probability density function (pdf) has the parameter: $N_f$, the number of
+degrees of freedom. It is:
+\begin{displaymath}
+P(x)=\frac{\frac{1}{2}\left(\frac{x}{2}\right)^{(N_f/2)-1}}{\Gamma\left(
+\frac{N_f}{2}\right)}
+\end{displaymath}
+The mean of this pdf is: $\mu=N_f$ and the variance is: $\sigma^2=2N_f$.
+The pdf is of considerable use in physics. It is used extensively in the 
+fitting of histogrammed data.  
+\newpage 
+
+\appendix{Linear Least Squares}
+
+
+Consider a set of experimental results measured as a function of some
+parameter $x$, i.e., $E(x_i)$. Suppose that these results are expected to
+be represented by a theoretical function $T(x_i)$ and that $T(x_i)$ is
+in turn linearly expandable in terms of independent functions $f_j(x_i)$:
+\begin{displaymath}
+T(x_i)=\sum_ja_jf_j(x_i)
+\end{displaymath}
+Suppose now one wants to find the coefficients $a_j$ by minimizing $\chi^2$,
+the sum of differences between the experimental results and the theoretical
+function, squared, i.e., minimize:
+\begin{displaymath}
+\chi^2=\sum_i\left(\sum_ja_jf_j(x_i)-E(x_i)\right)^2
+\end{displaymath}
+This is found by finding:
+\begin{displaymath}
+0=\frac{\partial}{\partial a_k}\chi^2=
+2\cdot \sum_i\left(\sum_ja_jf_j(x_i)-E(x_i)\right)\cdot f_k(x_i)
+\end{displaymath}
+This may be rewritten as:
+\begin{equation}\label{meq}
+\sum_i\left(\sum_ja_jf_j(x_i)f_k(x_i)\right)=\sum_iE(x_i)f_k(x_i)
+\end{equation}
+The rest is algebra. The formal solution, which can in fact be 
+easily implemented, is to first define: 
+\begin{eqnarray}
+M_{j,k}&=&\sum_if_j(x_i)f_k(x_i\\
+V_k(i)&=&\sum_iE(x_i)f_k(x_i)
+\end{eqnarray}
+So that Eq. \ref{meq}. becomes:
+\begin{displaymath}
+\sum a_jM_{j,k}=V_k
+\end{displaymath}
+The $a_j$ may then be found by finding the inverse of $M_{j,k }$
+\begin{figure}:
+\begin{displaymath}
+a_j=\sum_kV_k\cdot M^{-1}_{k,j}
+\end{displaymath}
+Question: How does this procedure change if:
+\begin{displaymath}
+\chi^2=\sum_i\frac{(T(x_i)-E(x_i))^2}{\sigma(x_i)^2}
+\end{displaymath}
+where $\sigma(x_i)$ is the error in the measurement of $E(x_i)$?
+
+\centerline{\epsfig{width=\linewidth,angle=-90, file=datafg.eps}}
+\caption{\label{lsqf} Data Fit to a Straight Line.}
+\end{figure}
diff --git a/unused_chapters/fabry-perot.tex b/unused_chapters/fabry-perot.tex
new file mode 100644
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+%\chapter*{Fabry-Perot Interferometer and the  Sodium Doublet}
+%\addcontentsline{toc}{chapter}{Fabry-Perot Interferometer}
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+    \oddsidemargin  0.0in
+    \evensidemargin 0.0in
+    \textwidth      6.5in
+    \headheight     0.0in
+    \topmargin      0.0in
+    \textheight=9.0in
+
+\begin{document}
+\title{Fabry-Perot Interferometer and the  Sodium Doublet}
+\date {}
+\maketitle
+
+
+\noindent
+ \textbf{Experiment objectives}: Assemble and align Fabry-Perot interferometer,
+ and use it to measure differential wavelength for the Na doublet.
+
+ \section*{Theory}
+
+\subsection*{The Fabry-Perot Interferometer}
+
+Any interferometer relies on interference between two or more light field. In a Fabry-Perot configuration 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, for example, 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 high spectral resolution of the Fabry-Perot
+interferometer to resolve two very closely-spaces emission lines in Na spectra by observing changes in a
+overlapping interference fringes from these two lines.
+\begin{figure}[h]
+\begin{center}
+\includegraphics[width=0.8\linewidth]{./pdf_figs/pfig1}
+\caption{\label{fpfig1}Sequence of Reflection and
+Transmission for a ray arriving at the treated inner surfaces $P_1 \& P_2$.}
+\end{figure}
+\end{figure}
+
+A Fabry-Perot interferometer consists of two parallel glass plates, flat to better than 1/4 of an optical
+wavelength $\lambda$, and coated on the inner surfaces with a partially transmitting metallic layer. Such
+two-mirror arrangement is normally called an {\it optical cavity}. The light in a cavity by definition bounces
+back and forth many time before escaping; the idea of such a cavity is crucial for the construction of a laser.
+Any light transmitted through such cavity is a product of interference between beams transmitted at each bounce
+as diagrammed in Figure~\ref{fpfig1}. When the incident ray arrives at interface point $A$, a fraction $t$ is
+transmitted and the remaining fraction $r$  is reflected, such that $t + r = 1$ ( this assumes no light is lost
+inside the cavity). The same thing happens at each of the points $A,B,C,D,E,F,G,H\ldots$, splitting the initial
+ray into parallel rays $AB,CD,EF,GH,$ etc. Between adjacent ray pairs, say $AB$ and $CD$, there is a path
+difference of :
+\begin{equation}
+ \delta = BC+CK
+\end{equation}%eq1
+    where $BK$ is normal to $CD$.  In a development
+similar to that used for the Michelson interferometer, you can show
+that:
+\begin{equation}
+ \delta = 2d\cos\theta
+\end{equation}%eq.2
+     If this path difference produces
+constructive interference, then  $\delta$  is some integer multiple of   ,
+$\lambda$ namely,
+\begin{equation}
+  m\lambda = 2d\cos\theta %eq.3
+\end{equation}%eq.3
+
+This applies equally to ray pairs $CD$ and $EF, EF$ and $GH$, etc, so that all parallel rays to the right of
+$P2$ will constructively interfere with one another when brought together.
+
+Issues of intensity of fringes \& contrast between fringes and dark background
+are addressed in Melissinos, {\it Experiments in Modern Physics}, pp.309-312.
+
+\subsection*{The Sodium Doublet}
+
+    In this lab you will measure the separation between the two
+    famous ``sodium doublet'' lines, the two closely spaced lines
+    which occur at 589 $nm$ and 589.59 $nm$, respectively. This ``doublet''
+    emission is evidence that the atomic electron has the property
+    of intrinsic angular momentum, or spin S.  As you are learning
+    in Modern Physics 201, the discrete spectral lines in atomic
+    emission are due to the quantization of electron energies in
+    the atom. As Niels Bohr postulated, electrons in atoms are
+    only allowed to absorb and emit energy in discrete
+    quantities. When an electron moves from one orbit to another
+    in an atom, a well-defined amount of energy is emitted as
+    light at a fixed wavelength. Later in this class we will
+    explore the spectra of various atomic gases.
+\begin{figure}[h]
+\centerline{\epsfig{height=5cm, file=fpfig2.eps}} \caption{\label{fpfig2.fig}Fine Structure Splitting in sodium
+giving rise to the sodium doublet lines}
+\end{figure}
+    For many
+     atoms, {\bf atomic levels are further split}, for example,
+    by interactions of electrons with each other (Russell-Saunders
+    coupling), external magnetic fields (Zeeman effect), and even
+    the interaction between the spin of an electron and the
+    magnetic field created by its orbital angular momentum
+    (spin-orbit coupling). This is known as fine structure
+    splitting (FSS). The fine structure splitting for the sodium
+    3P state is due to spin-orbit coupling, and is illustrated in
+    Figure \ref{fpfig2.fig}.  The "3P" state refers to sodium's
+valence electron
+    which has a principal quantum number of $n=3$ and an orbital
+    quantum number of $l=1$ (a P-state). Further, the electron has
+    an intrinsic spin (like a top), described by a spin quantum
+    number $S$, which is either +1/2 or -1/2. The electron has a
+    magnetic moment due to its intrinsic spin, given by $m_S$. Due to
+its orbital angular momentum around a charged nucleus, it
+    senses a magnetic field ${\mathbf H}$. The energy of interaction of a
+    magnetic moment in a field is given by $E = -\mu\cdot {\mathbf H}$.
+This gives
+    rise to the splitting and two spectral emission lines.
+
+
+\section*{Procedure}
+
+\subsection*{Set Up}
+\textbf{Equipment needed}: Pasco precision interferometry kit, Na lamp,
+adjustable-hight platform.
+
+\begin{figure}
+\centerline{\epsfig{width=0.7\linewidth,file=fpfig3new.eps}} \caption{\label{fpfig3.fig}The Fabry-Perot
+Interferometer}
+\end{figure}
+
+The interferometer layout is shown in Figure \ref{fpfig3.fig}. The inner spacing  $d$ between two
+partially-reflecting mirrors ($P1$ and $P2$) can be roughly adjusted by loosening the screw that mounts $P2$ to
+its base. It is important that the plates are as closely spaced as possible. Move the plates to within  $1.0 -
+1.5$~mm of each other, but make sure the mirrors do not touch!
+
+\subsection*{Data acquisition}
+
+\begin{enumerate}
+\item \textbf{Turn on the sodium lamp as soon as you arrive. It should warm up for about 20 minutes
+before starting}.
+\item Turn the micrometer close to or at 0.00.
+\item Remove the diffuser sheet from in front of the lamp. Look through
+plate $P2$ towards the lamp.  If the plates are not parallel, you will see
+multiple images of the lamp filament. Adjust the knobs on $P1$ until the images
+collapse into one. At this point, you should see faint circular interference
+fringes appear.
+\item Place the diffuser sheet in
+front of the lamp so you will now only see the fringes. Continue to adjust the
+knobs on one plate (not the knobs to move the plate back and forth, but the
+ones to bring it parallel) to get the best fringe pattern. It is the most
+convenient to view the interference picture directly.
+\item
+Seek the START condition illustrated in Fig.(\ref{fpfig4.fig}), in which all bright fringes are evenly spaced.
+You do this by moving the micrometer.  Note that alternate fringes may be of somewhat different intensities, one
+corresponding to fringes of  $\lambda_1$, the other to those for $\lambda_2$. If you do not see this condition,
+try moving the mirror $P2$ across the range of micrometer screw. If you still cannot find them, you can also
+move the whole plate by loosening one plate and sliding it a little.
+\item  Practice going through the fringe conditions as shown in Fig.(\ref{fpfig4.fig})
+by turning the micrometer and viewing the fringes. Do not be surprised if you
+have to move the micrometer quite a bit to go back to the original condition.
+\item Find a place on the micrometer ($d_1$) where you
+have the ``START'' condition for fringes shown in Fig.(\ref{fpfig4.fig}). Now
+advance the micrometer rapidly while viewing the fringe pattern ( NO COUNTING
+OF FRINGES IS REQUIRED ).  Note how the fringes of one intensity are moving to
+overtake those of the other intensity (in the manner of
+Fig.(\ref{fpfig4.fig})).  Keep turning until the ``STOP'' pattern is achieved
+(the same condition you started with).  Record the micrometer reading as $d_2$.
+\emph{Remember that 1 tick mark is 1 micrometer ($10^{-6}m$). That means if you
+read 1.24, your really move 124 $\mu m$.}
+\end{enumerate}
+
+\noindent \fbox{\parbox{\linewidth}{\textbf{Experimental tip:} You may have to
+``home in'' on the best START and STOP conditions. Let's say that the even
+fringe spacing for the START condition ($d_1$) is not exactly in view. Now move
+the micrometer, looking to see if the pattern moves toward even spacing. If so,
+stop and read the micrometer for $d_1$. Move a bit more. If this second fringe
+spacing looks better than the first, then accept this for $d_1$. The same
+``homing in'' procedure should be used to select the reading for $d_2$. In
+other words as you approach the even spacing condition of the STOP pattern,
+start writing down the micrometer positions. Eventually you will favor one
+reading over all the others.}}
+
+\section*{Analysis}
+
+    Since the condition we are seeking above for ``START'' places
+    the bright fringes of   $\lambda_1$ at the point of destructive
+    interference for  $\lambda_2$, we can express this for the bull's eye
+    center ($\theta= 0 $) as:
+\begin{equation}
+2d_1=m_1\lambda_1=\left(m_1+n+\frac{1}{2}\right)\lambda_2
+\end{equation}
+
+  Here the integer n accounts for the
+    fact that   $\lambda_1 >  \lambda_2$ ,  and the  $1/2$  for the
+condition of
+    destructive interference for   $\lambda_2$  at the center. Since the
+    net action of advancing by many fringes has been to increment
+    the fringe count of   $\lambda_2$ by one more than that of
+$\lambda_1$  ,
+    then we express the ``STOP'' condition as:
+\begin{equation}
+2d_2=m_2\lambda_1=\left(m_2+n+\frac{3}{2}\right)\lambda_2
+\end{equation}
+   Subtracting the
+    two interference equations gives us:
+\begin{equation}
+2(d_2-d_1)=(m_2-m_1)\lambda_1=(m_2-m_1)\lambda_2+\lambda_2
+\end{equation}
+ Eliminating  $(m_2-m_1)$
+    in this equation we obtain:
+
+\begin{equation}
+2(d_2-d_1)=\frac{\lambda_1\lambda_2}{(\lambda_1-\lambda_2)}
+\end{equation}
+
+ Solving this for $\Delta \lambda = \lambda_1-\lambda_2$, and
+    accepting as valid the approximation that  $\lambda_1\lambda_2\approx
+\lambda^2$   ( where $\lambda$ is the
+    average of $\lambda_1$  and $\lambda_2 \approx 589.26 nm$ ), we obtain:
+\begin{equation}
+\boxed{\Delta\lambda=\frac{\lambda^2}{2(d_2-d_1)}}
+\end{equation}
+
+Each lab partner should independently align the interferometer and make at least \textit{two} measurements of
+``START'' and ``STOP'' positions. A sample table to record the data is shown below. \\{\large
+\begin{tabular}{|p{27mm}|p{27mm}|p{27mm}|p{27mm}|}
+\hline
+ $d_1$ $\pm \dots$ & $d _2$ $\pm \dots$& $(d_1-d_2)$ $\pm \dots$&
+$\Delta \lambda(nm) $ $\pm \dots$\\
+\hline
+&&&\\
+\hline &&&\\ \hline &&&\\ \hline &&&\\ \hline &&&\\ \hline
+\end{tabular}
+}
+
+\vspace{1cm} 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.
+
+
+\begin{figure}[h]
+\centerline{\epsfig{width=0.8\linewidth,file=fpfig4.eps}} \caption{\label{fpfig4.fig}The Sequence of fringe
+patterns encountered in the course of the FSS measurements. Note false colors: in your experiment the background
+is black, and both sets of rings are bright yellow.}
+\end{figure}
+
+\end{document}
+
+\newpage
+\noindent
+Physics 251 Section:\\
+\hskip 4.5in Name:\\
+\hskip 4.5in Partners:\\
+\vskip 0.5in
+\subsection*{The Fabry-Perot Interferometer}
+1. Briefly describe how the Fabry-Perot interferometer gives and interference
+pattern (in one or two sentences):\\
+\vskip 1.2in
+2. How does the interferometer's resolving power of the fringes depend on the
+reflectivity of plates, r ? That is, does the sharpness of the fringes increase
+or decrease with r ? Consult Melissinos or Professor Kane's Mathview program.
+(The reflectivity of the plates defines the {\it finess} of the cavity).\\
+\vskip 1in.
+
+
+{\large
+\noindent
+Fill in:
+
+The sodium doublet lines arise because an atomic$\underline{\hskip 1.in}$
+is split into two by$\underline{\hskip 1.in}$ coupling.
+The electron has
+intrinsic $\underline{\hskip 1.in}$, like a top, with values of
+$\underline{\hskip 1.in}$ or$\underline{\hskip 1.in}$. Because of
+this, the electron has in intrinsic magnetic$\underline{\hskip 1.in}$  and
+has magnetic
+energy in a magnetic field given by E=$\underline{\hskip 1.in}$
+case comes from the electron's $\underline{\hskip 1.in}$ motion.
+
+}
+
+\subsection*{DATA:}
+{\large
+\begin{tabular}{|p{27mm}|p{27mm}|p{27mm}|p{27mm}|}
+\hline
+ $d_1$ $\pm \dots$ & $D _2$ $\pm \dots$& $(d_1-d_2)$ $\pm \dots$&
+$\Delta \lambda(nm) $ $\pm \dots$\\
+\hline
+&&&\\
+\hline
+&&&\\ \hline
+&&&\\ \hline
+&&&\\ \hline
+&&&\\ \hline
+\end{tabular}
+}
+\vskip .2in
+$\Delta \lambda=$\hskip 1.5in nm\\
+\vskip .2in
+Standard deviation= \hskip 1.5in nm
+\newpage
+\end{document}
diff --git a/unused_chapters/hspect.tex b/unused_chapters/hspect.tex
new file mode 100644
index 0000000..565c64f
--- /dev/null
+++ b/unused_chapters/hspect.tex
@@ -0,0 +1,436 @@
+%\chapter*{Atomic Spectroscopy of the Hydrogen Atom}
+%\addcontentsline{toc}{chapter}{Hydrogen Spectrum}
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+    \oddsidemargin  0.0in
+    \evensidemargin 0.0in
+    \textwidth      6.5in
+    \headheight     0.0in
+    \topmargin      0.0in
+    \textheight=9.0in
+
+\begin{document}
+\title{Atomic Spectroscopy of Hydrogen Atoms}
+\date {}
+\maketitle \noindent
+ \textbf{Experiment objectives}: test and calibrate a diffraction grating-based spectrometer
+ and measure the energy spectrum of atomic hydrogen.
+
+\subsection*{History}
+
+    The observation of discrete lines in the emission spectra of
+    atomic gases gives insight into the quantum nature of
+    atoms. Classical electrodynamics cannot explain the existence
+    of these discrete lines, whose energy (or wavelengths) are
+    given by characteristic values for specific atoms. These
+    emission lines are so fundamental that they are used to
+    identify atomic elements in objects, such as in identifying
+    the constituents of stars in our universe. When Niels Bohr
+    postulated that electrons can exist only in orbits of discrete
+    energies, the explanation for the discrete atomic lines became
+    clear.  In this laboratory you will measure the wavelengths of
+    the discrete emission lines from hydrogen gas, which will give
+    you a measurement of the energy levels in the hydrogen atom.
+
+\section*{Theory}
+
+    The hydrogen atom is composed of a proton nucleus and a single
+electron in a bound state orbit. Bohr's groundbreaking hypothesis, that the
+electron's orbital angular momentum is quantized, leads directly to the
+quantization of the atom's energy, i.e., that electrons in atomic systems exist
+only in discrete energy levels.  The energies specified for a Bohr atom of
+atomic number $Z$ in which the nucleus is fixed at the origin (let the nuclear
+mass $\rightarrow \infty$) are given by the expression:
+\begin{equation}\label{Hlevels_inf}
+E_n=- \frac{2\pi^2m_ee^4Z^2}{(4\pi\epsilon_0)^2h^2n^2}
+ = -hcZ^2R_{\infty}\frac{1}{n^2}
+\end{equation}
+%
+where  $n$  is the  label for  the {\bf principal quantum number}
+ and $R_{\infty}=\frac{2\pi m_ee^4}{(4\pi\epsilon_0)^2ch^3}$   is called the
+{\bf Rydberg wave number} (here $m_e$ is the electron mass).  Numerically,
+$R_{\infty}
+= 1.0974 \times  10^5 cm^{-1}$ and $hcR_{\infty} = 13.605 eV$.
+
+An electron can change its state only by making a transition ("jump") from an
+``initial'' excited state of energy  $E_1$ to a ``final'' state of lower energy
+$E_2$ by emitting a photon of energy  $h\nu  = E_1 - E_2$ that carries away the
+excess energy.  Thus frequencies of spectral emission lines are proportional to
+the difference between two allowed discrete energies for an atomic
+configuration. Since  $h\nu = hc/\lambda$, we can write for this case:
+\begin{equation} \label{Hlines_inf}
+\frac{1}{\lambda}=\frac{2\pi^2m_ee^4Z^2}{(4\pi\epsilon_0)^2ch^3}
+\left[\frac{1}{n_2^2}-\frac{1}{n_1^2}\right]=
+R_{\infty}Z^2\left[\frac{1}{n_2^2}-\frac{1}{n_1^2}\right]
+\end{equation}
+Based on this description it is clear that by measuring the frequencies (or
+wavelengths) of photons emitted by an excited atomic system, we can glean
+important information about allowed electron energies in atoms.
+
+To make more accurate calculation of the Hydrogen spectrum, we need to take
+into account that a hydrogen nucleus has a large, but finite mass, M=AMp (mass
+number A=1 and Mp = mass of proton)\footnote{This might give you the notion
+that the mass of any nucleus of mass number $A$ is equal to $AM_p$. This is not
+very accurate, but it is a good first order approximation.} such that the
+electron and the nucleus orbit a common center of mass.  For this two-mass
+system the reduced mass is given by $\mu=m_e/(1+m_e/AM_p)$. We can take this
+into account by modifying the above expression (\ref{Hlines_inf}) for
+1/$\lambda$ as follows:
+\begin{equation}\label{Hlines_arb}
+\frac{1}{\lambda_A}=R_AZ^2\left[\frac{1}{n_2^2}-\frac{1}{n_1^2}\right] \mbox{
+where } R_A=\frac{R_{\infty}}{1+\frac{m_e}{AM_p}}
+\end{equation}
+In particular, for the hydrogen case of  ($Z=1$; $M=M_p$) we have:
+\begin{equation}\label{Hlines_H}
+\frac{1}{\lambda_H}=R_H\left[\frac{1}{n_2^2}-\frac{1}{n_1^2}\right]
+\end{equation}
+Notice that the value of the Rydberg constant will change slightly for
+different elements. However, these corrections are small since nucleus is
+typically several orders of magnitude heavier then the electron.
+
+
+    Fig. \ref{spec} shows a large number of observed transitions between
+    Bohr energy levels in hydrogen, which  are grouped into series.  Emitted photon
+    frequencies (wavelengths) span the spectrum from the UV
+    (UltraViolet) to the IR (InfraRed).  Given our lack of UV or
+    IR spectrometers, we will focus upon the optical spectral lines
+    that are confined to the Balmer series (visible).  These are
+    characterized by a common final state of $n_2$ = 2.  The
+    probability that an electron will make a particular
+$n_1\rightarrow  n_2$
+    transition in the Balmer series can differ considerably,
+    depending on the likelihood that the initial $n_1$ level is
+    populated from above in the deexcitation process.  This
+    results in our being able to observe and measure only the following four
+    lines: $6 \rightarrow  2$, $5 \rightarrow  2$, $4 \rightarrow 2$,
+ and $3 \rightarrow 2$.
+
+
+\begin{figure}
+\includegraphics[width=0.7\linewidth]{spec.eps}
+\caption{\label{spec}Spectrum of Hydrogen. The numbers on the left show the
+energies of the hydrogen levels with different principle quantum numbers $n$ in
+$eV$. The wavelength of emitted photon in ${\AA}$ are shown next to each
+electron transition. }
+\end{figure}
+
+In this lab, the light from the hydrogen gas is broken up into its spectral
+components by a diffraction grating.  You will measure the angle at which each
+line occurs on the left ($\theta_L$) and ($\theta_R$) right sides for as many
+diffraction orders $m$ as possible, and use Eq.(\ref{mlambda}) to calculate
+$\lambda$, using the following expression, derived in the Appendix.
+\begin{equation}\label{mlambda}
+m\lambda = \frac{h}{2}\left(\sin\theta_L+\sin\theta_R\right)
+\end{equation}
+ Then the same
+expression will be used to check/calibrate the groove spacing $h$ by making
+similar measurements for a sodium spectral lines with known wavelengths.
+
+We will approach the data in this experiment both with an eye to confirming
+    Bohr's theory and from Balmer's early perspective of someone
+    trying to establish an integer power series linking the
+    wavelength of these four lines.
+
+\section*{Spectrometer Alignment Procedure}
+
+Fig. \ref{expspec} gives a top view of the Gaertner-Peck optical spectrometer
+used in this lab.
+\begin{figure}
+\includegraphics[height=4in]{expspec.eps}
+\caption{\label{expspec}Gaertner-Peck Spectrometer}
+\end{figure}
+
+\subsubsection*{Telescope Conditions:} Start by adjusting the
+telescope eyepiece in
+    or out to bring the crosshairs into sharp focus.  Next aim the
+    telescope out the window to view a distant object such as
+    leaves in a tree.  If the distant object is not in focus or if
+    there is parallax motion between the crosshairs and the
+    object, pop off the side snap-in button to give access to a
+    set screw.  Loosen this screw and move the ocular tube in or
+    out to bring the distant object into sharp focus.  This should
+    result in the elimination of parallax.  Tighten the set screw
+    to lock in this focussed condition.
+
+\subsubsection*{Collimator Conditions:} Swing the telescope to view the collimator
+    which is accepting light from the hydrogen discharge tube
+    through a vertical slit of variable width.  The slit opening
+    should be set to about 5-10 times the crosshair width to
+    permit sufficient light to see the faint violet line and to be
+    able to see the crosshairs.  If the bright column of light is
+    not in sharp focus, you should remove a side snap-in button
+    allowing the tube holding the slit to move relative to the
+    collimator objective lens.  Adjust this tube for sharp focus
+    and for elimination of parallax between the slit column and
+    the crosshairs.  Finally, tighten the set screw.
+
+\subsubsection*{  Diffraction Grating Conditions:}
+\textbf{Appendix in this handout describes the operation of a diffraction
+grating!}
+    Mount a diffraction grating which nominally
+    has 600 lines per mm in a grating baseclamp.
+    %Put a piece of
+   % doublesided scotch tape on the top surface of the table plate.
+    Fix the grating baseclamp to the table such that the grating's
+    vertical axis will be aligned with the telescope pivot axis.
+    Since the table plate can be rotated, orient the normal of the
+    grating surface to be aligned with the collimator axis.  Use
+    the AUTOCOLLIMATION procedure  to achieve a fairly accurate
+    alignment of the grating surface.  This will determine how to
+    adjust the three leveling screws H1, H2, and H3 and the
+    rotation angle set screw for the grating table.
+
+    \textbf{AUTOCOLLIMATION} is a sensitive way to align an optical
+    element.  First, mount a ``cross slit'' across the objective lens of
+    the collimator, and direct a strong light source into the
+    input end of the collimator.  Some of the light exiting through
+    the cross slit will reflect from the grating and return to the
+    cross slit.  The grating can then be manipulated till this
+    reflected light retraces its path through the cross slit
+    opening.  With this the grating surface is normal to the
+    collimator light.
+     Then, with the hydrogen tube ON and in place at
+    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
+    lines seem to climb uphill or drop downhill
+    the grating will have to be rotated in its baseclamp to
+    bring them all to the same elevation.
+
+\section*{Data acquisition and analysis}
+
+Swing the rotating telescope slowly and determine which spectral lines from
+Balmer series you observe.
+
+\emph{Lines to be measured:}
+\begin{itemize}
+\item \emph{Zero order} (m=0): All spectral lines merge.
+\item \emph{First order} (m=1): Violet, Blue, Green, \& Red on both Left \&
+    Right sides.
+\item \emph{Second order} (m=2): Violet, Blue, Green, \& Red on
+    both Left \& Right sides.
+\item \emph{Third order} (m=3):  Blue, \& Green.
+\end{itemize}
+    You might not see the Violet line due to its low
+    intensity. Red will not be seen in 3rd  order.
+
+Read the angle at which each line occurs, measured with the crosshairs centered
+on the line as accurately as possible. Each lab partner should record the
+positions of the spectral lines at least once. Use the bottom scale to get the
+rough angle reading in degrees, and then use the upper scale for more accurate
+reading in minutes. The width of lines is controlled by the Collimator Slit
+adjustment screw. If set too wide open, then it is hard to judge the center
+    accurately; if too narrow, then not enough light is available
+    to see the crosshairs. For Violet the intensity is noticeably
+    less than for the other three lines.  Therefore a little
+    assistance is required in order to locate the crosshairs at
+    this line.  We suggest that a low intensity flashlight be
+    aimed toward the Telescope input, and switched ON and OFF
+    repeatedly to reveal the location of the vertical crosshair
+    relative to the faint Violet line.
+
+\subsubsection*{ Calibration of Diffraction Grating:} Replace the hydrogen tube with
+    a sodium (Na) lamp and take readings for the following two
+    lines from sodium: $568.27$~nm (green) and $589.90$~nm (yellow).  Extract from
+    these readings the best average value for $h$ the groove
+    spacing in the diffraction grating.  Compare to the statement
+    that the grating has 600 lines per mm.  Try using your measured value
+    for $h$ versus the stated value $600$ lines per mm in
+    the diffraction formula when obtaining the measured
+    wavelengths of hydrogen. Determine which one provide more accurate results, and discuss the conclusion.
+
+\subsubsection*{ Data analysis}
+\textbf{Numerical approach}: Calculate the wavelength $\lambda$ for each line
+observed. For lines observed in more than one order, obtain the mean value
+$\lambda_ave$ and the standard error of the mean $\Delta \lambda$. Compare to
+the accepted values which you should calculate using the Bohr theory.
+
+\textbf{Graphical approach}: Make a plot of $1/\lambda$  vs  $1/n_1^2$  where
+$n_1$ = the principal quantum number of the electron's initial state.  Put all
+$\lambda$ values you measure above on this plot.  Should this data form a
+straight line? If so, determine both slope and intercept and compare to the
+expected values for each.  The slope should be the Ryberg constant for
+hydrogen, $R_H$. The intercept is $R_H/(n_2)^2$. From this, determine the value
+for the principal quantum number $n_2$. Compare to the accepted value in the
+Balmer series.
+
+\textbf{Example data table for writing the results of the measurements}:
+
+\noindent
+\begin{tabular}{|p{1.in}|p{1.in}|p{1.in}|p{1.in}|}
+\hline
+ Line &$\theta_L$&$\theta_R$&Calculated $\lambda$  \\ \hline
+ m=1 Violet&&&\\ \hline
+ m=1 Blue&&&\\ \hline
+ m=1 Green&&&\\ \hline
+ m=1 Red&&&\\ \hline
+ m=2 Violet&&&\\ \hline
+ \dots&&&\\ \hline
+ m=3 Blue&&&\\ \hline
+ \dots&&&\\\hline
+\end{tabular}
+
+\section*{Appendix: Operation of a diffraction grating-based optical spectrometer}
+
+%\subsection*{Fraunhofer Diffraction at a Single Slit}
+%Let's consider a plane electromagnetic wave incident on a vertical slit of
+%width $D$ as shown in Fig. \ref{frn}. \emph{Fraunhofer} diffraction is
+%calculated in the far-field limit, i.e. the screen is assume to be far away
+%from the slit; in this case the light beams passed through different parts of
+%the slit are nearly parallel, and one needs  a lens to bring them together and
+%see interference.
+%\begin{figure}[h]
+%\includegraphics[width=0.7\linewidth]{frnhfr.eps}
+%\caption{\label{frn}Single Slit Fraunhofer Diffraction}
+%\end{figure}
+%To calculate the total intensity on the screen we need to sum the contributions
+%from different parts of the slit, taking into account phase difference acquired
+%by light waves that traveled different distance to the lens. If this phase
+%difference is large enough we will see an interference pattern. Let's break the
+%total hight of the slit by very large number of point-like radiators with
+%length $dx$, and we denote $x$ the hight of each radiator above the center of
+%the slit (see Fig.~\ref{frn}). If we assume that the original incident wave is
+%the real part of $E(z,t)=E_0e^{ikz-i2\pi\nu t}$, where $k=2\pi/\lambda$ is the
+%wave number. Then the amplitude of each point radiator on a slit is
+%$dE(z,t)=E_0e^{ikz-i2\pi\nu t}dx$. If the beam originates at a hight $x$ above
+%the center of the slit then the beam must travel an extra distance $x\sin
+%\theta$ to reach the plane of the lens. Then we may write a contributions at
+%$P$ from a point radiator $dx$ as the real part of:
+%\begin{equation}
+%dE_P(z,t,x)=E_0e^{ikz-i2\pi\nu t}e^{ikx\sin\theta}dx.
+%\end{equation}
+%To find the overall amplitude one sums along the slit we need to add up the
+%contributions from all point sources:
+%\begin{equation}
+%E_P=\int_{-D/2}^{D/2}dE(z,t)=E_0e^{ikz-i2\pi\nu
+%t}\int_{-D/2}^{D/2}e^{ikx\sin\theta}dx = A_P e^{ikz-i2\pi\nu t}.
+%\end{equation}
+%Here $A_P$ is the overall amplitude of the electromagnetic field at the point
+%$P$. After evaluating the integral we find that
+%\begin{equation}
+%A_P=\frac{1}{ik\sin\theta}\cdot
+%\left(e^{ik\frac{D}{2}\sin\theta}-e^{-ik\frac{D}{2}\sin\theta}\right)
+%\end{equation}
+%After taking real part and choosing appropriate overall constant multiplying
+%factors the amplitude of the electromagnetic field at the point $P$ is:
+%\begin{equation}
+%A=\frac{\sin (\frac{\pi D}{\lambda}\sin\theta)}{\frac{\pi
+%D}{\lambda}\sin\theta}
+%\end{equation}
+%The intensity is proportional to the square of the amplitude and thus
+%\begin{equation}
+%I_P=\frac{(\sin (\frac{\pi D}{\lambda}\sin\theta))^2}{(\frac{\pi
+%D}{\lambda}\sin\theta)^2}
+%\end{equation}
+%The minima of the intensity occur at the zeros of the argument of the sin. The
+%maxima are near, but not exactly equal to the solution of:
+%\begin{equation}
+%  (\frac{\pi D}{\lambda}\sin\theta)=(m+\frac{1}{2})\pi \end{equation}
+%for integer $m$.
+%
+%The overall pattern looks like that shown in Fig. \ref{sinxox}.
+%\begin{figure}
+%\includegraphics[width=\linewidth]{sinxox.eps}
+%\caption{\label{sinxox}Intensity Pattern for Fraunhofer Diffraction}
+%\end{figure}
+
+%\subsection*{The Diffraction Grating}
+A diffraction grating is a common optical element, which consists of a pattern
+with many equidistant slits or grooves. Interference of multiple beams passing
+through the slits (or reflecting off the grooves) produces sharp intensity
+maxima in the output intensity distribution, which can be used to separate
+different spectral components on the incoming light. In this sense the name
+``diffraction grating'' is somewhat misleading, since we are used to talk about
+diffraction with regard to the modification of light intensity distribution  to
+finite size of a single aperture.
+\begin{figure}[h]
+\includegraphics[width=\linewidth]{grating.eps}
+\caption{\label{grating}Intensity Pattern for Fraunhofer Diffraction}
+\end{figure}
+
+To describe the properties of a light wave after passing through the grating,
+let us first consider the case of 2 identical slits separated by the distance
+$h$, as shown in Fig.~\ref{grating}a. We will assume that the size of the slits
+is much smaller than the distance between them, so that the effect of
+Fraunhofer diffraction on each individual slit is negligible. Then the
+resulting intensity distribution on the screen is given my familiar Young
+formula:
+\begin{equation} \label{2slit_noDif}
+I(\theta)=\left|E_0 +E_0e^{ikh\sin\theta} \right|^2 = 4I_0\cos^2\left(\frac{\pi
+h}{\lambda}\sin\theta \right),
+\end{equation}
+where $k=2\pi/\lambda$, $I_0$ = $|E_0|^2$, and the angle $\theta$ is measured
+with respect to the normal to the plane containing the slits.
+%If we now include the Fraunhofer diffraction on each slit
+%same way as we did it in the previous section, Eq.(\ref{2slit_noDif}) becomes:
+%\begin{equation} \label{2slit_wDif}
+%I(\theta)=4I_0\cos^2\left(\frac{\pi h}{\lambda}\sin\theta
+%\right)\left[\frac{\sin (\frac{\pi D}{\lambda}\sin\theta)}{\frac{\pi
+%D}{\lambda}\sin\theta} \right]^2.
+%\end{equation}
+
+An interference on $N$ equidistant slits illuminated by a plane wave
+(Fig.~\ref{grating}b) produces much sharper maxima. To find light intensity on
+a screen, the contributions from all N slits must be summarized taking into
+account their acquired phase difference, so that the optical field intensity
+distribution becomes:
+\begin{equation} \label{Nslit_wDif}
+I(\theta)=\left|E_0
++E_0e^{ikh\sin\theta}+E_0e^{2ikh\sin\theta}+\dots+E_0e^{(N-1)ikh\sin\theta}
+\right|^2 = I_0\left[\frac{sin\left(N\frac{\pi
+h}{\lambda}\sin\theta\right)}{sin\left(\frac{\pi h}{\lambda}\sin\theta\right)}
+\right]^2.
+\end{equation}
+ Here we again neglect the diffraction form each individual slit, assuming that the
+ size of the slit is much smaller than the separation $h$ between the slits.
+
+The intensity distributions from a diffraction grating with illuminated
+ $N=2,5$ and $10$ slits are shown in Fig.~\ref{grating}c. The tallest (\emph{principle}) maxima occur when the denominator
+ of Eq.(~\ref{Nslit_wDif}) becomes zero: $h\sin\theta=\pm m\lambda$ where
+ $m=1,2,3,\dots$ is the diffraction order. The heights of the principle maxima are
+ $I_{\mathrm{max}}=N^2I_0$, and their widths are $\Delta \theta =
+ 2\lambda/(Nh)$.
+ Notice that the more slits are illuminated, the narrower diffraction peaks
+ are, and the better the resolution of the system is:
+ \begin{equation}
+\frac{ \Delta\lambda}{\lambda}=\frac{\Delta\theta}{\theta} \simeq \frac{1}{Nm}
+\end{equation}
+For that reason in any spectroscopic equipment a light beam is usually expanded
+to cover the maximum surface of a diffraction grating.
+
+\subsection*{Diffraction Grating Equation when the Incident Rays are
+not Normal}
+
+Up to now we assumed that the incident optical wavefront is normal to the pane
+of a grating. Let's now consider more general case when the angle of incidence
+$\theta_i$ of the incoming wave is different from the normal to the grating, as
+shown in Fig. \ref{DGnotnormal}a. Rather then calculating the whole intensity
+distribution, we will determine the positions of principle maxima. The path
+length difference between two rays 1 and 2 passing through the consequential
+slits us  $a+b$, where:
+\begin{equation}
+a=h\sin \theta_i;\,\, b=h\sin \theta_R
+\end{equation}
+Constructive interference occurs for order $m$ when $a+b=m\lambda$, or:
+\begin{equation}
+h\sin \theta_i + \sin\theta_R=m\lambda
+\end{equation}
+\begin{figure}[h]
+\includegraphics[width=\columnwidth]{pic4i.eps}
+%\includegraphics[height=3in]{dn.eps}
+\caption{\label{DGnotnormal}Diagram of the light beams diffracted to the Right
+(a) and to the Left (b).}
+\end{figure}
+Now consider the case shown in Fig. \ref{DGnotnormal}. The path length between
+two beams is now $b-a$ where $b=h\sin\theta_L$. Combining both cases we have:
+\begin{eqnarray} \label{angles}
+h\sin\theta_L-\sin\theta_i&=&m\lambda\\
+h\sin\theta_R+\sin\theta_i&=&m\lambda \nonumber
+\end{eqnarray}
+Adding these equations and dividing the result by 2 yields Eq.(\ref{mlambda}):
+\begin{equation}m\lambda=\frac{h}{2}\left(\sin\theta_L+\sin\theta_R\right)
+\end{equation}
+
+\end{document}
+\newpage
diff --git a/unused_chapters/intro.tex b/unused_chapters/intro.tex
new file mode 100644
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--- /dev/null
+++ b/unused_chapters/intro.tex
@@ -0,0 +1,145 @@
+\chapter*{Introduction}
+\addcontentsline{toc}{chapter}{Introduction}
+	Welcome to Experimental Atomic Physics Laboratory! What is
+	this class all about?  In this class you will learn more
+	details about how experimental physics is done. The
+	experiments you do here will help you further learn the
+	concepts you are being introduced to in Physics 201, Modern
+	Physics. You will learn by doing. You will learn about the
+	scientific process and be introduced to what it takes to be a
+	physicist. Hopefully, you will have fun too! You will be doing
+.	some experiments which are very fundamental, some of which
+	have won the Nobel Prize!
+
+The goals of this class are to:
+
+\begin{enumerate}
+\item  Gain understanding of physical principles.
+\item  Become familiar with the setup of experimental equipment, how to
+ use equipment, and how to make measurements.
+\item  Learn how to analyze your data, determine the error in your data, 
+how to graph data and how to fit the data to a curve to extract parameters.
+\item Learn how to draw conclusions from your data.
+\item  Learn how to keep a scientific journal.
+\item Learn how to approach a problem
+\item Learn to communicate your findings to other people in a way which is 
+clear and concise. 
+\end{enumerate}
+
+Some or most of these principles you were introduced to in Physics
+Laboratory 101. How is this class different? The experiments you will
+do are taking you a step closer to the work that actual physicsist do
+in the laboratory. You will be repeating some very fundamental,
+complex experiments through which physical principles were discovered.
+You will be carrying out the steps required to do experimental
+physics: setup equipment, make measurements, record data, analyze
+data, draw conclusions and communicate your findings in a scientific
+report.  You may say, well, I am only going to be a theorist, or a
+banker, why should I care about experimental physics? Well, atleast
+you should learn about the scientific process so that when you hear
+about some major scientific discovery you can judge its merit. In this
+way you will learn what it takes to extract a physical principle from
+an experiment, so you understand how scientists make the connections
+that they do, and what the limitations are to scientific
+experimentation.
+
+This laboratory manual briefly summarizes the principles of general
+laboratory practice, treatment of error and curve fitting, how to
+write a laboratory report, and then each of the laboratories you will
+be conducting this semester. Please read the chapter on the experiment
+you will do before you do the actual experiment.
+
+
+\section*{General Laboratory Practices}
+
+\begin{enumerate}
+\item When conducting your experiments- be safe! You will be using
+   equipment which poses some hazards, such as lasers and high-voltage
+   power supplies. Listen to the safety instructions and heed
+   them. Also, if a piece of equipment isn’t working even after you
+   have followed all the instructions, be careful what you fiddle
+   with! Some fiddling is good, but if you are planning to do anything
+   major (like take a piece of equipment apart), it is best to ask an
+   instructor first. Also, it is generally good lab practice not to
+   eat or drink in the lab. It keeps crumbs and liquid out the
+   equipment, and prevents you from eating or drinking something you
+   didn’t intend to.
+
+ 
+\item Keep a good laboratory book and record your data and the steps you
+   take! It is recommended you buy a separate notebook to keep as a
+   laboratory journal. Don’t scribble inledigbly on pieces of scrap
+   paper you will only lose later. When conducting an experiment,
+   right down what you did, how you setup the equipment and if
+   anything unusual happened. Write down data in a neat and organized
+   way. The goal is to read and understand what you did after you
+   leave the laboratory. Don’t think this is trivial! Major scientific
+   discoveries were made because of some anomaly in data, which
+   scientists were able to exactly repeat because they had recorded
+   exactly what they did! If you are a research scientist in a
+   corporation and you make a discovery like this and couldn’t repeat
+   the conditions under which it was found- you would be in big
+   trouble!
+
+\item  Related to the last point: don’t leave this laboratory for the day
+without making sure you understand your data. You won’t be able to go
+back and redo the experiment- so it is best to check your data and
+make sure it is reasonable.  4. +Do not fudge data! If your data is
+off and you admit it and speculate why it is off, you will be given
+credit for this. Everyone has a bad day. Forging data not only breaks
+the Honor Code but is also a very, very bad habit which can have
+serious consequences in the future. Some sceintists have been tempted
+under pressure to do this. Those who did were usually found out and
+the ramifications are very serious. Not only does it hurt society, but
+the scientists found doing this ruined their careers. See the book, “”
+for further discussion of this problem.  
+
+\item  Treatment of errors/curve
+fitting
+
+\item  How to Write a Lab Report
+
+\framebox{You are not writing a laboratory report just for a grade! It is
+important that you learn how to communicate your findings. In reading
+your report, someone should be able to understand: your hypothesis or
+theory, 1) how you did the experiment, 2) what equipment you used 3)
+did anything unusual happen? conditions? data – in table and graph
+form, analysis you did, conclusions, If anything strange happened-
+mention it! If someone cannot tell what you did or gather useful
+information, your paper is worthless!}
+
+\begin{description}
+
+\item[TITLE OF EXPERIMENT]
+\item[LIST PARTNERS by name]
+
+\end{description}
+
+
+The components of your laboratory report shall include:
+
+\begin{description}
+\item[INTRODUCTION]:      Briefly state objective(s) of experiment 
+\item[THEORY]:    Introduce important equations or at least restate in 
+your own words;
+                Specify any "Working Eqs.", defining the variables involved.
+\item[PROCEDURES] :
+                Describe in terms of equipment and layout diagrams,
+                Describe important steps in producing data,
+                Describe variables to be measured.
+\item[DATA / ANALYSIS TABLES]:
+                Present data in spreadsheet form (rows \& columns which are 
+clearly defined). 
+                Analyzed results can be listed in the same spreadsheet.
+\item[DATA ANALYSIS]: Carry out explicit "sample calculations" to show how 
+results are produced
+Results  can appear in DATA / ANALYSIS TABLES
+\item[CONCLUSIONS]: Conclusions should be developed; attempt to put them in 
+quantitative terms
+
+\end{description}
+\end{enumerate}
+
+\fbox{this is some text.}
+\newpage
+
diff --git a/unused_chapters/michelson.tex b/unused_chapters/michelson.tex
new file mode 100644
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+++ b/unused_chapters/michelson.tex
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+%\chapter*{Michelson Interferometer}
+%\addcontentsline{toc}{chapter}{Michelson Interferometer}
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+    \oddsidemargin  0.0in
+    \evensidemargin 0.0in
+    \textwidth      6.5in
+    \headheight     0.0in
+    \topmargin      0.0in
+    \textheight=9.0in
+
+\begin{document}
+\title{Michelson Interferometer}
+\date {}
+\maketitle
+
+\noindent
+ \textbf{Experiment objectives}: Assemble and align a Michelson
+interferometer, and use it to measure wavelength of unknown laser, and the
+refractive index of air.
+
+\section*{History}
+
+Michelson interferometer is an extremely important apparatus. It was 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  fictious medium for light wave propagation) and providing the insight into
+the true nature of electromagnetic radiation. Nowedays, Michelson interferometer remains a widely used tool in
+many areas of physics and engineering. In this laboratory you will use the interferometer to accurately measure
+the wavelength of laser light and the index of refraction of air.
+\begin{figure}[h]
+\centerline{\epsfig{width=0.8\linewidth,file=fig1.eps}} \caption{\label{fig1mich.fig}A Michelson Interferometer
+setup.}
+\end{figure}
+
+\section*{Theory}
+
+    The interferometer works by combining two light waves
+    traversing two path lengths. A diagram of this type of
+    interferometer is shown in Figure!\ref{fig1mich.fig}
+ 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 (reflected by the
+    beamsplitter) travels at 90 degrees toward mirror $M_2$ and back
+    again, passing twice through a clear glass plate called the
+    compensator plate.  At the beamsplitter one-half of
+    this light is transmitted to an observer (you will use a
+    viewing screen). At the same time the other beam (that was initially transmitted by the beamsplitter)
+    travels to
+    a fixed mirror $M_1$ and back again. One-half of this amplitude
+    is reflected from the partially-silvered surface and directed
+    at 90 degrees toward the observer.  Thus, the total amplitude of the light the observer
+    records 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}
+
+Here $k\Delta l$ is a phase shift (``optical delay'') between the two wavefronts caused by the difference in
+pathlengths  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 pathlength of the light beams in both interferometer arms will be exactly the same. Therefore,
+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}
+% or
+%\begin{displaymath}\mathbf{E}_1(t) = -\mathbf{E}_2(t).
+\end{displaymath}
+It is easy to see that constructive interference happens when the difference between pathlengths in two
+interferometer arms is equal to the integer number of wavelengths $\Delta l = m\lambda$, and destructive
+interference corresponds to the 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.
+
+
+
+
+%Figure 1. The Michelson Interferometer
+
+To simplify the alignment of a Michelson interferometer, it is convenient to work with diverging optical beams.
+In this case an interference pattern will look like a set of concentric bright and dark circles, since the
+components of the diverging beam travel at slightly different angles, and therefore acquire different phase, as
+illustrated in Figure \ref{fig2mich.fig}. Suppose that the actual pathlength difference between two arms is $d$.
+Then the path length difference for two off-axis rays arriving at the observer is $\Delta l = a + b$ where $a =
+d/\cos \theta$ and  $b = a\cos 2\theta$:
+\begin{equation}
+\Delta l=\frac{d}{\cos \theta}+\frac{d}{\cos \theta}\cos 2\theta
+\end{equation}
+Recalling that  $\cos 2\theta = 2(\cos \theta)^2-1$, we obtain $ \Delta l=2d\cos\theta$. The two rays interfere
+constructively for any angle $\theta_c$ for which $ \Delta l=2d\cos\theta = m\lambda$ ($m$=integer); at the same
+time, two beams traveling at the angle $\theta_d$ interfere destructively when $ \Delta l=2d\cos\theta =
+(m+1/2)\lambda$ ($m$=integer). Because of the symmetry about the normal direction to the mirrors, this will mean
+that interference ( bright and dark fringes) appears in a circular shape. If fringes are not circular, it means
+simply that the mirrors are not parallel, and additional alignment of the interferometer is required.
+
+\begin{figure}
+\centerline{\epsfig{width=0.8\linewidth,file=fig2.eps}} \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.}
+\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 known distance, we can determine
+the wavelength of light in the media using the condition for constructive interference, $\Delta l = 2d\cos
+\theta = m\lambda$.
+
+For simplicity, we might concentrate on the center of the fringe bullseye 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}
+
+\section*{Procedure}
+
+\subsection*{Laser Safety}
+While this is a weak laser caution should still be used. \textbf{Never look directly at the laser beam!} Align
+the laser so that it is not at eye level.
+
+\subsection*{Set Up}
+\textbf{Equipment needed}: Pasco precision interferometry kit, a laser,
+adjustable-hight platform.
+
+Set up the interferometer as shown in Figure~\ref{fig1mich.fig} using the components of Pasco precision
+interferometry  kit. A mirrors $M_{1,2}$ are correspondingly a movable and an adjustable mirror from the kit.
+Make initial alignment of the interferometer with a non-diverging laser beam. Adjust the beams so that it is
+impinging on the beamsplitter and on the viewing screen. Make sure the beam is hitting 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.
+
+Then insert a convex lens after the laser to spread out the beam (ideally the laser beam should be pass through
+the center of the lens to preserve alignment). After the beams traverse through the system, the image of the
+interfering rays will be a circular pattern projected onto a screen. The two beam reflected off the mirrors
+should be aligned as parallel as possible to give you a circular pattern.
+
+\subsection*{ Measurement of laser wavelength}
+
+Note the reading on the micrometer. Focus on a particular fringe (the center is a good place). Begin turning the
+micrometer so that the fringes move (for example, from bright to dark to bright again is the movement of 1
+fringe). Count a total of about 100 fringes and record the new reading on the micrometer. Calculate the
+wavelength from Eq. \ref{old3} above, remembering that you may need to convert the distance traveled on the
+micrometer to the actual distance traveled by the mirror.
+
+
+    Each lab group must make at least four (4) measurements of  $\lambda$. Each
+    partner must do at least one. For each trial, a minimum of 100
+    fringes should be accurately counted, and related to an
+    initial $X_1$ and final $X_2$ micrometer setting.  A final mean
+    value of $\lambda$ and its uncertainty  should be
+    generated. Compare your value with the accepted value (given
+    by the instructor).
+
+\textbf{\emph{Experimental tips}}:
+\begin{enumerate}
+\item Avoid touching the face of the front-surface mirrors, the beamsplitter, and any other optical elements!
+\item Engage the micrometer with both hands as you turn, maintaining
+positive torque.
+\item The person turning the micrometer should also do the counting of
+fringes. It can be easier to count them in bunches of 5 or 10 (\textit{i.e.}
+100 fringes = 10 bunches of 10 fringes).
+\item  Before the initial position $X_1$ is read make sure that the micrometer has engaged the
+drive screw (There can be a problem with "backlash").
+\item  Before starting the measurements make sure you understand how to read a
+micrometer! See Fig.\ref{fig3mich.fig}.
+\item Move the travel plate to a slightly different location for the
+four readings.  This can done by loosening the large nut atop the traveling
+plate,and then locking again.
+\item  Avoid hitting the table which can cause a sudden jump in the
+number of fringes.
+
+\end{enumerate}
+
+\begin{figure}[h]
+\centerline{\epsfig{width=0.7\columnwidth,file=fig3.eps}} \caption{\label{fig3mich.fig}Micrometer readings. The
+course scale is in mm, and smallest division on the rotary dial is 1~$\mu$m (same as 1 micron). The final
+measurements is the sum of two. }
+\end{figure}
+
+
+\subsection*{Measurement of the index of refraction of air}
+
+     If you recall from the speed of light experiment, the value
+for air's index of refraction  $n_{air}$  is very close to unity:
+$n_{air}$=1.000293.  Amazingly, a Michelson interferometer is precise enough to
+be able to make an accurate measurement of this quantity!
+
+Let's remind ourselves that a Michelson interferometer is sensitive to a phase
+difference acquired by the beams travelling in two arms
+\begin{equation}\label{phase}
+k\Delta l=2\pi n\Delta l/\lambda.
+\end{equation}
+In previous calculations we assumed that the index of refraction of air $n$ is exactly one, like in vacuum.
+However, it is actually slightly varies with air pressure, as shown in Fig.~\ref{fig4mich.fig}. Any changes in
+air pressure affect the phase $k\Delta l$.
+%
+\begin{figure}
+\centerline{\epsfig{file=macfig1add.eps}} \caption{\label{fig4mich.fig}Index of refraction as a function of air
+gas pressure}
+\end{figure}
+
+To do the measurement, place a cylindrical gas cell which can be evacuated in
+the path of light heading to mirror $M_1$ and correct alignment of the
+Michelson interferometer, if necessary. Make sure that the gas cell is
+initially at the atmospheric pressure.
+
+Now pump out the cell  by using a hand pump at your station and count the number of fringe transitions $\delta
+m$ that occur. When you are done, record $\delta m$ and the final reading of the vacuum gauge $p_{fin}$.
+\textbf{Note}: most vacuum gauges display the difference between  measured and atmospheric pressure . If
+absolute pressure is needed, it should be found by subtracting the gauge reading from the atmospheric pressure
+($p_0=76$~cm Hg). For example, if the gauge reads $23$~cm Hg, the absolute pressure is $53$~cm Hg.
+Alternatively, you can pump out the air first, and then admit air is slowly to the cell while counting the
+number of fringes that move past a selected fixed point.
+
+The shifting fringes indicate a change in relative optical phase difference for the two arms caused by the the
+difference in refractive indices of the gas cell at low and atmospheric pressures $\Delta n$. According to
+Eq.(\ref{phase}), this difference is
+\begin{equation} \label{delta_n}
+\Delta n=\delta m \frac{\lambda}{2d_{cell}}
+\end{equation}
+where $d_{cell}=3$~cm is the length of the gas cell.
+
+Since the change in the refractive index $\Delta n$ is linearly depends on the
+air pressure $\Delta p=p_0-p_{fin}$, it is now easy to find out the
+proportionality coefficient $\Delta n/\Delta p$ and calculate the value of the
+refractive index at the atmospheric pressure $n_{air}$.
+
+Each partner should make one measurement of the fringe shift quantity $\delta m$. Use Eq.(\ref{delta_n}) to find
+mean values of the relative change of the refractive index $\Delta n$,  proportionality coefficient $\Delta
+n/\Delta p$ and $n_{air}$ with corresponding uncertainties. Compare your measurements to the following
+accepted experimental values: \\
+Index of Refraction of Air(STP) = 1.000293 \\
+
+
+\subsection*{\emph{Detection of Gravitational Waves}}
+
+\textbf{\emph{A Michelson interferometer can help to test the theory of
+relativity!}} \emph{
+%
+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).}
+%
+\begin{figure}[h]
+\centerline{\epsfig{file=LIGO.eps}} \caption{\label{LIGO.fig}For more details see http://www.ligo.caltech.edu/}
+\end{figure}
+\emph{
+%
+Laser Interferometry Gravitational-wave Observatory (LIGO) sets the ambitious
+goal to direct detection of gravitational wave. The measuring tool in this
+project is a giant Michelson interferometer. 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
+is allowed to bounce between the mirrors repeatedly before it returns to the
+beam splitter. If the two arms have identical lengths, then interference
+between the light beams returning to the beam splitter will direct all of the
+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.}
+
+\emph{
+%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}
+ \centerline{\epsfig{file=LISA.eps}} \caption{\label{LISA.fig}For
+more details see http://lisa.nasa.gov/}
+\end{figure}
+
+\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)!
+%
+}
+
+\end{document}
+\newpage
diff --git a/unused_chapters/millikan.tex b/unused_chapters/millikan.tex
new file mode 100644
index 0000000..085c22f
--- /dev/null
+++ b/unused_chapters/millikan.tex
@@ -0,0 +1,254 @@
+%\chapter*{Millikan Oil Drop Experiment}
+%\addcontentsline{toc}{chapter}{Millikan Oil Drop Experiment}
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+    \oddsidemargin  0.0in
+    \evensidemargin 0.0in
+    \textwidth      6.5in
+    \headheight     0.0in
+    \topmargin      0.0in
+    \textheight=9.0in
+
+\begin{document}
+\title{Millikan Oil Drop Experiment}
+\date {}
+\maketitle
+\noindent
+
+\textbf{Experiment objectives}: \\ \textbf{Week 1}: explore the experimental
+apparatus and data
+ acquisition procedure; develop the data analysis routing using a mock Millikan experiment. \\ \textbf{Week 2}: extract the value of a unit charge $e$ by observing the motion
+ of charged oil drops in gravitational and electric field.
+
+ \begin{boxedminipage}{\linewidth}
+\textbf{Warning: this is a hard experiment!} \\
+%
+You have two class sessions to complete this experiment - for a good reason:
+this experiment is very hard! After all, it took R. A. Millikan 10 years to
+collect and analyze enough data to make accurate measurement of the electron
+charge. It takes some (often considerable) time to learn how to use the
+apparatus and get reliable data with it, so make sure you take take good notes
+during the first session on what gives you good and bad results. Also prepare
+and debug all the data analysis routines (such as calculations of drop
+parameters from the velocity measurements). Then you will hopefully have enough
+time
+ to make reliable measurements during the second session.
+\end{boxedminipage}
+
+    \section*{Introduction and Theory}
+The electric charge carried by a particle may be calculated by measuring the
+force experienced by the particle in an electric field of known strength.
+Although it is relatively easy to produce a known electric field, the force
+exerted by such a field on a particle carrying only one or several excess
+electrons is very small. For example, a field of $1000$~Volts per cm would
+exert a force of only $1.6\cdot l0^{-14}$~N dyne on a particle bearing one
+excess electron. This is a force comparable to the gravitational force on a
+particle with a mass of $l0^{-l2}$~gram.
+
+The success of the Millikan Oil Drop experiment depends on the ability to
+measure forces this small. The behavior of small charged droplets of oil,
+having masses of only $l0^{-l2}$~gram or less, is observed in a gravitational
+and an electric field. Measuring the velocity of fall of the drop in air
+enables, with the use of Stokes’ Law, the calculation of the mass of the drop.
+The observation of the velocity of the drop rising in an electric field then
+permits a calculation of the force on, and hence, the charge carried by the oil
+drop.
+
+Consider the motion of a small drop of oil inside the apparatus shown in Fig.
+\ref{moplates}.
+\begin{figure}[h]
+\centerline{\epsfig{width=3in, file=modexp.eps}} \caption{\label{moplates}
+Schematic Millikan Oil Drop System with and without electric field.}
+\end{figure}
+
+
+Because of the air drag tiny droplets fall very slowly with some constant
+terminal velocity $v_f$:
+\begin{equation}\label{fall}
+mg=kv_f
+\end{equation}
+where  $q$ is the charge on the droplet, $m$ is the mass of the droplet, $g$ is
+the acceleration due to gravity, and $k$ is a drag coefficient which will be
+related to the viscosity of air and the radius of the droplet.
+
+Because of its small mass the motion of the droplets is sensitive to an
+external electric field $E$ even if they carry charges of only a few electrons.
+A sufficient electric field can cause the oil drop to rise with a constant
+velocity $v_r$, such that:
+\begin{equation}\label{rise}
+Eq=mg+kv_r
+\end{equation}
+Combining Eqs.~(\ref{rise},\ref{fall}) we can find the charge $q$:
+\begin{equation}\label{q}
+q=\frac{mg(v_f+v_r)}{Ev_f}
+\end{equation}
+
+Therefor, the charge of the droplet can be found by measuring its terminal
+velocity $v_t$ and rising velocity in the external magnetic field $v_r$.
+However, we also need to know the mass and the radius of a drop. These data has
+to be extracted from the same data. The drag coefficient, $k$, can be
+determined from the viscosity, $\eta$, and the radius of the droplet, $a$,
+using Stokes law:
+\begin{equation}
+k=6\pi a\eta
+\end{equation}
+The mass of a drop can be related to its radius:
+\begin{equation}\label{m}
+m=\frac{4}{3}\pi a^3 \rho,
+\end{equation}
+and one may solve for $a$ using Eq.~(\ref{fall}):
+\begin{equation}\label{simple}
+a=\sqrt{\frac{9\eta v_f}{2g\rho}}
+\end{equation}
+Here $\rho=.886\cdot 10^3 \mathrm{kg/m}^3$ is the density of the oil.
+
+The air viscosity at room temperature is $\eta=1.832\cdot 10^{-5}$Ns/m$^2$ for
+relatively large drops. However, there is a small correction for this
+experiment for a small drops because the oil drop radius is not so different
+from the mean free path of air. This leads to an effective viscosity:
+\begin{equation}\label{etaeff}
+\eta_{eff}=\eta\frac{1}{1+\frac{b}{Pa}}
+\end{equation}
+where $b\approx 8.20 \times 10^{-3}$ (Pa$\cdot$m) and $P$ is atmospheric
+pressure (1.01 $10^5$ Pa). The idea here is that the effect should be related
+to the ratio of the mean free path to the drop radius. This is the form here
+since the mean free path is inversely proportional to pressure. The particular
+numerical constant can be obtained experimentally if the experiment were
+performed at several different pressures. A feature Milikan's apparatus had,
+but ours does not.
+
+To take into the account the correction to the air viscosity, one has to
+substitute the expression for $\eta_{eff}$ of Eq.~(\ref{etaeff})  into Eq.~(
+\ref{simple}) and then solve this more complex equation for $a$:
+\begin{equation}\label{complex}
+a=\sqrt{\frac{9\eta v_f}{2g\rho}+\left(\frac{b}{2P}\right)^2}-\frac{b}{2P}
+\end{equation}
+
+Therefor, the calculation of a charge carried by an oil drop will consists of
+several steps:
+\begin{enumerate}
+\item Measure the terminal velocities for a particular drop with and without
+electric field.
+\item Using the falling terminal velocity with no electric field, calculate
+the radius of a droplet using Eq.~(\ref{complex}), and then find the mass of
+the droplet using Eq.~(\ref{m}).
+\item Substitute the calculated parameters of a droplet into Eq.~(\ref{q}) to
+find the charge of the droplet $q$.
+
+\end{enumerate}
+%This second approach leads to:
+%
+%
+%Having found $a$ one can then find $m$ using Eq. \ref{m} and then find
+%$q$ from Eq. \ref{q}. I would use this approach rather than the Pasco one.
+
+
+
+
+\section*{Experimental procedure}
+
+\subsection*{Mock Millikan experiment - practice of the data analysis}
+\textit{The original idea of this experiment is described here:
+http://phys.csuchico.edu/ayars/300B/handouts/Millikan.pdf}
+
+The goal of this section is to develop an efficient data analysis routine for
+the electron charge measurements. You will be given a number of envelopes with
+a random number of Unidentified Small Objects (USOs), and your goal is to find
+a mass of a single USO (with its uncertainty!) without knowing how many USOs
+each envelope has. This exercise is also designed to put you in Robert Millikan
+shoes (minus the pain of data taking).
+
+Each person working on this experiment will be given a number of envelopes to
+weight. Each envelope contain unknown number of USO plus some packing material.
+To save time, all the data will be then shared between the lab partners.
+
+Then analyze these data to extract the mass of a single USO and its uncertainty
+in whatever way you’d like. For example, graphs are generally useful for
+extracting the data - is there any way to make a meaningful graph for those
+measurements? If yes, will you be able to extract the mean value of USO mass
+and its uncertainty from the graph? \textit{Feel free to discuss your ideas
+with the laboratory instructor!}
+
+After finding the mass of a USO, work with your data to determine how the size
+of the data set affects the accuracy of the measurements. That will give you a
+better idea how many successful measurements one needs to make to determing $e$
+in a real Millikan experiment.
+
+This part of the experiment must be a part of the lab report, including the
+results of your measurements and the description of the data and error analysis
+routine.
+
+
+
+\subsection*{Pasco Millikan oil drop setup}
+
+Follow the attached pages from Pasco manual to turn on, align and control the
+experimental apparatus. Take time to become familiar with the experimental
+apparatus and the measurement procedures. Also, it is highly recommended that
+you develop an intuition about ``acceptable'' drops to work with (see Pasco
+manual, ``Selection of the Drop'' section).
+
+\subsection*{Data acquisition and analysis}
+
+\begin{itemize}
+
+\item Choose a ``good'' drop and make about 10 measurements for its fall and rise
+velocities $v_t$ and $v_r$ by turning the high voltage on and off. Try to find
+a drop that does not rise too quickly for it will likely have a large number of
+electrons and, further, it will be difficult to determine the $v_r$. If you
+can't find slow risers, then lower the voltage so as to get better precision.
+
+
+\item Calculate the charge on the droplet. If the result of this first
+determination for the charge on the drop is greater than 5 excess electron, you
+should use slower moving droplets in subsequent determinations. Accepted value
+of the electron charge is $e=1.6\times10^{-19}$~C.
+
+\item If the drop is still within viewing range, try to change its charge. To
+do that bring the droplet to the top of the field of view and move the
+ionization lever to the ON position for a few seconds as the droplet falls. If
+the rising velocity of the droplet changes, make as many measurements of the
+new rising velocity as you can (10 to 20 measurements). If the droplet is still
+in view, attempt to change the charge on the droplet by introducing more alpha
+particles, as described previously, and measure the new rising velocity 10–20
+times, if possible. Since making measurements with the same drop with changing
+charge allows does not require repeating calculations for the drop mass and
+radius, try ``recharging'' the same drop as many times as you can.
+
+\item Be sure to measure the separation $d$ between the electrodes and the voltage potential in order to
+determine the field from the voltage.
+
+\end{itemize}
+
+Each lab partner should conduct measurements for at least one drop, and the
+overall number of measurements should be sufficient to make a reliable
+measurement for the unit electron charge. Make a table of all measurements,
+identify each drop and its calculated charge(s). Determine the smallest charge
+for which all the charges could be multiples of this smallest charge. Estimate
+the error in your determination of $e$.
+
+% Answer these questions somewhere in your report:
+%
+%\begin{enumerate}
+%\item You will notice that some drops travel upward and others downward
+%   in the applied field. Why is this so? Why do some drops travel
+%   very fast, and others slow?
+%\item Is the particle motion in a straight line? Or, do you notice that
+%   the particle "dances" around ever so slightly? This is due to
+%   Brownian motion: the random motion of a small particle in a gas or
+%   fluid.
+%
+%
+%\item We made three assumptions in determining the charge from Equation 1
+%   above. What are they? Hint: They are related to Stoke's Law.
+%
+%
+%\item Would you, like Millikan, spend 10 years on this experiment?
+%
+%\end{enumerate}
+%
+%Extra credit:  Millikan and his contemporaries were only able to
+%measure integer values of electron charge (as you are). Has anyone
+%measured free charges of other than integer multiples of e?
+
+\end{document}
diff --git a/unused_chapters/mo.tex b/unused_chapters/mo.tex
new file mode 100644
index 0000000..2a52bea
--- /dev/null
+++ b/unused_chapters/mo.tex
@@ -0,0 +1,156 @@
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+\begin{document}
+\title{Millikan ``Oil Drop'' Experiment}
+\author{} \date{} 
+\maketitle
+	\section*{Introduction and Theory}
+Consider Fig. \ref{moplates}
+\begin{figure}[h]
+\centerline{\epsfig{width=3in, file=moplates.eps}}
+\caption{\label{moplates}Very schematic Millikan Oil Drop System}
+\end{figure}				
+It turns out that very small droplets fall very slowly. Clouds, for
+example, are very small water droplets, trying to fall, but held aloft 
+by very slight air currents.
+
+
+An electric field can take the place of the air current and 
+even cause the oil drop
+to rise. Thus, for a rising oil drop:
+
+\begin{equation}\label{rise}
+Eq=mg+kv_r
+\end{equation}
+where $E$ is the electric field, $q$ is the charge on the droplet, $m$
+is the mass of the droplet, $g$ is the acceleration due to gravity, $v_r$
+is the velocity rising, and $k$ is a drag coefficient which will be 
+related to the viscosity of air and the radius of the droplet.
+
+If the field is off and the droplet is just falling, then:
+\begin{equation}\label{fall}
+mg=kv_f
+\end{equation}
+Combining Eqs. \ref{rise} and \ref{fall} we can find the charge $q$:
+\begin{equation}\label{q}
+q=\frac{mg(v_f+v_r)}{Ev_f}
+\end{equation}
+
+
+The drag coefficient, $k$, can be determined from the viscosity, $\eta$, and
+the radius of the droplet, $a$:
+ using Stokes law: 
+\begin{equation}
+k=6\pi a\eta
+\end{equation}
+
+Since 
+\begin{equation}\label{m}
+m=\frac{4}{3}\pi a^3 \rho 
+\end{equation}
+one may solve for $a$:
+\begin{equation}\label{simple}
+a=\sqrt{\frac{9\eta v_f}{2g\rho}}
+\end{equation}
+Here $rho=.886\cdot 10^3 kg/m^3$ is the density of the oil. (We ignore the
+density of air, which is roughly 1/1000 less.) 
+
+There is a 
+small correction because  the oil drop radius is not so different 
+from the mean free path of air. This leads to an effective viscosity:
+\begin{equation}\label{etaeff}
+\eta_{eff}=\eta\frac{1}{1+\frac{b}{pa}}
+\end{equation}
+where $b\approx 8.20 \times 10^{-3}$ (Pa m) and $p$ is atmospheric
+pressure (1.01 $10^5$ Pa). The idea here is that the effect should be 
+related to the
+ratio of the mean free path to the drop radius. This is the form 
+here since the mean free path is inversely proportional to pressure.
+The particular numerical constant can be obtained experimentally if
+the experiment were performed at several different pressures. A feature
+Milikan's apparatus had, but ours does not.
+
+There are two approaches at this point that one could take. 
+\begin{enumerate}
+\item  One could use Eq. \ref{simple} to determine $a$ using an uncorrected
+$\eta$, then use this to determine $\eta_{eff}$ then use this viscosity
+in Eq. \ref{simple} again to find a somewhat better $a$, and then proceed
+around the loop again until convergence is achieved. If the correction
+is large, this can get tedious.
+
+\item Put $\eta_{eff}$ of Eq. \ref{etaeff}  into Eq. \ref{simple} and
+then solve this more complex equation for $a$. 
+\end{enumerate}
+This second approach leads to:
+\begin{equation}\label{complex}
+a=\sqrt{\frac{9\eta v_f}{2g\rho}+\left(\frac{b}{2p}\right)^2}-\frac{b}{2p}
+\end{equation}
+
+Having found $a$ one can then find $m$ using Eq. \ref{m} and then find
+$q$ from Eq. \ref{q}. I would use this approach rather than the Pasco one.
+Try to find drops that do not rise too quickly for they will likely have
+a large number of electrons on them and, further, it will be difficult to
+determine the $V_r$.  If you can't find slow risers, then lower the voltage
+so as to get better precision. Be sure to measure the space thickness in
+order to determine the field from the voltage.
+
+
+
+\newpage\
+ 
+
+
+
+\subsection*{Required for your report}:
+
+Make a table of your measurements. Identify the drop and charge.
+Determine  the charge in each case. Make a table of charge differences.
+Determine the smallest charge for which all the charges could be multiples
+of this smallest charge.  Estimate the error in your determination of e.
+
+ Answer these questions somewhere in your report:
+
+\begin{enumerate}
+\item You will notice that some drops travel upward and others downward
+   in the applied field. Why is this so? Why do some drops travel
+   very fast, and others slow?
+\item Is the particle motion in a straight line? Or, do you notice that
+   the particle "dances" around ever so slightly? This is due to
+   Brownian motion: the random motion of a small particle in a gas or
+   fluid.
+
+\item Do you notice distinct steps in the terminal velocity in applied
+   field? That is, do the terminal velocities appear to clump around
+   similar values? What does this say about the discrete nature of
+   charge?
+
+\item We made three assumptions in determining the charge from Equation 1
+   above. What are they? Hint: They are related to Stoke's Law.
+
+\item How does the average particle diameter you extracted from the
+   terminal velocity without the field on compare to the value given
+   on the bottle? Try to explain any discrepancies.
+
+\item Would you, like Millikan, spend 10 years on this experiment?
+
+\end{enumerate}
+
+Extra credit:  Millikan and his contemporaries were only able to
+measure integer values of electron charge (as you are). Has anyone
+measured free charges of other than integer multiples of e? 
+
+
+
+
+\end{document}
+
+
+
+
+
+
+
+
+
+
+
diff --git a/unused_chapters/naspec.tex b/unused_chapters/naspec.tex
new file mode 100644
index 0000000..8f88b83
--- /dev/null
+++ b/unused_chapters/naspec.tex
@@ -0,0 +1,229 @@
+%\chapter*{Spectrum of Sodium }
+%\addcontentsline{toc}{chapter}{Spectrum of Sodium}
+
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+    \oddsidemargin  0.0in
+    \evensidemargin 0.0in
+    \textwidth      6.5in
+    \headheight     0.0in
+    \topmargin      0.0in
+    \textheight=9.0in
+
+\begin{document}
+\title{Spectrum of Sodium}
+\date {}
+\maketitle \noindent
+ \textbf{Experiment objectives}: measure the energy spectrum of sodium (Na),
+ determine values of quantum defects of low angular momentum states, and measure fine splitting
+using Na yellow doublet.
+
+\section*{Theory}
+Sodium (Na) belongs to the chemical group of \emph{alkali metals}, together
+with lithium (Li), potassium (K), rubidium (Rb), cesium (Cs) and Francium (Fr).
+All elements of this group have a closed electron shell with one extra unbound
+electron. This makes energy level structure for this free electron to be very
+similar to that of hydrogen, as shown in Fig.~\ref{nae}.
+
+For example, a Na atom has 11 electrons, and its electronic configuration is
+$1s^22s^22p^63s$, as determined from the Pauli exclusion principle.  Ten
+closed-shell electrons effectively screen the nuclear charge number ($Z=11$) to
+an effective charge $Z^*\approx 1$, so that the $3s$ valent electron experience
+the electric field potential similar to that of a hydrogen atom. As a result,
+the electron spectrum of all alkali metal atoms is quite similar to that of
+hydrogen:
+\begin{equation}\label{Hlevels_Naexp}
+E_n=-hcRy\frac{1}{n^2}
+\end{equation}
+%
+where $n$ is the principle quantum number, and $Ry=\frac{2\pi
+m_ee^4}{(4\pi\epsilon_0)^2ch^3}$   is  the  Rydberg constant ($Ry = 1.0974
+\times 10^5 cm^{-1}$ and $hcRy = 13.605 eV$). For each particular value of
+angular momentum $l$ the energy spectrum follows the same scaling as hydrogen
+atom. However, the absolute values of energies obey Eq.(\ref{Hlevels_Naexp})
+only for electron energy states with orbits far above closed shell - the ones
+with large value of an angular momentum $l$. Electron with smaller $l$ spends
+more time closer to the nuclear, and ``feels'' stronger bounding electrostatic
+potential. As a result the corresponding energy levels are pulled down compare
+to those of hydrogen, and the states with the same principle number $n$ but
+different angular momenta $l$ are split (\emph{i.e.} have different energies).
+\begin{figure}
+\includegraphics[height=\columnwidth]{nae.eps}
+\caption{\label{nae}Energy spectrum of Na. The energy states of H are shown in
+far right for comparison.}
+\end{figure}
+
+For each particular value of angular momentum $l$ the energy spectrum follows
+the same scaling as hydrogen atom, but with an effective charge $Z^*$:
+\begin{equation}\label{heq}
+E_n=-\frac{1}{2}\frac{Z^{*2}e^4}{(4\pi\epsilon_0)^2}\frac{mc^2}{\hbar^2c^2}
+\frac{1}{n^2}=-Z^{*2}\frac{hcRy}{n^2}
+\end{equation}
+The value of the effective charge $Z^*$ depends on the angular momentum $l$,
+and does not vary much between states with different principle quantum numbers
+$n$ but same $l$\footnote{The accepted notation for different electron angular
+momentum states is historical, and originates from the days when the proper
+quantum mechanical description for atomic spectra has not been developed yet.
+Back then spectroscopists had categorized atomic spectral lines corresponding
+to their appearend: for example any spectral lines from electron transitions
+from $s$-orbital ($l=0$) appeared always \textbf{S}harp on a photographic film,
+while those with initial electron states of $d$-orbital ( $l=2$) appeared
+always \textbf{D}iffuse. Also spectral lines of \textbf{P}rinciple  series
+(initial state is $p$-orbital, $l=1$) reproduced the hydrogen spectrum most
+accurately (even though at shifted frequencies), while the \textbf{F}undamental
+(initial electron state is $f$-orbital, $l=3$) series matched the absolute
+energies of the hydrogen most precisely. The orbitals with higher value of the
+angular momentum are denoted in an alphabetic order ($g$,
+$h$, \textit{etc}.) }:\\
+\begin{tabular}{ll}
+States&$Z^*$\\
+s~($l=0$)&$\approx$ 11/9.6\\
+p~($l=1$)&$\approx$ 11/10.1\\
+d~($l=2$)&$\approx$ 1\\
+f~($l=3$)&$\approx $ 1\\
+\end{tabular}
+\\These numbers mean that two states with the lowest angular momentum ($s$ and
+$p$) are noticeably affected by the more complicated electron structure of Na,
+while the energy levels of the states with the higher values of angular
+momentum ($d$, $f$) are identical to the hydrogen energy spectrum.
+
+An alternative (but equivalent) procedure is to assign a {\it quantum defect}
+to the principle quantum  $n$ instead of introducing an effective nuclei
+charge. In this case Eq.(\ref{heq}) can be written as:
+\begin{equation}\label{qdef}
+E_n=-\frac{hcRy}{(n^*)^2}=-\frac{hcRy}{(n-\Delta_l)^2}
+\end{equation}
+where $n*=n-\Delta_l$, and $\Delta_l$  is the corresponding quantum defect.
+Fig. \ref{nadell} shows values of quantum defects which work approximately for
+the alkalis. One sees that there is one value for each value of the angular
+momentum $l$. This is not exactly true for all alkali metals, but for Na there
+is very little variation in $\Delta_l$ with $n$ for a given $l$.
+
+\begin{figure}
+\includegraphics[width=0.5\columnwidth]{nadell.eps}
+\caption{\label{nadell}Quantum Defect $\Delta_l$ versus $l$ for different
+alkali metals. Taken from Condon and Shortley p. 143}
+\end{figure}
+%\begin{figure}
+%\includegraphics[height=3in]{nadel.eps}
+%\caption{\label{nadel}Quantum Defect $\Delta_l$ variation with $n$. The
+%difference between the quantum defect of each term and that of the lowest term
+%of the series to which it belongs is plotted against the difference between
+%the total quantum numbers of these terms. Again from Condon and Shortley p. 144.}
+%\end{figure}
+
+The spectrum of Na is shown in Fig. \ref{nae}. One can immediately see that
+there are many more optical transitions because of the lifted degeneracy of
+energy states with different angular momenta. However, not all electronic
+transition are allowed: since the angular momentum of a photon is $1$, then the
+electron angular momentum cannot change by more than one while emitting one
+spontaneous photon. Thus, it is important to remember the following
+\emph{selection rule} for atomic transitions:
+\begin{equation}\label{selrules}
+\Delta l = \pm 1.
+\end{equation}
+According to that rule, only transitions between two ``adjacent'' series are
+possible: for example $p \rightarrow s$ or $d \rightarrow p$ are allowed, while
+$s \rightarrow s$ or $s \rightarrow d$ are forbidden.
+
+The strongest allowed optical transitions are shown in Fig. \ref{natrns}.
+\begin{figure}
+\includegraphics[height=\columnwidth]{natrans.eps}
+\caption{\label{natrns}Transitions for Na. The wavelengths of selected
+transition are shown in {\AA}. Note, that $p$ state is now shown in two
+columns, one referred to as $P_{1/2}$ and the other as $P_{3/2}$. The small
+difference between their energy levels is the ``fine structure''.}
+\end{figure}
+%\begin{figure}
+%\includegraphics[height=4in]{series.eps}
+%\caption{\label{series}Series for Hydrogen, Alkalis are similar.}
+%\end{figure}
+Note that each level for given $n$ and $l$ is split into two because of the
+\emph{fine structure splitting}. This splitting is due to the effect of
+electron \emph{spin} and its coupling with the angular momentum. Proper
+treatment of spin requires knowledge of quantum electrodynamics and solving
+Dirac equation; for now spin can be treated as an additional quantum number
+associated with any particle. The spin of electron is $1/2$, and it may be
+oriented either along or against the non-zero electron's angular momentum.
+Because of the weak coupling between the angular momentum and spin, these two
+possible orientation results in small difference in energy for corresponding
+electron states.
+
+\section*{Procedure and Data Analysis}
+Align a diffraction-grating based spectrometer as described in ``Atomic
+Spectroscopy of Hydrogen Atoms'' experimental procedure.
+
+Then determine the left and right angles for as many spectral lines  and
+diffraction orders as possible. Each lab partner should measure the postilions
+of all lines at least once.
+
+Reduce the data using Eq. \ref{nlambda} to determine wavelengths for each
+spectral line (here $m$ is the order number):
+\begin{equation}\label{nlambda}
+m\lambda=\frac{d}{2}(\sin\theta_r+\sin\theta_l)
+\end{equation}
+Determine  the wavelengths of eight Na spectral lines measured in both first
+and second order. Combining first and second order results obtain the mean and
+standard deviation (error) of the mean value of the wavelength for each line.
+Compare these measured mean wavelengths to the accepted values given in
+Fig.~\ref{natrns} and in the table below:
+
+\begin{tabular}{lll}
+  Color&Line$_1$(\AA)&Line$_2$(\AA)\\
+Red&6154.3&6160.7\\
+Yellow & 5890.0&5895.9\\
+Green & 5682.7&5688.2\\
+&5149.1&5153.6\\
+& 4978.6&4982.9\\
+Blue&4748.0&4751.9\\
+&4664.9&4668.6\\
+Blue-Violet&4494.3&4497.7\\
+\end{tabular}
+
+Line$_1$ and Line$_2$ corresponds to transitions to two fine-spitted $3p$
+states $P_{1/2}$ and $P_{3/2}$. These two transition frequencies  are very
+close to each other, and to resolve them with the spectrometer the width of the
+slit should be very narrow. However, you may not be able to see some weaker
+lines then. In this case you should open the slit wider to let more light in
+when searching for a line. If you can see a spectral line but cannot resolve
+the doublet, record the reading for the center of the spectrometer line, and
+use the average of two wavelengthes given above.
+
+ Identify  at least seven of the lines with a particular transition, e.g.
+$\lambda = 4494.3${\AA} corresponds to $8d \rightarrow 3p$ transition.
+
+\subsection*{Calculation of a quantum defect for $n=3, p$ state}
+Identify spectral lines which corresponds to optical transitions from $d$ to
+$n=3,p$ states. Since the energy states of $d$ series follows the hydrogen
+spectra almost exactly, the wavelength of emitted light $\lambda$ is given by:
+\begin{equation}
+\frac{hc}{\lambda}=E_{nd}-E_{3p}=-\frac{hcRy}{n^2}+\frac{hcRy}{(3-\Delta_p)^2},
+\end{equation}
+or
+\begin{equation}
+\frac{1}{\lambda}=\frac{Ry}{(3-\Delta_p)^2}-\frac{Ry}{n^2},
+\end{equation}
+ where $n$ is the principle number of the initial $d$ state. To verify this
+expression by plotting $1/\lambda$ versus $1/n^2$ for the $n$= 4,5, and 6. From
+the slope of this curve determine the value of the Rydberg constant $Ry$. From
+the intercept determine the energy $E_{3p}$ of the $n=3,p$ state, and calculate
+its quantum defect $\Delta_p$.
+\subsection*{Calculation of a quantum defect for $s$ states}
+Now consider the transition from the $s$-states ($n=5,6,7$) to to the $n=3, p$
+state. Using $hc/\lambda=E_{ns}-E_{3p}$ and the results of your previous
+calculations, determine the energies $E_{sn}$ for different $s$ states with
+$n=5,6,7$  and calculate $\Delta_s$. Does the value of the quantum defect
+depends on $n$?
+
+Compare the results of your calculations for the quantum defects $\Delta_s$ and
+$\Delta_p$ with the accepted values given in Fig. \ref{nadell}.
+
+\subsection*{Calculations of fine structure splitting}
+For the Na D doublet measure the splitting between two lines
+$\Delta\lambda=\lambda_{3/2}-\lambda_{1/2}$ in the second diffraction order
+(why the second order is better than the first one?). Compare to the accepted
+value: $\Delta\lambda=$5.9\AA . Compare this approach to the use of the
+Fabry-Perot interferometer.
+
+\end{document}
+\newpage
diff --git a/unused_chapters/report_template.tex b/unused_chapters/report_template.tex
new file mode 100644
index 0000000..c4f2436
--- /dev/null
+++ b/unused_chapters/report_template.tex
@@ -0,0 +1,138 @@
+\documentclass[aps,prb,preprint]{revtex4}

+%\documentclass[aps,twocolumn,prl]{revtex4}

+\usepackage{epsfig}

+\begin{document}

+

+\title{Compton Scattering Lab}

+\author{Y. O. Urname, P. A. Rtner1, and P. B. Rtner2}

+\affiliation{Physics 251 College of William and Mary}

+\date{today}

+\begin{abstract}

+This lab demonstrates Compton scattering. A Na$^{22}$ $\gamma$-ray source is

+used. The decay $\gamma$-ray has an energy of approximately .66 MeV. 

+\end{abstract} 

+\maketitle

+

+

+

+

+

+

+\section{Introduction}

+\subsection{Overview ...}

+

+Start writing here ..

+

+g

+%++++++++++++++++++++++++++++++++++++++++

+How to cite a reference:

+In 1989, experiments at CERN \cite{EMC} reported ...

+

+%++++++++++++++++++++++++++++++

+How to make a nice equation:

+\begin{equation}

+\label{equ:aperp}

+A_{\perp} = \frac{\sigma^{\downarrow\leftarrow} - 

+\sigma^{\uparrow\leftarrow}} {\sigma^{\downarrow\leftarrow} + 

+\sigma^{\uparrow\leftarrow}} = f_kE^{\prime}\sin\theta\left(g_1(x,Q^2) 

++ \frac{2E}{\nu}g_2(x,Q^2)\right),

+\end{equation}

+

+%++++++++++++++++++++++++++++++

+How to include a figure into the document:

+%%%%%%%%%%%%%%%%%%%%%%%%% Figure - Helicity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

+\begin{figure}[hbt]

+\begin{center}

+\epsfysize=2.5in \epsfxsize=1.5in 

+\rotatebox{70}{\leavevmode\epsffile{mypicture.eps}}

+\end{center}

+\caption{Every figure MUST have a caption}

+\label{fig:helicity}

+\end{figure}

+%%%%%%%%%%%%%%%%%%%%%%%% End Figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

+

+%+++++++++++++++++++++++++++++++++++++

+An easier way to include a figure in a document:

+%%%%%%%%%%%%%%%%%%%%%%%%% Figure - Helicity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

+\begin{figure}[hbt]

+\begin{center}

+\epsfig{file=mypicture.eps, width=3in, angle=270}

+\end{center}

+\caption{Did you hear that every figure needs a caption?}

+\label{fig:helicity1}

+\end{figure}

+%%%%%%%%%%%%%%%%%%%%%%%% End Figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

+\section{Theory}

+\section{Experiment}

+

+

+

+%++++++++++++++++++++++++++++++++

+How to make a nice table. Note that I had to put the newpage in to get it

+placed right. (Take the newpage out and see what happens.)

+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Table bins %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

+\begin{table}[h]

+\begin{center}

+\caption{Every table needs a caption

+    }

+\label{tbl:bins}

+\begin{tabular}{|ccccccc|} \hline

+\multicolumn{1}{|c}{Polarization} &

+\multicolumn{1}{c}{Target} &

+\multicolumn{1}{c}{Bin} &

+\multicolumn{1}{c}{$<x>$} &

+\multicolumn{1}{c}{$<Q^2>$} &

+\multicolumn{1}{c}{$A_{\perp}^{meas}$} &

+\multicolumn{1}{c|}{$\Delta A_{\perp}$} \\

+\hline

+$-$ & LiD     & 1 &   0.0233323 &   0.8429978  &   0.0044151 &   0.0030871 \\

+    &         & 2 &   0.0638046 &   1.5017358  &   0.0021633 &   0.0021343 \\

+    &         & 3 &   0.1892825 &   3.1877837  &   0.0006640 &   0.0022467 \\

+    &         & 4 &   0.4766562 &   7.1827556  &  -0.0197585 &   0.0085528 \\

+    & NH$_3$  & 1 &   0.0232572 &   0.8454089  &   0.0003600 &   0.0018642 \\

+    &         & 2 &   0.0633156 &   1.4870013  &   0.0023831 &   0.0013287 \\

+    &         & 3 &   0.1923955 &   3.1753302  &  -0.0024246 &   0.0013771 \\

+    &         & 4 &   0.4830315 &   7.3245904  &  -0.0284834 &   0.0047061 \\

+$+$ & LiD     & 1 &   0.0233503 &   0.8340932  &  -0.0086018 &   0.0031121 \\

+    &         & 2 &   0.0638688 &   1.4785886  &  -0.0018465 &   0.0021452 \\

+    &         & 3 &   0.1892192 &   3.1277721  &  -0.0017860 &   0.0022525 \\

+    &         & 4 &   0.4778486 &   7.0313856  &  -0.0041773 &   0.0084659 \\

+    & NH$_3$  & 1 &   0.0232964 &   0.8439092  &  -0.0022961 &   0.0018851 \\

+    &         & 2 &   0.0633764 &   1.4814540  &   0.0021355 &   0.0013354 \\

+    &         & 3 &   0.1924094 &   3.1580557  &  -0.0065302 &   0.0013775 \\

+    &         & 4 &   0.4825868 &   7.3191291  &  -0.0290878 &   0.0047329 \\

+\hline

+\end{tabular}

+\end{center}

+\end{table}

+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

+\newpage

+\subsection{The Target} %For example

+\section{Results}

+\section{Conclusions}

+

+%+++++++++++++++++++++++++++++++++++++++

+%Here's how to do references:

+

+%\begin{thebibliography}{99} % Remove leading % if this style is to your taste.

+%\bibitem{EMC}

+%J.~Ashman {\it et al.}  [European Muon Collaboration],

+%``An investigation of the spin structure of the proton in deep inelastic  scattering of polarized muons on polarized protons,''

+%Nucl.\ Phys.\  {\bf B328}, 1 (1989).

+%\end{thebibliography}

+

+\bibliography{dummy} 

+

+\end{document}

+

+

+

+

+

+

+

+

+

+

+

+

diff --git a/unused_chapters/sched.tex b/unused_chapters/sched.tex
new file mode 100644
index 0000000..8227a18
--- /dev/null
+++ b/unused_chapters/sched.tex
@@ -0,0 +1,58 @@
+\noindent
+Wednesday/Thursday, 2-5 pm in Rooms 203\& 205 of Small Hall\\
+Instructors:\\
+
+\begin{tabular}{llll}
+W. J. Kossler & Rm 129 & 221 3519 & kossler@physics.wm.edu\\
+&& home 229  8060&\\
+Assistant: Cara Campbell &Rm  243 &cell 540 850 4606 & cacamp@wm.edu\\
+\end{tabular}
+\vskip .2in
+
+ 
+ Reports are due one week after the lab work. Collaboration is
+allowed and in fact expected, but the writeup should be individually done. 
+
+
+\section*{Schedule}
+
+The content of the cells is the week(s) during which the experiment
+will be carried out. 
+\vskip .2in   
+
+\begin{tabular}{||l||l|l|l|l|l|l||}\hline\hline
+Exp$\setminus$Group& 1 & 2 & 3 & 4 & 5 & 6\\\hline\hline
+C&1&2&3&4&5&6\\\hline
+Michelson&2&1&1&1&6&5\\\hline
+Fabry Perot&3&3&2&2&7&9\\\hline
+e/m&4&4&5&5&8&11\\\hline
+$\hbar$/e&5&5&4&6&3&3\\\hline
+Electron Diffraction& 6&6&6&3&4&4\\\hline
+Black Body& 9&9&7&7&1&1\\\hline
+Oil Drop& 7,8&7,8&9,10&9,10&9,10&7,8\\\hline
+Hydrogen Spectrum  & 11 & 11 & 8 & 8 & 2 & 2\\\hline
+Na Spectrum &10 & 10 &12 &12 &12 &10\\\hline
+Superconductivity &12& 12 &11 &11 &11 &12\\\hline
+Tour & 13 & 13 & 13 & 13 & 13 & 13 \\\hline\hline
+\end{tabular}
+
+
+\subsection*{Mapping Date $\rightarrow$ Week Number}
+\begin{tabular}{||l|l||}\hline\hline
+Aug. 30,31 & 0\\\hline
+Sept 6, Sept. 7& 1\\\hline
+Sept. 13,14& 2 \\\hline
+Sept. 20,21 &3 \\\hline
+Sept. 27,28 & 4\\\hline
+Oct.  4,5 & 5 \\\hline
+Oct. 11,12 & 6 \\\hline
+Oct. 18,19 8& 7 \\\hline
+Oct. 25,26 & 8 \\\hline
+Nov. 1,2 & 9 \\\hline
+Nov. 8,9 & 10 \\\hline
+Nov. 15,16 & 11 \\\hline
+Nov. 22,23 &Thanksgiving \\\hline
+Nov. 29,30& 12\\\hline
+Dec. 6,7 & 13\\\hline\hline
+\end{tabular}
+\newpage
diff --git a/unused_chapters/spol.tex b/unused_chapters/spol.tex
new file mode 100644
index 0000000..6c0446e
--- /dev/null
+++ b/unused_chapters/spol.tex
@@ -0,0 +1,141 @@
+%\chapter*{Measuring the Speed of Light}
+%\addcontentsline{toc}{chapter}{Measuring the Speed of Light}
+\documentclass{article}
+\usepackage{tabularx,amsmath,boxedminipage,epsfig}
+    \oddsidemargin  0.0in
+    \evensidemargin 0.0in
+    \textwidth      6.5in
+    \headheight     0.0in
+    \topmargin      0.0in
+    \textheight=9.0in
+
+\begin{document}
+\title{Measuring the Speed of Light}
+\date {}
+\maketitle
+
+\noindent
+ \textbf{Experiment objectives}: Determine the speed of light directly by
+ measuring time delays of pulses.
+
+\section*{History}
+
+ The speed of light is a fundamental constant of nature, the value
+we now take for granted. In 1983, the internationally adopted value in vacuum became:
+
+\[
+c = 2.99792458 \times 10^8 m/s\,\, \mbox{exactly}
+\]
+
+But considering that light travels seven and a half times around the world in one second, you can imagine how
+challenging a measurement it would be to determine the exact value of the speed of light. In fact, it took
+several attempts over many centuries to determine the value (some of the measurements are shown in Table 1).
+\begin{figure}[hbt]
+\centerline{\epsfig{file=ctable.eps, width=6in, angle=0}} \label{fig:ctable}
+
+\end{figure}
+
+The first attempt at a measurement was made by Galileo in 1600 using two lanterns on hills. He had an assistant
+on a distant mountain who would signal when he saw a lantern be masked, and then Galileo would measure the
+interval between his own signaling and the response of his assistant. He only could find the speed of light to
+be ``very fast''. But interestingly enough, the technique you will use is nowhere near the best, but it is
+direct and in some ways similar to Galileo's.
+
+Several other experiments followed over the centuries until Michelson and Morely made a very accurate
+measurement in 1887 using a specially design interferometer (which by lucky coincidence you explore during
+another lab in our course). The currently accepted value was not determined until the advent of the laser.
+
+You might wonder why the speed of light is now a defined quantity. The
+measurements at the end of the Table are measurements of the wavelength
+and frequency of light, both referenced to the wavelength of atomic transitions
+and to the frequency of atomic transitions. Distances can be measured to
+small fractions of the wavelength of light, and this over distances of
+meters. Frequencies are compared by beating one light signal against another
+so that the difference frequency can be directly compared to atomic clocks.
+You can estimate the accuracy of this by considering a meter to be measured
+to $10^{-3}$ of $\lambda$ of some visible lightwave, and $\nu$, the frequency
+can be measured to $10^{-5}$ Hz out of the frequency of an atomic transition.
+
+\section*{Procedure}
+
+\subsection*{Laser Safety}
+While this is a weak laser caution should still be used. \textbf{Never look directly at the laser beam!} Align
+the laser so that it is not at eye level.
+
+\subsection*{Set Up}
+\textbf{Equipment needed}: diode laser, photodetector, lens, Pasco magnetic platform, large mirror on a rolling
+table, small reference mirror, function generator, oscilloscope.
+
+In the experiment you modulate the power sent to the laser to produce short pulses of light, and then measure
+the time it takes for these pulses to travel from the laser to the mirror and back to the photodetector, as
+shown in the layout for the experiment in Fig. \ref{fig:solapp}. This measurement is repeated for several
+displacements of the mirror (the more the better) by rolling the table with the mirror along the corridor (if
+you like challenges, you can try to see how far you can go).
+
+
+%
+\begin{figure}[hbt]
+\begin{center}
+\epsfig{file=solapp.eps, width=5in, angle=0}
+\end{center}
+\caption{Speed of light Apparatus} \label{fig:solapp}
+\end{figure}
+%
+\subsection*{Data acquisition}
+
+\begin{itemize}
+
+\item Put a rolling table as close as possible to the stationary table with the laser and the photodetector. Make
+sure you have enough clearance to push the table along the corridor (you may need to move the tables). Make sure
+that the laser beam hits the mirror relatively close to the center, and use fine tuning on the mirror to reflect
+the beam to the photodetector - first without the lens, then with the lens in place.
+
+\item Plug in the output of the photodetector to the oscilloscope, and use a TTL pulse output as a trigger. If
+everything works, you will see a train of nearly square pulses. Before starting the measurements, you first need
+to think about two issues (\textit{the instructor will ask you about them}!): \\
+1) How will the detected signal change as you start pushing the mirror farther and farther? \\
+2) What is a suitable characteristic feature(s) of the detected signal to trace this change? Also,  Make
+yourself familiar with the scope features, such as ``measurements'' and ``save traces'' (your instructor or TA
+will be able to help you with that). That will make your data acquisition easier.
+
+
+\item Vary the position of the mirror by moving the rolling table from as close as possible to as far as possible
+in about $10$ steps (the more measurements the more accurate final result you will have). For each step measure
+the position of the table $D$. The floor tiles make a reasonable gauge - each tile is a 9 inch square (remember
+to convert to meters!). Count the tile squares and double check.
+
+For each position each member of the group determine the light pulse time delay $T_{1,2,\cdots}$ by comparing
+the time difference between the chosen characteristic features for the light reflected off the large ``distant''
+mirror and small ``reference'' mirror placed near the detector. Calculate average value $T_{ave}$ and the
+uncertainty $\Delta T$. Below is the example of a table for data recording.
+
+\end{itemize}
+
+\vskip .1in
+
+\begin{tabular}{|l|l|l|l|l|l|l|}\hline
+$D \pm \Delta D$ ($\#$ of tiles)& $D \pm \Delta D$ (m) &$T_1$($\mu$s)& $T_2$($\mu$s)
+& $T_3$($\mu$s) & $T_{ave}$ ($\mu$s) & $\Delta T$ ($\mu$s) \\
+\hline &&&&&&\\\hline
+&&&&&&\\$\dots$&$\dots$&$\dots$&$\dots$&$\dots$&$\dots$&$\dots$\\\hline
+&&&&&&\\\hline &&&&&&\\\hline &&&&&&\\\hline
+
+\end{tabular}
+
+\vskip .2in
+\noindent
+
+\subsection*{Analysis}
+
+Plot the results of the measurements as a distance vs time delay graph $D vs. T$. If the measurements are done
+properly, the data will be scattered close to a straight line, and the slope of this line is inversely
+proportional to the speed of light $1/v$. Thus, the measured $v$ and its uncertainty can be extracted from
+fitting the experimental data. This method should give more accurate results than calculating $v$ from each
+measurements, since it allows avoiding systematic errors due to an offset in the distance measurements.  From
+same fit determine the distance intercept. It the obtained value reasonable?
+
+In the lab report compare the measured speed of light with the theoretical
+value. Is it within experimental uncertainty? If it is not, discuss possible
+systematic errors which affected your results.
+
+\end{document}