FIGURE CP34.80 shows a light ray that travels from point A to point B. The ray crosses the boundary at position x, making angles θ₁and θ₂in the two media. Suppose that you did not know Snell??s 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. There??s one value of x for which the light travels from A to B in the shortest possible time. We??ll call it x_min. Write an expression (but don??t try to solve it!) from which x_min could be found.c. Now, by using the geometry of the figure, derive Snell??s law from your answer to part b.?

You??ve proven that Snell??s law is equivalent to the statement that ??light traveling between two points follows the path that requires the shortest time.?? This interesting way of thinking about refraction is called Fermat??s principle.

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b B FIGURE CP34.80