Chapter 37, Problem 37.66AP

A plano-convex lens has index of refraction n. The curved side of the lens has radius of curvature R and rests on a flat glass surface of the same index of refraction, with a film of index n_flim between them, as shown in Figure P36.42. The lens is illuminated from above by light of wavelength λ. Show that the dark Newton’s rings have radii given approximately by

$r=\sqrt{\frac{m\lambda R}{n_{\text{film}}}}$

where r << R and m is an integer.

Figure P36.42