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

Options

A. `(I_(0))/(2)`
B. ` (I_(0))/(4)`
C. ` (I_(0))/(8)`
D. ` (I_(0))/(16)`

Answer

C

Explanation

`I_(2)=(I_(0))/(2) cos^(2) 45^(@)`
`=(I_(0))/(2)xx (1)/(2)`
` =(I_(0))/(4)`
` I_(3)=(I_(0))/(4) cos^(2) 45^(@)`
`I_(3)=(I_(0))/(8)`