Wave Optics of Rainbows

Ray optics explains the main bow, but it does not explain everything we actually see. In particular, it misses the fine intensity oscillations that can appear just inside the primary rainbow.

Those extra bands are a wave effect. Once light is treated as a coherent wave field rather than as isolated rays, interference becomes unavoidable, and the rainbow develops a richer structure.

This post will move from the ray picture to the wave picture and show what changes when phase is included.