Two polaroids are placed in the path of unpolarized beam of intensity `I_(0)` such that no light is emitted from the second polarid. If a third polaroid whose polarization axis makes an angle `theta` with the polarization axis of first polaroid, is placed between these two polariods then the intensity of light emerging from the last polaroid will be

Options

A. `((I_(0))/(8))sin^(2)2theta`
B. `((I_(0))/(4))sin^(2)2theta`
C. `((I_(0))/(2))cos^(4)theta`
D. `I_(0)cos^(4)theta`

Answer

A

Explanation

As no light is emitted from the second polaroid, so `P_(1)` and `P_(2)` are perpendicular to each other.
Intensity after pass from `P_(1), I_(1)= (I_(0))/(2)`
Intensity after pass from `P_(3), I_(2)= I_(1) cos^(2)theta= (I_(0))/(2) cos^(2) theta`
Intensity after `P_(2)` i.e, final intensity
`I= I_(2) cos^(2)(90-theta) implies (I_(0))/(2) cos^(2) sin^(2)theta`
`implies (I_(0))/(8) (2sinthetacostheta)^(2)= (I_(0))/(8) sin^(2) 2theta`