31.5 The principle of least time for refraction by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.

## 31.5 The principle of least time for refraction (optional)

r / The principle of least time applied to refraction.

We have seen previously how the rules governing straight-line motion of light and reflection of light can be derived from the principle of least time. What about refraction? In the figure, it is indeed plausible that the bending of the ray serves to minimize the time required to get from a point A to point B. If the ray followed the unbent path shown with a dashed line, it would have to travel a longer distance in the medium in which its speed is slower. By bending the correct amount, it can reduce the distance it has to cover in the slower medium without going too far out of its way. It is true that Snell's law gives exactly the set of angles that minimizes the time required for light to get from one point to another. The proof of this fact is left as an exercise (problem 9, p. 883).

31.5 The principle of least time for refraction by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.