Problem 5.181

White natural light falls on a system of two crossed Nicol prisms having between them a quartz plate \(1.50 \mathrm{~mm}\) thick, cut parallel to the optical axis. The axis of the plate forms an angle of \(45^{\circ}\) with the principal directions of the Nicol prisms. The light transmitted through that system was split into the spectrum. How many dark fringes will be observed in the wavelength interval from 0.55 to \(0.66 \mu \mathrm{m}\) ? The difference of refractive indices for ordinary and extraordinary rays in that wavelength interval is assumed to be equal to 0.0090 .