Problem 5.92

The spherical surface of a plano-convex lens comes into contact with a glass plate. The space between the lens and the plate is filled up with carbon dioxide. The refractive indices of the lens, carbon dioxide, and the plate are equal to $n_{1}=1.50, n_{2}=1.63$, and $n_{3}=1.70$ respectively. The curvature radius of the spherical surface of the lens is equal to $R=100 \mathrm{~cm} .$ Determine the radius of the fifth dark Newton's ring in reflected light with wavelength $\lambda=0.50 \mu \mathrm{m}$