A secondary rainbow is formed when the incident light undergoes two internal reflections in a spherical drop of water as shown in Fig. 33.20e.
(a) In terms of the incident angle θAa A and the refractive index n of the drop, what is the angu1ar deflection Δ of the ray? That is, what is the angle between the ray before it enters the drop and after it exits?
(b) What is the incident angle θ2 for which the derivative of Δ with respect to the incident angle θAa A is zero?
(c) The indexes of refraction for red and violet light in water are given in part (e) of Challenge Problem 33.66. Use the results of parts (a) and (b) to find θ2 and Δ for violet and red light. Do your results agree with the angles shown in Fig. 33.20e? When you view a secondary rainbow, is red or violet higher above the horizon? Explain.