Geometrical Optics of Rainbows
The ray-optics picture of refraction, reflection, and rainbow angles.
Geometrical optics gives the first clean explanation of the primary rainbow. Light enters a droplet, refracts, reflects once inside, and refracts again on the way out.
The key point is that the outgoing angle is not spread uniformly. Many nearby rays bunch near a particular deviation angle, which is why the rainbow appears bright along a well-defined arc instead of being smeared across the sky.
This post will focus on that ray picture and on the geometric origin of the rainbow angle.