Why are rainbows perceived as curved or circular? And why do they seem to be a relatively condensed band of the different stripes of color?

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Why are rainbows perceived as curved or circular? And why do they seem to be a relatively condensed band of the different stripes of color?

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Rainbows are circles.

Or rather, they are cones, with you – the viewer – at the point. Because of geometry.

You might find [this diagram](https://www.asu.edu/courses/phs208/patternsbb/PiN/mod/light/opticsnature/diagram2.gif) (from [this page](https://www.asu.edu/courses/phs208/patternsbb/PiN/rdg/rainbow/rainbow4.shtml)) useful.

Light from the Sun is hitting all the rain drops, from an (effectively) infinite distance away. For physics reasons the *red* light from the Sun gets reflected by the raindrops at an angle of about 42 degrees.

Imagine a line running from the Sun, through your eyes, and then out towards where the rain is. The only places where you will see *red* reflected from those raindrops will be points 42 degrees off that line in any direction (as in the diagram). That [makes the surface of a cone](https://www.asu.edu/courses/phs208/patternsbb/PiN/mod/light/opticsnature/cone.jpg), which when looking at it from the point, becomes a circle.

The red light from any raindrops outside that circle (or cone) will be reflected at 42 degrees – too much to hit you – and so will cross behind you, missing you. The red light from any raindrops inside the circle won’t be reflected enough to hit you and so will cross in front of you, missing you. Only the ones at just the right angle will hit you – and so you can only see them.

The different colours of light are reflected at different angles (blue being reflected the most, at about 40 degrees), so you get a series of cones, each inside the other (although all meeting at the point).

So a raindrop that is in the red part of the rainbow for you is still reflecting blue light, that blue light is just going behind you, missing you – someone standing in the right spot behind you might see it as the blue part of the rainbow. Similarly, a raindrop in the blue part of the rainbow for you is also reflecting red light, but that red light is passing in front of you so you can’t see it, but someone standing there would see it as being in the red part of the rainbow.

Light from the sun runs into water droplets in the air and gets bounced back to you. The sun light is actually made up of all sorts of different colors. Red light, for example, “likes to” bounce off water at a certain angle, which is different from the angle the blue light “likes to” bounce off water. So when you look at a rainbow the red circle is the one hitting your eyeball from the angle the color red likes. The blue circle is the one hitting your eyeball from the angle the color blue likes. And so on.

Double rainbows happen when there is another rainbow above the main rainbow that is caused by sunlight bouncing *two times* in a water droplet and then hitting your eyeball. That’s why the second rainbow is less bright than the first – more light escapes each time the sunlight bounces.