Refraction and the minimization of light travel time

This is a Java application designed to enable you to learn about refraction. Let's say you have two points, and you want light to travel from one point to the other. In this simulation, by the way, the first point is colored red and the other point is colored purple.

If you want the light to travel between the points in the smallest possible time, then the light should travel along the straight line connecting the two points. This is true, at least, if the light travels through just one medium (air, for instance) between the two points.

Things get a little more interesting if the light changes medium along the way, however. In this simulation, there are two different media. Point 1, where the light originates, is in medium 1 (air, for instance), while point 2, where the light ends up, is in medium 2 (glass, for instance).

You can adjust the index of refraction of each medium, and you can also adjust the position of points 1 and 2. You can also adjust the position of a third point (colored green in the simulation) that is on the interface (the boundary) between the two media, and through which the light passes on its way from point 1 to point 2.

Your goal is to adjust the position of the point on the boundary so that the light takes the smallest possible time to travel from point 1 to point 2, and then you have to think about how this relates to reality. In other words, which of the many possible paths the light could take does the light actually take?