Rainbow figure shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflection (see Figure a). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation θ dev

(a) Show that θ dev is θ dev = 180? + 2θi - 4θr, where θ i is the angle of incidence of the ray on the drop and θ r, is the angle of refraction of the ray within the drop.

(b) Using Snell's law, substitute for θ r terms of θ i and the index of refractor n of the water. Then, on a graphing calculator or with a computer graphing package, graph θ dev versus θ i for the range of possible θ; values and for n = 1.331 for red light and n = 1.333 for blue light. The red light curve and the blue-light curve have different minima which mean that there is a different angle of minimum deviation for each color. The light of any given color that leaves the drop at that color's angle of minimum deviation is especially bright because rays bunch up at that angle. Thus, the bright red light leaves the drop at one angle and the bright blue light leaves it at another angle. Determine the angle of minimum deviation from the θ dev curve for

(c) Red light and

(d) Blue light.

(e) If these colors form the inner and outer edges of a rainbow (Figure a), what is the angular width of the rainbow?

Transcribed Image Text:

Water drop -0, Incident ray