Over the rainbow

Wednesday 23 August 2023

A couple of days ago I wrote a post about Chat GPT's explanation of rainbows. I mentioned that the reason for the rainbow being an arc was not given. Well how would I explain it? I wouldn't I would show it. The reason is due to the fact that the light from the sun is approximately parallel and the raindrop is a sphere. For a droplet to appear blue the blue light must be reflected by the raindrop into the observers eye. As shown in this 2D representation.

If the sky is full of raindrops i.e. it is raining then all raindrops with light passing through it at this angle will appear blue to the observer. If we move this raindrop along an arc we can see that the light always passes through at the same angle so all drops along the arc will appear blue. (I wish I had made the sphere blue instead of red).

This simulation was made with GeoGebra, an extremely useful tool.

Here is the simulation: Move point B to rotate the drop and right click drag to rotate 3D view. Note that the incident rays are parallel and the reflected ray always ends up at the same point.

By the way if you build the situation in Algodoo you find out that this isn't total internal reflection at all.

See how the ray emerges from the raindrop.