Question

A quartz plate cur parallel to the optical axis placed between two crossed Nicol prisms. The angle between the principal directions of the Nicol prism and the plate is equal to `45^(@)`. The thckness of the plate is `d = 0.50mm`. At what wavelengths in the interval from `0.50` to `0.60 mu m` is the intensity of light which passed through that system independent of rotation of the rear prism? The difference of refractive indices for ordinary and extraordinary rays in that wavelength interval is assumed to be `Deltan = 0.0090`.

Answer 1

As in the previous problem the quartz plate introduces a phase difference `delta` between the `O & E` components. When `delta = pi//2` (modulo `pi`) the resultant wave is circularly polarized. In this case intensity is independent of the rotation of the rear prism. Now
`delta = (2pi)/(lambda) (n_(e) - n_(0)) d`
`= (2pi)/(lambda)0.009 xx 0.5 xx 10^(-3) m`
`= (9pi)/(lambda),lambda`in `mu m`
For `lambda = 0.50mu m. delta = 18 pi`. The relevent values of `delta` have to be shosen in the form
`(k +(1)/(2))pi`. For `k = 17, 16, 15` we get
`lambda = 0.5143mum, 0.5435mu m` and `0.806 mu m`
These are the values f `lambda` which lie between `0.50 mu m` and `0.60mum`.