Two Polaroids `P_(1)` and `P_(2)` are placed with their axis perpendicular to eachother. Unpolarised light `I_(0)` is nicident on `P_(1)`. A third polaroid `P_(3)` is kept in between `P_(1)` and `P_(2)` such that its axis makes an angle `45^(@)` with that of `P_(1)`. The intensity of transmitted light through `P_(2)` is

Answer

`3 I_(0)//32`

Explanation

Intensity of polarised light from `P_(1) = I_(0)//2`
Intensity of polarised light from `P_(3)`
`= ((I_(0))/(2)) cos^(2) 60^(@) = (I_(0))/(8)`
Intensity of Polarised light from `P_(2)`
`= (I_(0))/(8) cos^(2) (90^(@) - 60^(@)) = (I_(0))/(8) (sqrt(3)//2)^(2) = (3 I_(0))/(32)`