diff options
Diffstat (limited to 'faraday_prelab.tex')
| -rw-r--r-- | faraday_prelab.tex | 40 |
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? |