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Diffstat (limited to 'single-photon-interference.tex')
| -rw-r--r-- | single-photon-interference.tex | 30 |
1 files changed, 18 insertions, 12 deletions
diff --git a/single-photon-interference.tex b/single-photon-interference.tex index 112913d..1b20598 100644 --- a/single-photon-interference.tex +++ b/single-photon-interference.tex @@ -68,7 +68,8 @@ components of the experiment: bulb}. A toggle switch on the front panel of the light source control box switches power from one source to the other. -\item Various \emph{slit holders} along the length of the long box: one to hold a two-slit mask, one for slit blocker, +\item Various \emph{slit holders} along the length of the long box: one to + hold a two-slit mask, one for the slit blocker, and one for a detector slit. Make sure you locate the \emph{slits} (they may be installed already) and two \emph{micrometer drives}, which allow you to make mechanical adjustments to the two-slit apparatus. \textbf{Make sure you figure out how to read the micrometer dials!} On the barrel there are two scales with division of @@ -104,7 +105,8 @@ photons. \subsection*{Visual observation of a single- and two-slit interference} For this mode of operation, you will be working with the cover of the apparatus open. Switch the red diode laser -on using the switch in the light source control panel, and move the laser in the center of its magnetic pedestal +on using the switch in the light source control panel, and move the laser +to the center of its magnetic pedestal so that the red beam goes all the way to the detector slit. The diode laser manufacturer asserts that its output wavelength is $670 \pm 5$~nm, and its output power is about 5~mW. \emph{\textbf{As long as you don't allow the full beam to fall directly into your eye, it presents no safety hazard.}} Place a double-slit mask on the holder @@ -125,8 +127,9 @@ sure you find and record the ranges of micrometer reading where you observe the \item light emerges only from the other slit; \item the light from both slits is blocked. \end{enumerate} -It is essential that you are confident enough in your ability to read, and to set, these five positions that -you'll be able to do so even when the box cover is closed. In your lab book describe what you see at the viewing +It is essential that you are confident enough in your ability to read, and +to set, these five positions and that +you are able to do so even when the box cover is closed. In your lab book describe what you see at the viewing card at the far-right end of the apparatus for each of the five settings. \textbf{One slit is open:} According to the wave theory of light, the intensity distribution of light on the @@ -152,7 +155,7 @@ by wave theory: I(x)= 4 I_0 \cos^2\left(\frac{\pi d}{\lambda}\frac{x}{\ell} \right)\left[\frac{\sin (\frac{\pi a}{\lambda}\frac{x}{\ell})}{\frac{\pi a}{\lambda}\frac{x}{\ell}} \right]^2, \end{equation} -where an additional parameter $d$ is the distance between centers of the two slits. Discuss how this picture +where an additional parameter $d$ is the distance between the centers of the two slits. Discuss how this picture would change if you were to vary the width or the separation of the two slits or the wavelength of the laser. Make a note of your predictions in the lab book. @@ -169,7 +172,7 @@ to emerge and interfere. The shutter of the detector box will still be in its closed, or down, position: this blocks any light from reaching the PMT, and correctly positions a 1-cm$^{2}$ photodiode, which acts just like a solar cell in actively generating electric current when it's illuminated. The output current is proportional to total power -illuminating the detector area, so it is important to use a narrow slit allow only a selected part of the +illuminating the detector area, so it is important to use a narrow slit to allow only a selected part of the interference pattern to be measured. Make sure that a detector slit mask (with a single narrow slit) on a movable slit holder at the right-hand side of the apparatus is in place. By adjusting the micrometer screw of the detector slit, you can move the slit over the interference pattern, eventually mapping out its intensity @@ -181,8 +184,9 @@ The electric \emph{current} from the photodiode, proportional to the \emph{light thin coaxial cable to the INPUT BNC connector of the photodiode-amplifier section of the detector box, and converted to \emph{voltage} signal at the OUTPUT BNC connector adjacent to it. Connect to this output a digital multimeter set to 2 or 20-Volt sensitivity; you should see a stable positive reading. Turn off the laser first -to record the ``zero offset'' - reading of the multimeter with no light. You will need to subtract this reading -from all the other readings you make of this output voltage. +to record the ``zero offset'' - the reading of the multimeter with no light. You will need to subtract this reading +from all of the other readings you make with this photodiode, amplifier, and voltmeter +combination. Turn your laser source back on, and watch the photodiode's voltage-output signal as you vary the setting of the detector-slit micrometer. If all is well, you will see a systematic variation of the signal as you scan over the @@ -196,7 +200,8 @@ any point on the screen by half, while the wave theory predicts much more dramat points in the screen. Which theory provides a more accurate description of what you see? \begin{itemize} -\item Find the highest of the maxima --- this is the ``central fringe'' or the ``zeroth-order fringe'' that theory +\item Find the highest of the maxima --- this is the ``central fringe'' or + the ``zeroth-order fringe'' that the theory predicts --- and record the photodiode reading. Then adjust the position of the slit-blocker to let the light to pass through only one of the slits, and measure the change in the photodiode signal. @@ -206,7 +211,7 @@ minima immediately adjacent to the central maximum; take some care to find the v Record what happens when you use the slit-blocker to block the light from one, or the other, of the two slits. \item Check your experimental results against the theoretical predictions using Eqs.~(\ref{1slit}) and (\ref{2slit_wDif}). -Do your observation confirm or contradict wave theory? +Do your observations confirm or contradict wave theory? \end{itemize} @@ -218,8 +223,9 @@ make such {\bf measurements in two slit-blocker positions: when both slits are open, and when only one slit is open}. You will need to take enough data points to reproduce the intensity distribution in each case. Taking points systematically every 0.05 or \unit[0.1]{mm} on the tick lines will produce a very high quality dataset. One person should turn the dial and the other should record readings directly to paper or a spreadsheet (if you do this, print it out and tape into your logbook). Estimate your uncertainties from the dial and the voltmeter. Cycle through multiple maxima and minima on both sides of the central maximum. It is a good idea to plot the data points immediately along with the data taking -- nothing beats an emerging graph for teaching you what is going on, and your graph will be pretty impressive. \emph{Note: due to large number of points you don't need to include the tables with these measurements in the lab report -- the plotted distributions should be sufficient. Be clear on your uncertainties though.} \textbf{Slit separation calculations}: Once you have enough data points for each graph to clearly see the -interference pattern, use your data to extract the information about the distance between two slits $d$. To do -that find the positions of consecutive interference maxima or minima, and calculate average $d$ using +interference pattern, use your data to extract the information about the +distance between the two slits $d$. To do +that, find the positions of consecutive interference maxima or minima, and calculate average $d$ using Eq.~\ref{2slit_wDif}. Estimate the uncertainty in these parameters due to laser wavelength uncertainty. Check if your measured values are within experimental uncertainty from the manufacturer's specs: the center-to-center slit separation is 0.353 mm (or 0.406 or 0.457 mm, depending on which two-slit mask you have installed). |