Rainbows

A rainbow is one of the most beautiful natural sights: a giant arch of seven colours across the sky after rain, when the Sun comes out. Rainbows are made by sunlight passing through millions of raindrops in the sky. Each raindrop acts like a tiny prism, bending the light and splitting it into the colours of the spectrum. To see a rainbow, you need three things: the Sun behind you, rain in front of you, and the Sun fairly low in the sky. Rainbows have inspired poets, painters, scientists and stories from cultures all over the world.

  • What it isSunlight split by raindropsInto a coloured arc
  • How many coloursSeven traditionallyROYGBIV
  • Best conditionsSun behind, rain in frontSun low in sky
  • Always at 42 degreesFrom the antisolar pointWhere Suns shadow points
  • Double rainbowTwo reflections in raindropOuter ring has reversed colours
  • From a planeCan see a full circleNot just an arc

How a rainbow forms

The cause of a rainbow is the way water bends and reflects light. Inside a raindrop:

  1. Sunlight enters the front of the raindrop, slowing down and bending (refracting) as it crosses from air into water.
  2. The light reflects off the back inner surface of the raindrop.
  3. It exits the front of the raindrop, refracting again as it returns to air.

At each refraction, the different colours of white sunlight bend by slightly different amounts. Red bends the least, violet the most. After leaving the raindrop, the colours are separated into a small spread of about 2 degrees.

You see millions of raindrops at slightly different angles in the sky. The drops at exactly the right angle send a particular colour to your eye. Drops at slightly different angles send a different colour. The result is a big band of colours: a rainbow.

Why an arch?

The geometry of the bending is precise: the rainbow always appears at 42 degrees from the antisolar point (the point in the sky directly opposite the Sun, where your shadows head points). Drops at any angle around that 42-degree cone send the rainbow colours to you.

When the Sun is low and the antisolar point is just below the horizon, you see most of the cone as a large arc reaching across the sky. When the Sun is high (above about 42 degrees), the antisolar point is too far below the horizon for any rainbow to be visible. That is why rainbows mostly appear in the early morning and late afternoon, never at noon (in summer at high latitudes).

From a plane, the antisolar point can be well below you, so you might see the full circle of a rainbow if conditions are right.

Fact Two people standing side by side actually see slightly different rainbows. Each one sees the light that happens to be at 42 degrees from their own antisolar point. The rainbows arc shifts a little for each viewer. No two people ever see exactly the same rainbow.

Order of the colours

The colours always appear in the same order, from outside to inside:

Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV).

Red is on the outside of the arc because it bends the least and so appears at the highest angle. Violet is on the inside because it bends the most. The actual colour band is continuous; the eye groups them into the familiar seven names.

Double rainbows

Sometimes a second, fainter rainbow appears above and around the main one. This is a double rainbow. It is caused by light that bounces TWICE inside each raindrop before coming out, instead of just once. The extra reflection reverses the order of the colours and spreads them further.

You can spot the differences:

  • The outer (secondary) rainbow has colours in reverse order (violet on top, red on bottom).
  • The outer rainbow is dimmer, because the extra reflection loses about 90 per cent of the light.
  • The sky between the two rainbows is noticeably darker than outside (called Alexanders dark band, named after a Greek scientist who first described it).

Other kinds of rainbow

  • Moonbow (lunar rainbow): a rainbow at night made by moonlight instead of sunlight. Very rare and faint, sometimes seen near waterfalls on a moonlit night.
  • Fogbow: a rainbow made by tiny fog droplets instead of raindrops. The drops are too small to split the colours clearly, so a fogbow is mostly white.
  • Mist or spray bow: rainbows produced by water spray from a hose or fountain in sunlight. You can make your own this way.
  • Ice halo and sundog: circular bows made by ice crystals high in the atmosphere, not raindrops.
  • Circumzenithal arc: a small, very bright rainbow high in the sky, also produced by ice crystals.
Did you know? Rainbows have inspired stories around the world. In Greek mythology, the rainbow was the goddess Iris, messenger of the gods. In Norse mythology, the rainbow Bifrost was the bridge connecting the world of humans to Asgard, home of the gods. In Irish folklore, a pot of gold is hidden at the end of every rainbow (but you can never reach it, because the rainbow always moves with you). Even modern scientists still find rainbows fascinating, with new research into how light interacts with raindrop shapes and sizes.

Why you can never reach a rainbow

A rainbow is not a physical object in a fixed place. It is a pattern of light that depends entirely on where you are standing. The 42-degree angle is measured from each individual viewer. When you move, the rainbow moves with you, always staying at the same angle to your own position. It is impossible to reach the "end" of a rainbow because the rainbow is at the end of your own viewing geometry.

Try this Stand outside on a sunny day with a garden hose. Stand with the Sun behind you and spray a fine mist into the air in front. You should see a small rainbow in your spray. Move the mist around and watch the rainbow track with you, always at the same angle. You have just made your own rainbow on demand. The same trick works with a fountain or a watering can.
Deeper dive: Newton, Descartes and the puzzle of the rainbow

The rainbow is so beautiful and recurring that scientists have tried to explain it for thousands of years. Aristotle thought it was a kind of cloud reflection. Medieval Arabic scholar Ibn al-Haytham (about 1000 AD) tried to study it but did not have enough mathematics.

The first complete explanation came from the French scientist Rene Descartes in 1637. He did a careful experiment by passing a beam of sunlight through a large glass sphere full of water (a giant artificial raindrop). He traced the path of light inside and worked out (using geometry) why the rainbow appears at exactly 42 degrees. He could even explain the secondary rainbow at 51 degrees, with its reversed colours, as caused by a second internal reflection.

What Descartes COULD NOT explain was why the rainbow has colours at all. He knew the rainbow always had the same order, but did not know why white sunlight gave rise to red, orange, yellow, green, blue and violet.

The answer came from Isaac Newton in the 1660s. Newton showed that white light is actually a mixture of all the colours, and that a prism (or a raindrop) refracts different colours by different amounts, separating them. He spent years on these experiments and published his results in Opticks (1704).

Combining Descartess geometry with Newtons colour theory finally gave a complete explanation of the rainbow: white light enters a raindrop, splits into colours by refraction, reflects off the inside of the drop, and exits with the colours fanned out to between 40 and 42 degrees. Two centuries later, James Clerk Maxwells theory of electromagnetism explained why light has different colours in the first place (different wavelengths). And in the 20th century, quantum mechanics added an even deeper explanation.

The next time you see a rainbow after a summer shower, you are seeing physics that took three of the worlds greatest scientists, working over 250 years, to fully explain. Pretty good for something that lasts only a few minutes in the sky.

For more, see refraction and the visible spectrum.