Rainbows
Sunlight entering a raindrop. Builds on Snell's Law & Refraction.
You’re standing with the Sun behind you, facing a rain shower. You see a beautiful rainbow arcing across the sky. The red band is on the outside and the violet band is on the inside.
At what angle from the anti-solar point (the point directly opposite the Sun) do you see the primary rainbow?
About 42°! This magic number comes from the geometry of a single raindrop. White light enters, refracts at the front surface, reflects off the back, and refracts again on exit. Due to the spherical shape, there’s a maximum deviation angle (minimum angle from the anti-solar point) where light concentrates — about 42° for red, 40° for violet. This is why rainbows are always the same size.
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Watch white light enter a single raindrop. See it refract, reflect internally, then refract again on exit. Different colors exit at slightly different angles — creating the rainbow!
θ = 4r - 2i (Descartes)
Maximizing θ (minimizing deviation from anti-solar point) gives the rainbow angle. Calculus shows this maximum occurs at about 42° for water with n = 1.33.
The secondary rainbow at 51° involves two internal reflections. Its colors are reversed (violet outside, red inside). The region between the two bows — Alexander’s dark band — is visibly darker.
You can never reach the end of a rainbow. The rainbow is always at 42° from YOUR anti-solar point, so it moves as you move. Every observer sees their own personal rainbow.
From an airplane, you can see the rainbow as a complete circle. On the ground, the Earth blocks the lower half (unless you’re on a hilltop with spray below).
Moonlight can create rainbows too! Moonbows are much fainter and appear white to the naked eye because moonlight is too dim to activate our color vision.
“Every raindrop sends every color in every direction. The rainbow is the angle where billions of drops happen to send the same color toward YOUR eyes — geometry painted in light.”
Rainbow Lab
Explore rainbow optics with a single raindrop and a sky full of rain. Trace light paths through the drop, see dispersion in action, and discover primary and secondary rainbows, Alexander’s dark band, and how different wavelengths create the color sequence.
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Watch a single ray trace through the raindrop. Now change the wavelength (color) and see how the exit angle shifts. Toggle the secondary rainbow on — notice the two internal reflections and reversed color order. Look for Alexander’s dark band between the two bows!
The rainbow isn’t at a fixed place in space — it’s an angle. Every raindrop sends all colors in all directions, but your eye only catches the color that exits at the right angle (42° for red, 40° for violet). Different drops send you different colors.