The Hidden Geometry of a Rainbow
You don't have to wait for rain to see a rainbow. Pick a sunny afternoon, grab a garden hose, and you can make your own in about a minute.
The recipe
Stand with the Sun behind you — a low sun, like late afternoon, works best. Set the hose to a fine mist and spray it into the air ahead of you. Now look at the mist at a slightly downward angle, off to the side of your own shadow, and sweep your gaze slowly. At one particular spot, colors snap into view.
That "particular spot" is the whole secret, and it's the same every time: about 42 degrees away from the point directly opposite the Sun — which is the shadow of your own head.
What each droplet does
A rainbow is assembled one raindrop at a time. Inside each drop, sunlight:
- Refracts — bends as it crosses into the water.
- Reflects once off the inside of the drop's back surface.
- Refracts again on the way out, heading roughly back toward the Sun.
Because the drop bends different colors by slightly different amounts — red the least, violet the most — the colors leave at slightly different angles. Red exits at about 42°, violet at about 40°, and the rest fall in between. That's why the order is always identical: red on the outer edge of the arc, violet on the inside.
Why it's a circle (and why you can't reach it)
Every droplet sitting at 42° from that antisolar point sends its light to your eye; drops nearer or farther don't. Connect all the qualifying droplets and they trace a circle — a cone of light with your eye at the tip. The ground usually slices it into an arc, but from a plane or a high cliff you can sometimes see the whole ring.
This is also why the end of the rainbow keeps retreating:
A rainbow isn't an object sitting in a field. It's an angle, measured from your eye. Step toward it and the entire geometry travels with you — the droplets at 42° are simply different droplets now. The person beside you sees a slightly different rainbow, built from different drops. There's no end, and no pot of gold, because there's no there there.
Bonus round
Look above a bright rainbow for a fainter second one, with its colors reversed. That's light that bounced twice inside each drop, emerging near 51°. The band of darker sky between the two bows even has a name: Alexander's dark band.
None of this is the same as why the daytime sky glows blue — that's light scattering off molecules far tinier than a drop. Nor is it the interference that gives a soap bubble its shifting colours, where light bounces off a film thinner than a single wavelength. A rainbow comes from bending and bouncing inside drops big enough to act like little lenses. Same Sun, three different tricks of the light.