Shows a light ray that travels from point A to point B. The ray crosses the boundary at position x, making angles and in the two media. Suppose that you did not know Snellโs law.
A. Write an expression for the time t it takes the light ray to travel from A to B. Your expression should be in terms of the distances a, b, and w; the variable x; and the indices of refraction n1 and n2
B. The time depends on x. Thereโs one value of x for which the light travels from A to B in the shortest possible time. Weโll call it . Write an expression (but donโt try to solve it!) from which could be found.
C. Now, by using the geometry of the figure, derive Snellโs law from your answer to part b.
Youโve proven that Snellโs law is equivalent to the statement that โlight traveling between two points follows the path that requires the shortest time.โ This interesting way of thinking about refraction is called Fermatโs principle.
