small updates

1 files changed, 34 insertions, 6 deletions

diff --git a/faraday_prelab.tex b/faraday_prelab.tex
index 73a9931..dd9f1d7 100644
--- a/faraday_prelab.tex
+++ b/faraday_prelab.tex
@@ -5,16 +5,44 @@
 
 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}
+\section*{1. Check you understanding of polarized light}
 
-  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. Optimization of the measurement settings}
-Examine Eq.(4) to find the value of the angle $\theta$ that will provide maximum useful signal for measuring $\phi$.  
+\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*{3. Estimation of the expected Faraday rotation}
+
+\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:  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. 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?