Refraction

The lamp S is in air and the eye E is below the surface, where light is n times slower (1.333 for water). The gold line is the quickest path; the ivory one bends at P. Slide P along the surface: the corner gives the time along its path, and the small graph at the right, T(x), records that time for every position x of P. At its lowest point the graph is flat, and that is where the gold path bends. Only there does the ratio of the sines of the two angles at P, sin θ₁ / sin θ₂, come out equal to n: Snell's law of refraction. Drag n up and the light below gets slower: the quickest path runs steeper and shorter down there, and its bend moves towards E; at n = 1 both sides are equally fast and the quickest path is a straight line. S and E can be dragged too. The fine lines spreading from S are the wavefronts, each joining the places light first reaches at the same moment; below the surface they crowd closer together.