Rainbows from square drops. Suppose that, on some surreal world, raindrops had a

Question

Rainbows from square drops. Suppose that, on some surreal world, raindrops had a square cross section and always fell with one face horizontal. The figure shows such a falling drop, with a white beam of sunlight incident at = 70.60 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 = 1.330) and the blue light (n 1.334) that emerge at (a) point A and (b) point B? (This angular difference in the light emerging at, say point A would be the angular width of the rainbow you would see were you to intercept the light emerging there.) (a) Number Units Units (b) Number

Explanation / Answer

a) From snell's law

theta2 = sin-1[(1/1.334) * sin 70.6] = 44.99 deg

theta2r = sin-1[(1/1.330) * sin 70.6] = 45.17 deg

For second refractions

theta2b = sin-1[1.334 * sin (90 - 44.99)] = 70.64 deg

theta2r = sin-1[1.330 * sin (90 - 45.17)] = 69.66 deg

70.64 deg - 69.66 deg

= 0.98 deg

b) Both refracted rays emerge same angle 70.6 deg

no difference

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