Walker, Halliday & Resnick — Electromagnetic Waves: Problem 18

18 Rainbows from square drops. Suppose that, on some surreal world, raindrops had a square cross section and always fell with one face horizontal. Figure 33-36 shows such a falling drop, with a white beam of sunlight incident at \(\theta = 65.0^\circ\) at point P. The part of the light that enters the drop then travels to point A, where some of it refracts out into the air and the rest reflects. That reflected light then travels to point B, where again some of the light refracts out into the air and the rest reflects. What is the difference in the angles of the red light (\(n = 1.331\)) and the blue light (\(n = 1.343\)) that emerge at (a) point A and (b) point B? (This angular difference in the light emerging at, say, point A would be the rainbow's angular width.)