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\subsection{Direct Fit Method}  We plot the photodiode voltage versus angle of the polarizer with and without a magnetic field applied as shown in figure \ref{fig:directmethoddata}. It can be seen from the graph that the curve shifts a little bit, which is a direct result of the magnetic field. By applying curve fit to our data points, we find the phase shift between two curves is 4 degrees($d\theta$). We got 45 degrees after applying trigonometry to our previous fits since we used $cos$ function instead of $cos^2$ to fit our data in \ref{fig:directmethoddata}. This value is consistent with the value we got when we set the second derivative of $\frac{V}{\theta}$ to zero (the inflection point).  The current provided to induce a magnetic field is -3A, which can be translated to dB using equation \ref{magneticfield}. With these numbers, we are able to calculate Verdet constant using equation : \begin{equation}  c_v=\frac{1}{L}\frac{d\theta}{dB}  \end{equation}  where L is the length of the solenoid, which is 0.1m in our case.\newline  The direct fit method allowed us to find the angle of greatest sensitivity of the polarizer by looking at the shift in phase as shown in Figure \ref{fig:directmethoddata}. We got 45 degrees after applying trigonometry to our previous fits since we used $cos$ function instead of $cos^2$ to fit our data in \ref{fig:directmethoddata}.   %which is the point of inflection on the $V$ vs $\theta$ graph.   This value is consistent with the value we got when we set the second derivative of $\frac{V}{\theta}$ to zero (the inflection point). \newline  We can't guarantee that we turn the polarizer to the angel we want exactly, and we estimate there will be an uncertainty of 0.05 degrees in d$\theta$. By plugging in the maximum(4.05 degrees) and minimum(3.95 degrees) into our calculation, we are able to get an uncertainty of the Verdet constant.  In this way, we get:  $$V_{c}=20.96\pm 0.2650\frac{radians}{T \cdot m}$$