Chapter 24, Problem 61GP

A lens in a liquid. A lens obeys Snell s law, bending light rays at each surface an amount determined by the index of refraction of the lens and the index of the medium in which the lens is located. (a) Equation 24.20 assumes that the lens is surrounded by air. Consider instead a thin lens immersed in a liquid with refractive index n_liq. Prove that the focal length f is then given by Equation 24.20 with n replaced by n/n_liq. (b) A thin lens with index n has focal length f in vacuum. Use the result of part (a) to show that when this lens is immersed in a liquid of index n_liq, it will have a new focal length given by

$f\prime =\left[\frac{n_{\text{liq}}(n-1)}{n-n_{\text{liq}}}\right]f$.