Solved: A secondary rainbow is formed when the incident

Chapter 33, Problem 33.61

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A secondary rainbow is formed when the incident light undergoes two internal reflections in a spherical drop of water as shown in Fig. 33.19e. (See Challenge 33.60.) (a) In terms of the incident angle u A a and the refractive index n of the drop, what is the angular deflection 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 u2 for which the derivative of with respect to the incident angle u A a is zero? (c) The indexes of refraction for red and violet light in water are given in part (e) of Challenge 33.60. Use the results of parts (a) and (b) to find u2 and for violet and red light. Do your results agree with the angles shown in Fig. 33.19e? When you view a secondary rainbow, is red or violet higher above the horizon? Explain.