According to Descartes? theory of the formation of the rainbow, a ray of sunlight is refracted as it enters a spherical raindrop, undergoes a single internal reflexion, and is then refracted as it leaves the drop, as shown in figure.

The rainbow is formed from the rays whose deviation from the original direction is either maximum or minimum. Show that the rainbow should form an arc of radius 42^o round the point opposite to the Sun, and that it should have a width of approximately 1.6^o with the red part on the outside. (The refractive index of water is 1.330 for red light and 1.341 for violet light.)