Monochromatic light with circular polarization falls normally on a crystalline plate cut parallel to the optical axis. Behind the plate there is a Nicol prism whose principle direction froms an angle `varphi` with the optical axis of the plate. Demonsrate that the intensity of light transmitted through that system is equal to
`I = I_(0) (1 + sin2varphi. sin delta)`,
where `delta` is the phase difference between the ordianry and extraordinary rays which is introduced by the plate.

Explanation

Let the circularly polarized light be resolved into plane polarized components of amplitude `A_(0)` with a phase difference `(pi)/(2)` between then.
On passing through the crystal the phase difference becomes `delta + (pi)/(2)` and the components of the `E` and `O` wave in the direction `N` are respectively
`A_(0)cos varphi` and `A_(0) sin varphi`
They interfere to produce the amplitude squared
`R^(2) = A_(0)^(2) cos^(2) varphi + A_(0)^(2) sin^(2) varphi + 2A_(0)^(2) cos varphi sin varphi cos (delta + (pi)/(2))`
`= A_(0)^(2) (1+sin 2 varphi sin delta)`
Hence `I =I_(0) (1+ sin 2 varphi sin delta)`
Here `I_(0)` is the intensity of the light transmitted by the polaroid when there is no crystal plate.