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 `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_(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)2theta`
Therefore, the transmitted intensity will be maximum when `theta=pi//4`