How are rainbows formed. I know it’s about refraction from water droplets, but shouldn’t you see many tiny rainbows instead of one big one.
In: Physics
Watch the hidden beauty of rainbows by Walter Lewin its very detailed and reasonably easy to understand.
Bit of a cop out but it’s alot to explain. You’re not really asking a question that can be summed up without a fair bit of prior knowledge
If you have 2 hours, [this](https://www.youtube.com/watch?v=eDByEKf2IEM) lecture from IT explains it very simply. I haven’t looked at a rainbow the same way again since watching this.
Go outside on a sunny clear day. Get the water hose and spray a fine mist up in the air next to you. Rotate the mist around your body until you find the rainbow. Now if you look carefully you can see the water particles each acting as a prism.
Here’s an explanation I’ve stolen from *The Science of Discworld IV* by ian Stewart and Jack Cohen (and Terry Pratchett):
> Sunlight striking each drop gets refracted (and broken up into different colours) and then it bounces (total internal reflection) and passes out back towards the Sun, the different colours being further separated. Some fancy geometry shows that there is a focusing effect, because rays that enter the drop behave differently according to where they hit. Most of the light of a given colour comes out in a concentrated ‘beam’ at an angle of about 67˚ from the direction it went in. This angle depends on the wavelength, that is, the colour, of the light. So, if you’re standing with the Sun behind you, you see the backward-pointing coloured spray of rays from those raindrops that form a 67˚ circle in the sky. Someone standing a metre to your right doesn’t see your raindrops, but those corresponding to a different circle a metre to the right of yours.
Imagine you glue a tiny mirror to the side of your neighbor’s house. (Don’t do this in real life unless you get a parent or guardian’s permission.) If you stand near the mirror and look at it, you can see your whole house. But if you stand back, you might only see a tiny bit of your house reflected in the mirror.
Now, imagine you glue a whole bunch of tiny mirrors all over your neighbor’s house. First, where did you get all that glue? Second, now you can see your whole house whether you’re close to the mirrors or far away. But notice–you are seeing one big reflection of your house, rather than a bunch of small ones. That’s because the closer you are to the mirror, the more you can see at once, but as you back up, the mirrors all reflect pieces of the image together, making one big image. (fun fact–this is how telescope mirrors work!)
Now, when it comes to rainbows, the same principle applies. If you could examine a single water droplet in the air, you might see a tiny rainbow coming out of it, but it would be very small and very faint. But the further you get from the water droplets, the more their light combines into a single big image–the big rainbow image we are familiar with.
Draw an imaginary line from the sun, to your eye, to the centre of the rainbow. That will always be a straight line. Draw another line from the sun, to any red part of the rainbow, to your eye. This will always give you the same angle. It’s the angle that spherical drops of water like to reflect the colour red at. So you see red in this part of the rainbow. Doing this with blue will always give you another angle. Green another.
The sky is full of raindrops. They all scatter the sun’s light and split it into colours. But the ones that form the rainbow for your eye are the ones that form exactly the right angle with the sun, to reflect a specific colour into your eye.
For simplicity let’s just talk about a single color: red.
When red light comes out of the droplet it’s always at the same angle from the original ray of light and you can see it only if you are at that exact angle so now you can imagine two lines forming an angle with the vertex in the droplet, origin in the sun and end in your eye.
Now we must understand why all the droplets that can make us see red light are in an arc and not in some other shape.
Let’s say that imaginary angle is now a set square with the vertex on the droplet, one edge that follows the ray of light and another edge that points in your direction.
The ray of light edge can’t move because the ray of light doesn’t change its angle.
But if you rotate the set square on that edge you can find all the single points you could be to keep seeing the red light because they all are at the same angle so if you imagine the solid that comes out of the rotation you would find out it’s a cone and the section of a cone is a circle.
Rainbows are circles, not arcs, it’s just that the ground blocks the view.
If you still can’t get why you see an arc, imagine the cone coming out of your eye. If you were shooting out photons from your eye in a cone with that exact angle, all the points on the surface of that cone that intersect a droplet will end in the sun but that cone is the only part of space where you can aim to shoot photons in the sun. Therefore the rainbow must be formed on a section of that particular cone coming off of your eye and the perceived distance of where you see the rainbow depends on how far the droplet is but it’s pretty much just an illusion.
edit: typo
White light enters each drop.
Each drop ~~splits~~ *separates the light into different wavelengths, sending each colour out at a slightly different angle.
You only see the colours that are pointing in the direction of your eyeballs, so a very small range of wavelengths for each raindrop.
So for the raindrops that are lower down, you will only see the purple light, as the other colours are going off at different angles. You see a little bit of purple light from each raindrop which is at that particular angle to your eyeball.
From the raindrops higher up, you only see the red light.
and it’s the same for each raindrop in between.
[here is a picture](http://www.rebeccapaton.net/rainbows/rnbwbmp.gif)
Each drop if water is sending out all the colors, but in different directions. Where you are standing you see all the red from those at the correct angle from you. That’s why it’s a circle. all the red part of the rainbow is at the same angle from you just a different direction. Same for each of the other colors. The sun is behind you so the rainbow shifts a little bit when you move but not too much.
Every person sees a different rainbow. You aren’t even seeing the same rainbow from moment to moment. it’s all just an interesting effect of lots of little water drops in the sky refracting and reflecting to your eye.
If 1000 people are pointing two flashlights in two directions in a V shape like this V V V V V V V, you can’t see both sets of lights unless you stand really far away.
Certain colors are only viewable from certain angles. All the red light comes out of all the droplets in one direction. All the blue light in another.
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