The rainbow

Sunlight arrives from the left in parallel rays; each enters the drop, reflects once off the back and leaves, turned through an angle. Drag the entry height b / R, how far from the drop's centre the ray comes in (R is the drop's radius), or press play to sweep it: the gold ray swings with it, the corner gives its deviation, the angle it is turned through, and the small graph at the right records that angle for every b / R. The least is about 138°, at b / R ≈ 0.86, and the graph is flat there: rays entering a little higher or lower leave in almost the same direction, so the many rays of the fan that enter around there all leave bunched about 42° from the direction back towards the sun. The gold arc measures that angle for the gold ray, from the dashed line pointing back towards the sun; near b / R = 0.86 it reads 42.1°. Switch to seven colours: each colour bends by a slightly different amount in water, so each has its own least angle and its own bunching direction; the red bow sits 42.5° from the direction back towards the sun and the violet 40.7°, red outside, violet inside.