deletions | additions       diff --git a/subsection_Slope_Method_The_direct__.tex b/subsection_Slope_Method_The_direct__.tex  index 195c0f5..56cd0fe 100644  --- a/subsection_Slope_Method_The_direct__.tex  +++ b/subsection_Slope_Method_The_direct__.tex 
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\subsection{Slope Method}  The direct fit method allowed us to find the angle of greatest sensitivity of the polarizer, which 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).  To verify the value of the Verdet constant, we used a second method where the polarizer stayed at the angle of greatest sensitivity, which is 45 degrees in our case. We got the angle by setting the second derivative of $\frac{dV}{d\theta}$ to zero, which corresponds to the inflection point. We then varied the current of the solenoid, going in 0.5A steps from -3A to 3A, thereby varying the magnetic field within the solenoid between -33.3 mT and +33.3 mT. We could then graph voltage vs magnetic field, which results in a linear graph as shown in Figure \ref{fig:VB}. The slope of the graph is $\frac{\Delta V}{\Delta B}$. We calculated $\frac{\Delta V}{\Delta \theta}$ previously, so we can find $\frac{\Delta B}{\Delta\theta}$ and therefore the Verdet constant. %Initially, we fit our data to the form $V=V_{0}(sin(\theta_{1}+\theta_{2}))^2$, which using trigonometry, is $V=V_{0}\frac{(1-cos(\theta_{1}+\theta_{2})^2)}{2}$ (the actual equation that we fit to). However, we should have been fitting to the form $V=V_{0}cos(\theta_{1}-\theta_{2})^2$, which is $V=V_{0}\frac{(1+cos(\theta_{1}-\theta_{2})^2)}{2}$. Now,   %$$sin(\theta_{1}+\theta_{2})^2=sin2(θ1-(-θ2))$$