Problem 5.183

A quartz plate cut parallel to its optical axis is placed between two crossed Nicol prisms so that their principle directions form an angle of $45^{\circ}$ with the optical axis of the plate. What is the minimum thickness of that plate transmitting light of wavelength $\lambda_{1}=643 \mathrm{nm}$ with maximum intensity while greatly reducing the intensity of transmitting light of wavelength $\lambda_{2}=564$ nm? The difference of refractive indices for extraordinary and ordinary rays is assumed to be equal to $n_{e}-n_{0}=0.0090$ for both wavelengths.