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Alisha Vira deleted Suppose_then_that_the_original__.tex
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Suppose then that the original angle of polarization of the light emitted from the laser is $\theta_0$, the change in polarization angle due the application of the magnetic field (as the light passes through a rod-shaped material) is $\Delta \theta(B) = C_v L B$, the angle of the polarization of the light after passing through the rod is $\theta_1 = \theta_0 + \Delta \theta$, and the angle of the second polarizer though which the polarized light passes before being detected by the photodiode (but after exiting the rod) is $\theta_2$.
Then, as noted by \cite{Melissinos_2003} if the voltage output from the photodiode $V_{\textrm{ pd}}$ is proportional to the light intensity, the photodiode response is given by
\begin{equation}
\label{eq:Diode_Response}
V_{\mathrm{pd}}(B) = V_0 \cos^2[\phi(B)]
\end{equation}
and the photodiode sensitivity $\eta$ = $dV_{pd}/dB$ is given by
\begin{eqnarray}
\eta & = & - 2 V_0 \cos[\phi]\sin[\phi] \frac{d\phi}{dB} \\
& = & -V_0 \sin[2\phi] \frac{d\phi}{dB} \\
& = & + c_V LV_0 \sin[2\phi] \\
\end{eqnarray}
since $\phi = \theta_{2} - \theta_{1} = \theta_{2} - \left(\theta_0 + \Delta \theta(B)\right)$.
An example of a fit to Eq.~\ref{eq:Diode_Response} is shown in Fig.~\ref{fig:PolarizationDataAtZeroField}
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Abstract.tex
Introduction.tex
Ordinary text and paragraphs.tex
Suppose_then_that_the_original__.tex
Math symbols.tex
Displayed equations.tex
Figures.tex