After a heavy summer shower, the air turns unusually clear. The smell of rain rises off the wet asphalt, the clouds break, and sunlight slants down. Look up at the right moment and a rainbow hangs on one side of the sky. Stare at it for a few seconds and the question comes on its own. Where do these bands of color come from?
Rainbows don't show up on demand. The best window is that short stretch before the rain fully stops, when drops are still falling on one side of the sky while the sun is already out on the other. Bigger drops split the colors more strongly, which is why a rainbow right after a downpour looks far more vivid than one in a drizzle. With some luck, you'll also spot a second, fainter bow outside the first.
A rainbow is sunlight split apart by water droplets
Sunlight looks white, but it carries many colors at once. Normally they travel mixed together, so we just see brightness. They only become visible as separate bands when something sends each color down a slightly different path. That something is water droplets floating in the air. Right after a shower, the sky holds countless tiny droplets. Sunlight bends as it enters each one, reflects off the inside, and comes back out, and along the way the colors spread apart. Nothing solid is hanging in the sky. A rainbow is just that split light, gathered by your eyes from one particular direction.
Every droplet works like a tiny prism
When light passes from air into water, or from water back into air, its path bends at the boundary. That bending is called refraction. The catch is that each color bends by a slightly different amount. Reds bend less, blues and violets bend more. So when sunlight enters a droplet, it bends once going in, bounces off the back wall, and bends again coming out, and the colors fan out like a spread of cards. A glass prism does the same thing when it throws a colored band across a table. Every droplet in the sky is a miniature prism, and the rainbow you see is the combined work of a huge number of them.
That's why the sun has to be behind you
You may have heard that you need the sun at your back to see a rainbow. The reason is simple: the light that enters a droplet reflects off the inside and comes back toward you. Sunlight travels from behind you into the droplets, turns around inside them, and returns to your eyes. So a rainbow always appears directly opposite the sun, in the part of the sky your shadow points to. That's also why morning rainbows hang in the western sky and late-afternoon rainbows in the east. Face the sun and you won't see one, no matter how much water is in the air.
The arc exists because color only gathers at one angle
The light coming back out of the droplets doesn't scatter in every direction. It concentrates most strongly at about 42 degrees away from the point directly opposite the sun. Red gathers slightly toward the outside of that angle, violet slightly toward the inside. Connect every point that sits at 42 degrees and you get a circle. The rainbow curves because only the droplets at that exact angle can send color to your eyes. The ground blocks the lower half, so you usually get a semicircle at most. The lower the sun sits, the taller and rounder the arc looks. If the sun climbs higher than 42 degrees above the horizon, the whole arc sinks below it. That's the reason midday rainbows are so rare. From a mountaintop or an airplane window, with nothing in the way, a rainbow can appear as a complete circle.
A double rainbow means the light bounced twice
Sometimes a fainter rainbow appears outside the bright one. That outer bow forms when light reflects twice inside the droplets. The extra reflection pushes the exit angle out to about 51 degrees and flips the color order, so the inner bow is red on the outside while the outer bow is red on the inside. Each reflection costs some light, so the second bow is always dimmer. Between the two bows sits a strip of sky that is noticeably darker, called Alexander's dark band after the Greek philosopher who first described it about 1,800 years ago. Droplets can't send light into the gap between those two angles, so it's a genuine shadow.
Knowing how it all works doesn't make a rainbow any less strange. A rainbow is built around the position of your own eyes, so the person standing next to you is seeing light from a different set of droplets. Under the same sky, each of us is watching our own private rainbow. Maybe that's why we keep looking up at it.
Thanks for reading.
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