Each colour bends by a slightly different amount because the refractive index of water rises for shorter wavelengths (red n≈1.331, violet n≈1.343). For one internal reflection the total turn-around angle has a minimum near 138° — rays pile up at that angle (a caustic) and spread out by colour there: 180° − 138° = 42° back toward the Sun's direction. Violet bends more, so it sits inside the bow (40.6°) and red outside (42.4°).

Try sliding the impact parameter: near 0.86 the outgoing rays crowd together — that crowding is the rainbow. Move to ~0.95 with two internal reflections and you get the dimmer secondary bow at ~51° with the colours reversed. The dark gap between the two is Alexander's band (named ~200 AD).

No two people see the same rainbow: it is centred on the shadow of your head (the antisolar point), so walk toward it and it walks too. Full circles appear from aircraft; Moonbows are the same physics 1/1000 as bright.