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

Answer

B

Explanation

The intensity of transmitted light through `P_(1), I_(1)=(I_(0))/(2)`
The intensity of transmitted light through `P_(3)`
`I_(2)=I_(1)cos^(2)45^(@)=(I_(0))/(2)((1)/(sqrt(2)))^(2)=(I_(0))/(2)*(1)/(2)=(I_(0))/(4)`
Angle between polaroids `P_(3)` and `P_(2)=(90^(@)-45^(@))=45^(@)`
`:.` Intensity of transmitted light through `P_(2)`
`I_(3)=I_(1)cos^(2)45^(@)=(I_(0))/(4)((1)/(sqrt(2)))^(2)=(I_(0))/(8)`