Two polaroids A and B are kept in crossed position. How should a third polaroid C be placed between them so that the intensityof polarised light transmitted by polaroid B reduces to 1/8 th of the intensity of upolarised light incident on A?

Explanation

Intensity of incident light = `I_(0)`
Intensity of light after passing through polaroid
`A = (I_(0))/(2)`
Intensity of light after passing through polaroid
`C = (I_(0))/(2) cos^(2) theta`
where, `theta` be the angle between the pass axis of A and C polaroid.
`therefore` Intensity of light after passing through B,
I = `(I_(0))/(2) cos^(2) theta cos^(2) (90^(@) - theta) = (I_(0))/(8)sin^(2) 2theta`
`If I = (I_(0))/(8),`then `sin^(2)2theta = 1 or, theta = 45^(@)`
So the polaroid C should be placed making an angle `45^(@)` with the pass axis of polaroid A.