typos fixed, thanks to Jordan

1 files changed, 24 insertions, 7 deletions

diff --git a/single-photon-interference.tex b/single-photon-interference.tex
index f98f9ae..112913d 100644
--- a/single-photon-interference.tex
+++ b/single-photon-interference.tex
@@ -69,7 +69,7 @@ bulb}. A toggle switch on the front panel of the light source control box switch
 other.
 
 \item Various \emph{slit holders} along the length of the long box: one to hold a two-slit mask, one for slit blocker,
-and one for a detector slit. Make sure you locate \emph{slits} (they may be installed already) and two
+and one for a detector slit. Make sure you locate the \emph{slits} (they may be installed already) and two
 \emph{micrometer drives}, which allow you to make mechanical adjustments to the two-slit apparatus. \textbf{Make
 sure you figure out how to read the micrometer dials!} On the barrel there are two scales with division of
 $1$~mm, shifted with respect to each other by 0.5~mm; every fifth mark is labeled with an integer 0, 5, 10 and
@@ -78,10 +78,10 @@ the rotary scale is $0.01$~mm.
 
 \item Two distinct light detectors at the right-hand end of the apparatus: a \emph{photodiode}
 and a \emph{photomultiplier tube} (PMT for short). The photodiode is used with the much brighter laser light;
-it's mounted on light the shutter in such a way that it's in position to use when the shutter is closed (pushed
+it's mounted on the light shutter in such a way that it's in position to use when the shutter is closed (pushed
 down). The photomultiplier tube is an extremely sensitive detector able to detect individual photons (with energy
 of the order of $10^{-19}$~J), and it is used with the much dimmer light-bulb source. Too much light can easily
-damage it, so \textbf{PMT is safe to use only when the cover of the apparatus is in place, and only when the
+damage it, so \textbf{the PMT is safe to use only when the cover of the apparatus is in place, and only when the
 light bulb is in use}. It is exposed to light only when the shutter is in its up position.
 \end{itemize}
 
@@ -95,7 +95,7 @@ distribution of a laser beam on a viewing screen.
 \item Using the photodiode you will accurately measure the intensity distribution after single- and two-slit interference patterns,
 which can be compared to predictions of wave theories of light. \\
 These two steps recreate Young's original experiment.
-\item Then using a very weak light source you will record the two-slit interference pattern one photon at a time.
+\item Then, using a very weak light source, you will record the two-slit interference pattern one photon at a time.
 While this measurement will introduce you to single-photon detection technology, it will also show you that
 however two-slit interference is to be explained, it must be explained in terms that can apply to single
 photons.
@@ -239,7 +239,24 @@ Fit your data with Eqs.~(\ref{1slit}) and (\ref{2slit_wDif}). You will need to a
 
 Before you start the measurements you have to convince yourself that the
 rate of photons emitted by the weak filtered light bulb is low enough to
-have on average less than one photon detected in the apparatus at any time. Roughly estimate the number of photons per second arriving to the detector. First, calculate the number of photons emitted by the light bulb in a 10~nm spectral window of the green filter (between $541$ and $551$~nm), if it runs at 6V and 0.2A. Note that only 5\% of its electric energy turns into light, and this optical energy is evenly distributed in the spectral range between 500~nm and 1500~nm. These photons are emitted in all directions, but all of them are absorbed inside the box except for those passing through two slits with area approximately $0.1\times 10~\mathrm{mm}^2$. Next, assuming that the beam of photons passing through the slits diffracts over a $1~\mathrm{cm}^2$ area by the time it reaches the detector slit, estimate the rate of photons reaching the detector. Finally, adjust the detected photon rate by taking into account that for PMT only 4\% of photons produce output electric pulse at the output. That's the rate of events you expect. Now estimate the time it takes a photon to travel through the apparatus, and estimate the average number of detectable photons inside at a given moment of time. \emph{You may do this calculations before or after the lab period, but make sure to include them in the lab report.}
+have, on average, less than one photon detected in the apparatus at any
+time. Roughly estimate the number of photons per second arriving to the
+detector. First, calculate the number of photons emitted by the light bulb
+in a 10~nm spectral window of the green filter (between $541$ and
+$551$~nm), if it runs at 6V and 0.2A. Note that only 5\% of its electric
+energy turns into light, and this optical energy is evenly distributed in
+the spectral range between 500~nm and 1500~nm. These photons are emitted in
+all directions, but all of them are absorbed inside the box except for
+those passing through two slits with area approximately $0.1\times
+10~\mathrm{mm}^2$. Next, assuming that the beam of photons passing through
+the slits diffracts over a $1~\mathrm{cm}^2$ area by the time it reaches
+the detector slit, estimate the rate of photons reaching the detector.
+Finally, adjust the detected photon rate by taking into account that for
+PMT only 4\% of photons produce output electric pulse at the output. That's
+the rate of events you expect. Now estimate the time it takes a photon to
+travel through the apparatus, and estimate the average number of detectable
+photons inside at a given moment of time. \emph{You may do these
+calculations before or after the lab period, but make sure to include them in the lab report.}
 
 Now you need to change the apparatus to use the light bulb. Open the cover and slide the laser source to the side (do not remove the laser from the stand). Now set the 3-position toggle switch to the BULB position and dial the bulb adjustment up from 0 until you see the bulb light up. (\emph{The flashlight bulb you're using will live longest if you minimize the time you spend with it dialed above 6 on its scale, and if you toggle its power switch only when the dial is set to low values}). If the apparatus has been aligned, the bulb should now be in position to send light through the apparatus. Check that the green filter-holding structure is in place: the light-bulb should look green, since the green filter blocks nearly all the light emerging from the bulb, passing only wavelengths in the range 541 to 551 nm. The filtered light bulb is very dim, and you probably will not be able to see much light at the double-slit position even with room light turned off completely. No matter; plenty of green-light photons will still be reaching the double-slit structure -- in fact, you should now dim the bulb even more, by setting its intensity control down to about 3 on its dial.
 
@@ -335,7 +352,7 @@ work with complex numbers, we will assume that the original incident wave is a r
 $E(z,t)=E_0e^{ikz-i2\pi\nu t}$, where $k=2\pi/\lambda$ is the wave number. Then the amplitude of each point
 radiator on a slit is [a real part of] $dE(z,t)=E_0e^{ikz-i2\pi\nu t}dx$. A beam emitted by a radiator at the
 height $x$ above the center of the slit must travel an extra distance $x\sin \theta$ to reach the plane of the
-screen, acquiring an additional phase factor. Then we may write a contributions at the point $P$ from a point
+screen, acquiring an additional phase factor. Then we may write a contribution at the point $P$ 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.
@@ -364,7 +381,7 @@ The minima of the intensity (``dark fringes'') occur at the zeros of the argumen
 $\frac{\pi D}{\lambda}\sin\theta=m\pi$, while the maxima (``bright fringes'') almost exactly match
 $\frac{\pi D}{\lambda}\sin\theta=(m+\frac{1}{2})\pi$  for $m = 0, \pm1, \pm2, \cdots$.
 
-Let us now consider the case of interference pattern from two identical slits separated by the distance $d$, as
+Let us now consider the case of the interference pattern from two identical slits separated by the distance $d$, as
 shown in Fig.~\ref{interference.fig}(b). 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
 going through the similar steps the resulting intensity distribution on the screen is given by familiar Young