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\documentclass[./manual.tex]{subfiles}
\begin{document}
\chapter*{Faraday Rotation - 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. Check you understanding of polarized light}
\begin{figure}[h]
\centering
\includegraphics[width=0.8\linewidth]{./pdf_figs/faraday_polarizers.jpg}
\caption{Different combinations of polarizers. The angle between
polarizers is $0^\circ$ (case A), $45^\circ$ (case B), and $90^\circ$ (case C).}
\label{fig:faraday_polarizers}
\end{figure}
In the figure~\ref{fig:faraday_polarizers} a laser beam is passing through
two polarizers. Their polarization axes are shown as arrows. For each case,
how much of the initial intensity of the beam, $I_0$, is still present
after it has passed through both polarizers? You should estimate the rather
common angles that are shown. Answer for each case by stating your
estimated angle and also the numerical value of the intensity, assuming
$I_0 = 1.0$.
% \subsection*{Theoretical graph}
% Plot the expected dependence of the output intensity as a function of the angle $\theta$ between two polarizers, using Eq.(1). Estimate the number of points you need to take to reliably reproduce this curve in the experiment.
\section*{2. Estimation of the expected Faraday rotation}
Using Eq.(2) roughly estimate the value of the expected rotation angle for $B\approx 10$~mT. Check on-line sources to find a reasonable value for $C_V$ for glass.
\section*{3. Optimization of the measurement settings}
Examine Eq.(4) to find the value of the angle $\theta$ that will provide
maximum useful signal for measuring $\phi$.
Hint 1: Every time I hear maximum or minimum, I think about derivatives.
Hint 2: If you are having trouble, try this: for each of the angles in
question 1 compute the numerical value of the two terms in equation 4,
assuming $I_0=1.0$, and your value of $\phi$ from part 2. Is the intensity
$I$ in equation 4 sensitive to the value of $\phi$ for each of those angles? Compute
for other angles of your choice. How do we adjust $\theta$ to maximize the
useful signal?
\section*{4. The source of polarization}
The previous questions assumed that there are two polarizers in the system.
But, figure 2 in the manual shows only one. This experiment cannot work
with just one polarizer. So, where is the other one?
Hint: read the lab manual carefully.
% \section*{5. Error analysis}
% In this experiment you will be determining the error in the amplitude of an oscillating signal using its digitized form, recorded by an oscilloscope. A sample yellow trace, shown in Fig.(3), depicts the change in the signal voltage as a function of time. What would be a good measure of the uncertainty in its amplitude for such a measurement?
\end{document}
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