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\chapter*{Single Photon Interference - Pre-lab exercise}

You can use the lab report template to prepare the submission of the pre-lab exercises. Feel free to use calculations or graphs in your final report, but you don't need to include prelab with the report.

\section*{1. Theoretical graph}

This lab uses the most complex fitting functions of all. Make plots of Eqs.(1) and (2) using reasonable guesses for the necessary parameters (for example, the slit width $a$ is on the order of a $100~\mu$m, the two slits are separated by several slit widths, laser wavelength is $\lambda = 650$~nm, and the distance between the slits and the viewing screen is $\ell \approx 50$~cm). 

What would happen if we increased or decreased $d$, $a$, $\lambda$ and $\ell$.  Record your observations, and use these insights in setting the initial parameters when fitting your experimental data.
  
\section*{2. Experimental parameters estimation}

The main objective of this lab is to observe particle-like behavior of photons. To verify that photons interfere with themselves, rather than with other nearby photons, we have to be sure that the rate of photons in this measurement is low enough that only one of them is in the vicinity of the double slit at any given time.  You need to work through the steps in the Appendix B ``Computing the photon rate'', roughly estimating the photon flux in the apparatus. In this pre-lab summarize the results of such estimation, including the numbers you calculate at each stage.  Write a nice bit of narrative text, not just a bunch of bullets with numbers.

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