Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?

Explanation

Let `I_(0)` be the intensity of polarised light after passing through the first polariser P1. Then the intensity of light after passing through second polariser P2 will be
`I=I_(0)cos^(2)theta.`
Where `theta` is the angle between pass axes of `P_(1) and P_(2)`. Since `P_(1) and P_(3)` are crossed the angle between the pass axes of `P_(2) and P_(3)` will be `(pi//2-theta)`. Hence the intensity of light emerging from `P_(3)` will be
`I=I_(0)cos^(2)theta cos^(2)((pi)/(2)-theta)`
`=I_(0) cos^(2) theta sin^(2) theta =(I_(0)//4) sin ^(2)2 theta`
Therefore, the transmitted intensity will be maximum when `theta=pi//4.`