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A polaroid sheet is rotated in between t...

A polaroid sheet is rotated in between two crossed polaroids `P _(1) and P _(2)` At what ` theta` of pass axis of polaroid sheet with pass-axis of polaroid `P _(1)` must be kept so that the final intensity of transmitted light be maximum? (P = polaroid sheet axis)

A

`(pi)/(4)`

B

`(pi)/(6)`

C

`(pi)/(3)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Intensity of light after passing through `P_(1) " be " I_(0)`
`therefore` Intensity of light passing through P, i.e. `I_(P)= I_(0) cos^(2) theta`
Thus, Intensity of light passing through `P_(2)` will be
`I_(P_(2)) = (I_(0) cos^(2) theta) cos^(2) (90^(@)-theta)= I_(0) cos^(2) theta.sin^(2) theta = (I_(0))/(4) sin 2theta`
For maximum `I_(P_(2)) rArr sin 2 theta=1 therefore theta = (pi)/(4)`
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