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 forst polariser `P_(1)` . Then the intensity of light after passing through second polariser `P_(2)` will be `I = I_(0) cos^(2) theta `, where `theta` is the angle between pass axes of `P_(1) and P_(2) ` . Since `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`