Snell's law of refraction
Channel: Nils Berglund
Date: 2021-05-01

Today's video is brought to you by the association of physics teachers. Snell's law in geometric optics describes what happens when a light ray hits the boundary between two regions with different speeds of propagation. Part of the light ray is reflected, and part of it enters the other region, but at a different angle, that can be computed in terms of the speed of light in both media. Snell's law follows from Fermat's principle of least time, which states that light rays travel between points A and B on paths taking the shortest possible time. But what happens when we actually consider a real wave? This simulation shows the wave dynamics in a situation where the speed of propagation is half as large in the lower part. Think of the wave fronts as being at right angles to the light rays.

Music:  Emerald Therapy by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/
Artist: http://audionautix.com/ 

You can read more about Snell's law here: https://en.wikipedia.org/wiki/Snell%27s_law
The simulation solves the wave equation with a little bit of "elasticity" (a harmonic restoring force). The algorithm is adapted from this paper: https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf . The boundary conditions are chosen to minimize reflections on the outer boundary, following the method described in https://hal.archives-ouvertes.fr/hal-01374183
C code adapted from https://www.idpoisson.fr/berglund/vid_wave_billiard.c
Many thanks to my colleague Marco Mancini for helping me to accelerate my code!

You may be interested in some science outreach articles: https://images.math.cnrs.fr/_Berglund-Nils-1343_.html