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) sin^(2) theta=((I_(0))/4)sin^(2) 2 theta`
Therefore the transmitted intensity will be maximum when
`theta=(pi)/4`