How are rainbows formed in that arch shape?
In: Physics
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Rainbows are a circle, but you don’t see the bottom half of it because the ground is in the way.[ It’s possible to see it from an airplane though.](https://www.thetelegraphandargus.co.uk/resources/images/12594594/?type=responsive-gallery-fullscreen)
The middle part is actually also a part of the rainbow, we just can’t see it because it’s ultraviolet color and our eyes can’t sense that (also the atmosphere blocks a lot of it from even coming down)
Rainbows are not formed, as in they’re not objects. They’re simply a trick of the light that can be seen from certain angles. Like all other simillar phenomenons, like moon halos, they form a ring and not an arch. However since we usually see them from the ground, we only see half of them, so they look like arches. It is possible to view a fully circular rainbow if you’re somewhere high or in an airplane and conditions are right. You basically see them as long as there are water droplets in the air and the sun is at the right angle, which usually means being behind you. Since water is always refracted from the droplets at the same angle, if you’re seeing a rainbow, you’re at the right spot, and if you move it will either move with you or you’ll stop seeing it. As an observer you’re always at the center of the rainbow and that’s why it’s circular.
Think about how white light going into a prism makes a rainbow. This is because the different wavelengths of light are bent different amounts and so emerge from the prism at a slightly different angle. Raindrops work sort of like that prism, splitting light up into various colors emerging at different angles.
For a particular droplet of water depending on where you are standing you would only see light of a particular color coming from it. It is splitting light into the full spectrum but when you view it from a specific angle you are only seeing the one color. Other droplets elsewhere in the sky viewed at a different angle will show you a different color.
Because this all depends on the angle at which you view those droplets of water, a particular color is going to be visible at a specific angle from the sun. This applies to any angle from the sun which means a rainbow appears as a circle opposite the sun at about 42 degrees. It only appears as an arch because some of that light is being blocked by the ground; if you were flying in an airplane you can see the whole circle.
Geometry!
The rainbow itself isn’t actually an arch, it’s a collection of colored light, and that light flying all throughout the air. But the only way for you to see a rainbow is if that collection of colored light enters your eyes.
I could go into the physics of light refraction, but the bottom line is that, when sunlight hits a bunch of water droplets, the band of colors that makes the rainbow leaves at a specific angle (42 degrees, specifically).
That light goes in all different directions, but the only time you see that light is if there’s a 42 degree angle between your eyes, the water droplets, and the sun.
If the sun is coming from your back, and there’s a whole wall of water droplets in the air in front of you, there are likely to be a lot of droplets forming that exact angle with the sun. And that angle can be in any direction: above you, to the left, to the right, diagonally. If you were to trace out all the droplets that formed a 42 degree angle with your eyes and the sun, you know what that would form? A circle!
Now, it’s not a full circle, of course, because the ground gets in the way. It is, apparently, possible to see a rainbow as a full circle, but only under very specific circumstances. You need to be high enough for the sun’s rays to pass underneath you, bounce off water droplets that are also lower than you, and refract up to you, at a 42 degree angle. That means you need to be in an airplane (or something else that can get high enough), near sunrise or sunset, with the right weather conditions on the opposite side of the sun. It happens, but it’s rare to see.
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