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

`I_(2)=I_(1) cos^(2) theta=I_(0)/2 cos^(2) theta`
`I_(3)=I_(2) cos^(2) (90-theta)=I_(0)/2 cos^(2) theta sin^(2) theta`
`=I_(0)/8(2 sin theta cos theta)^(2)=I_(0)/8(sin 2theta)^(2)`