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 indies 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 cm`. Determine the radius of the fifth dark Newton's ring in reflected light with wavelength `lambda = 0.50 mu m`.

Explanation

The condition for minima are
`(r^(2))/(R ) n_(2) = (k + (1)/(2)) lambda`,
(There occur phase changes at both surfaces on reflection, hence minima when path difference is half interger multiple of `lambda`).
In this case `k = 4` for the fifth dark ring
(Counting from `k = 0` for the first dark ring).
Thus, we can write
`r = sqrt((2K - 1) lambdaR//2n_(2)), K = 5`
Substituting we get `r = 1.17 mm`.