What Physical Parameters Do the Slope and Y-Intercept Represent in Malus's Law?

[shawonna23]

From plotting a graph of Intensity vs. relative angle, there was a linear relationship. From this graph in Graphical Analysis, we obtained a slope (m) and a y-intercept (b). We then have to look at the original expression for the Law of Malus. My question is: What physical parameters do the slope and y-intercept represent?

 

[CarlB]

This is a tough one to answer. Malus's law is

$$I = I_0\; \cos^2(\theta)$$

so you can't possibly be getting a linear relationship over a wide range of angles.

I'm going to guess that in setting up this problem, they had you run the experiment with an angle of around 45 degrees. That is where you get the maximum change in intensity per change in angle.

To figure out what physical parameters slope and intercept represent, try taking the Malus law, differentiating it with respect to theta, and solving for m and b in terms of I and I_0, maybe.

Carl