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Ning Zhu edited subsection_Direct_Fit_Method_We__.tex
over 8 years ago
Commit id: 1dbd888c99b9085acd4436b69fd6828630a6af0d
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diff --git a/subsection_Direct_Fit_Method_We__.tex b/subsection_Direct_Fit_Method_We__.tex
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--- a/subsection_Direct_Fit_Method_We__.tex
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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:
$$V_{c}=20.96\pm 0.2650\frac{radians}{T \cdot m}$$