A rainbow feels like the most solid, locatable thing — a great coloured arch that seems to land in a specific field, with a pot of gold at the end. And yet you can never reach it, never walk under it, never photograph the exact same one your friend is seeing beside you. That is because a rainbow is not, in any real sense, there. It is an optical event assembled fresh in the air for each observer, out of sunlight, water droplets, and geometry. Here is how it is built.

It starts with light bending

The whole phenomenon rests on a property of light called refraction. When light passes from one transparent material into another — from air into water, say — it changes speed, and that change makes it bend. You can see the effect any time a straw looks “broken” where it enters a glass of water.

Crucially, different colours bend by different amounts. As we have known since Newton, white sunlight is a blend of every colour, each with its own wavelength, and when that light bends, the shorter wavelengths (toward violet) bend a little more than the longer ones (toward red). A glass prism exploits this to fan white light out into a spectrum. A rainbow is nature doing exactly the same thing, using millions of tiny spheres of water as prisms.

What happens inside a single raindrop

To understand the whole arc, follow a single ray of sunlight into a single spherical raindrop.

First, the ray strikes the surface of the drop and refracts as it enters, bending and beginning to separate into its colours. Then it travels across the inside of the drop and hits the far, back surface. There, much of it reflects off the inner wall, like light bouncing off the inside of a curved mirror, and heads back toward the front of the drop. Finally, as it exits the drop into the air, it refracts a second time, bending and spreading the colours even further apart.

So each droplet does three things to the light in quick succession: refract, reflect, refract. The combined effect is to take incoming white sunlight and send it back out, fanned into a spectrum — but only within a specific, narrow range of angles.

The magic angle of 42 degrees

This is the detail that explains a rainbow’s shape and its stubborn refusal to be approached. When you work through the geometry, the light leaving a raindrop comes out most intensely at an angle of about 42 degrees relative to the line running from the Sun, through you, to the point directly opposite the Sun. (Each colour peaks at a slightly different angle — red at roughly 42°, violet a little under 41° — which is what spreads the band into separate colours.)

What this means is that you only see the coloured light from a raindrop if that drop sits at just the right angle from your eye. Drops too high or too low send their light somewhere else, missing you entirely. The set of all the points in the sky that happen to lie at that special 42-degree angle from your line of sight forms a circle — and the rainbow you see is simply the arc of that circle filled in by raindrops.

Why it is an arc, and why it is yours alone

That circular geometry has two beautiful consequences.

First, a rainbow is genuinely circular, not an arch. We usually see only the top half because the ground gets in the way — there are no raindrops below the horizon to complete the lower part of the ring. But from an aeroplane or a high cliff, with rain and sun arranged correctly, you can see a rainbow as a full circle. The “arch” is just the part of the circle that fits above the landscape.

Second, and more wonderful: the rainbow is built around the antisolar point, which depends entirely on where your eyes are. The exact set of droplets bending light to your eye is different from the set bending light to the person standing next to you. You are each seeing your own private rainbow, made from different raindrops. And this is why you can never reach the end of one — as you move, the geometry moves with you, the 42-degree circle keeps its position relative to your eye, and the rainbow glides away. There is no fixed location, so there can be no pot of gold.

The order of the colours, and the second bow

The colours always run in the same order in a primary rainbow: red on the outer edge, then orange, yellow, green, blue, and violet on the inside. That order is fixed by the geometry — red, bending least, emerges at the wider 42-degree angle and lands on the outside of the band, while violet sits on the inner edge.

Look carefully after a strong shower and you may spot a fainter secondary rainbow arcing above the main one, with its colours reversed — red on the inside, violet on the outside. This second bow comes from light that reflected twice inside each raindrop before exiting. The extra bounce flips the colour order and sends the light out at a larger angle (around 51 degrees), placing the secondary bow higher in the sky. The double reflection also loses more light, which is why the second bow is always dimmer.

There is even a name for the dark band of sky often visible between the two bows — Alexander’s band — caused by the simple fact that almost no light is scattered back to your eye at the angles between the primary and secondary arcs.

Rainbows everywhere, once you know how to look

Because all a rainbow needs is sunlight and droplets at the right angle, you can find them far from any storm. The mist from a garden hose, the spray at the base of a waterfall, the fine droplets thrown up by a lawn sprinkler — any of these can produce a small, personal rainbow if you stand with the Sun behind you and look toward the spray at the correct angle. The recipe never changes: light source behind you, water droplets in front, and your eye at the centre of the geometry.

The short version

A rainbow forms when sunlight enters spherical raindrops, refracts and splits into colours, reflects off the back of each drop, and refracts again on the way out — emerging most strongly at about 42 degrees. Because only the droplets sitting at that precise angle from your eye send their colour to you, the result is a circle of light centred on the point opposite the Sun, of which we usually see only the upper arc.

It is, in the most literal sense, a trick of the light — and one that belongs to you alone. The rainbow your friend is admiring beside you is a different rainbow entirely, woven from different drops. Knowing that does not make it less beautiful. If anything, it makes that fleeting arch in the sky feel a little more like it was put there just for you.