Are Rainbows Actually Full Circles?

Yes. Every rainbow is a complete circle, and the ground is the only reason you usually see an arc. A rainbow forms at a fixed angle, about 42 degrees, all the way around the point in the sky directly opposite the sun. From ground level that point is below the horizon, so the lower part of the ring is cut off by the earth. Get high enough, on a mountain, in a plane, or looking down from a cliff into mist, with the sun behind you and water droplets in front, and the whole circle appears. Pilots see them often. Very occasionally, so does someone standing in a garden with a hose.

• Every rainbow is a full circle about 42 degrees across, centred on the point opposite the sun.
• The ground hides the bottom half; from a plane or with a hose at your feet, the ring closes.
• You cannot reach the end of a rainbow because it is a direction, not a place.
• Red is on the outside because water bends short wavelengths more than long ones.

Here is why it is a circle in the first place.

Because of a single angle. Sunlight enters a raindrop, bends, reflects off the back of the drop, bends again on the way out, and emerges concentrated at an angle of roughly 42 degrees from the direction it came in. Every drop does this. So every drop that happens to sit 42 degrees away from the line running from the sun through your eye sends light back to you, and the set of all such points is a circle around that line. The centre of the circle is the antisolar point, the spot directly opposite the sun, which is where the shadow of your own head falls. The rainbow is the rim of a cone with its tip at your eye. That is why it is always a circle, why it is always the same size, and why it moves when you do.

Because the antisolar point is as far below the horizon as the sun is above it. When the sun is 20 degrees up, the centre of the rainbow is 20 degrees down, and a circle of radius 42 degrees around that centre pokes 22 degrees above the horizon. That is your arc. The lower the sun, the higher the centre, and the more of the circle you see: a sunset rainbow can be a huge, tall semicircle. When the sun is higher than 42 degrees, the whole circle is below the horizon and you see no rainbow at all, which is why you almost never see one in the middle of the day.

Get the ground out of the way. From an aircraft window with the sun on the opposite side and cloud or rain below, a full ring sometimes appears on the cloud tops, often small, sometimes with the plane's shadow at its centre. From a high ridge looking down into a misty valley, the same. Closer to home, stand with your back to a low sun and spray a fine mist from a hose in front of you and slightly below: if the droplets fall low enough, the arc curves round and closes into a ring at your feet. It is the same rainbow. You have simply supplied the raindrops where the ground usually is.

Because it does not have one, and because it is not in a place. A rainbow is not an object hanging in the sky at some distance. It is a direction: the set of directions, 42 degrees from the antisolar point, along which light comes back to your eye from whatever droplets happen to be there. Walk towards it and the antisolar point walks with you, because it is defined by your own position. The rainbow keeps its distance perfectly, like your shadow. There is no pot of gold because there is no ground it touches.

No. Two people standing side by side see two different rainbows, each centred on their own antisolar point, made by different raindrops. They look the same because the geometry is the same, but the light reaching your eye from your rainbow came from drops a few metres from the ones lighting hers. Photograph a rainbow and the camera records its own, from the lens's position. A rainbow is one of the few things in the world that is genuinely personal to the viewer, and the reason is that it is made in your eye rather than in the sky.

Because 42 degrees is the maximum angle, not the only one. Drops send back some light at every angle smaller than 42 degrees too, all colours mixed together as white, so the whole disc inside the bow is faintly brighter than the sky outside it. The bow itself is where the light piles up at the edge, and the colours separate there because each wavelength has its own maximum angle: red at about 42 degrees, violet at about 40. That is why red is on the outside of a primary rainbow and violet on the inside. A second, fainter bow sometimes appears outside the first at about 51 degrees, from light that reflected twice inside each drop, with its colours reversed. The dark band between the two is called Alexander's band, and it is the region no drop can send light into.

Because water bends short wavelengths more than long ones. This is dispersion, the same effect a glass prism uses, and the refraction and reflection article explains it. Each drop is a tiny prism and mirror combined, and the circle you see is dispersion drawn around the whole sky. The colours run red, orange, yellow, green, blue, violet and then stop, because violet is the shortest wavelength your eye can see. There is no purple in it, for reasons the no purple in the rainbow article sets out.

You can make the colours of one, in a different way. A rainbow separates white light into wavelengths by bending them. A CMY Cube separates it by subtraction: its cyan, magenta and yellow faces each remove one part of the spectrum, and where they overlap you get the rainbow's colours one at a time, red, green, blue, in your hand. Turn a many-faced piece like the Mundus in a sunbeam and the overlaps run round the object in a ring. Different physics, same spectrum, no rain required.

Every rainbow is a full circle, 42 degrees across around the point opposite the sun, and the ground hides the bottom. Get above the rain, or spray mist at your feet with the sun behind you, and the ring closes. You cannot reach the end because a rainbow is a direction, not a place, and nobody else is seeing yours. The colours run red to violet from outside in because water bends short wavelengths more, and the sky inside the bow is brighter because that is where all the extra light goes.

Spin a spectrum in your hand, and see light through a different lens.