Question

A tanker leaks kerosene (n = 1.2) into the Persian Gulf, creating a large slick on top of the water (n = 1.3). (a) If you are looking straight down from an airplane onto a region of the slick where its thickness is 460 nm, for which wavelength() of visible light is the reflection the greatest? (b) If you are scuba-diving directly under this same region of the slick, for which wavelength() of visible light is the transmitted intensity the strongest.

Answer 1

(a) For the reflected rays, the condition for maxima is

The wavelength of visible light (for m = 2) is 552 nm.

(b) For the transmitted rays, the condition for maxima is

The wavelengths of visible light are 736 nm (when m = 1) and 441.6 nm (when m = 2). [For the transmitted rays an extra phase change of π is introduced in the ray AFBCG whereas no change of phase occurs in the ray AFH under the conditions stated in (b)].