What factors determine the radius of a rainbow?
In: Physics
*Disclaimer*: this comment assumes basic knowledge about how rainbows form. Watch [this Youtube video](https://www.youtube.com/watch?v=5cVX3eq6NUQ) for an ELI5 explanation of that.
The radius of a rainbow is always 42°. The only factor that determines it is the refractive index of the water in the raindrops – i.e. how much they bend light – which is basically always the same. But perhaps your question is “why is do rainbows seem to have different sizes?”
For a start you have to know that the center of the rainbow is always exactly on the opposite side of the sun. You also need to know that the shape of a rainbow is a part of a circle. This circle has a center point, like every circle. Draw a line from the sun to your head, and continue the line on the other side. Let’s call this the ‘solar axis’ (a term I just made up for simplicity). This axis – while looking away from the sun – marks the center of the rainbow. The rainbow itself (the arc) is always found at a certain angle from this center: 42°. This is (in short) because light always bends with the same angle inside a raindrop.
However, how much of the rainbow you see depends on the height of the sun. One extreme is when the sun is right overhead. The solar axis points towards the ground and you can see no rainbow at all, since the arc would need to form somewhere below the horizon, where there is no rain. Now imagine lowering the sun until you see a rainbow. When will you start seeing it?
Because the rainbow is 42° away from the solar axis, you can only start seeing a rainbow when the sun is at an angle of 42° or lower from the horizon! You can theoretically just see the top of the rainbow at this angle. The lower the sun goes, the more rainbow you’ll see, and the more spread out the base will appear.
Edit: better introduction video
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