Chapter 48: Problem 5

Question: Three polarizing plates are stacked. The first and third are crossed, the one between has its axes at $\theta~=~45^o$ to the axes of the other two. What fraction of the intensity of an incident unpo9larized beam is transmitted by the stack.

Solution: Sequentially applying Malus law, we have

$$I_3~=~I_2\cos^2\left({\pi\over 4}\right)~=~I_1\cos^4\left({\pi\over 4}\right) ~=~{1\over 2}I_0\cos^4\left({\pi\over 4}\right)~=~{1\over 8} I_0$$