GCSE physics lies: Rainbows and total internal reflection

When I said I was done with ray-tracing, I was lying.

I've not done any more coding, but I thought I'd just write down something that I only realised while doing the ray-tracing work.

The story you get at GCSE-level physics about rainbows is that they're caused by total internal reflection causing the spherical raindrops to act like mirrors, and the angle of the arc is thus related to the critical angle, etc. The refractive indices are supposed to be slightly different for the different frequencies, hence the colours.

This simplistic answer is rubbish. If you take the path the light takes once it refracts into the sphere, you can use symmetry to show that the angle between the entry point and its normal, and the exit point and its normal is the same. Therefore, the external angles will be the same, and you will certainly never get TIR under this simplistic model. A physicist friend suggests rainbows are really about Fresnel reflection, but I don't know anything about that.

I noticed this behaviour when writing the ray-tracer, as I'd left in a "TO DO" case for dealing with TIR, and noticed it never got called when doing my refracting spheres demo. I thought a little bit, and had an epiphany. It's taken me nearly 20 years to realise that the GCSE explanation couldn't work!

Posted 2015-01-04.