FIGURE CP34.80 shows a light ray that travels from point A

Chapter 34, Problem 34.119

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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 u1 and u2 in the two media. Suppose that you did not know Snells 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 a b. The time depends on x. Theres one value of x for which the light travels from A to B in the shortest possible time. Well call it xmin. Write an expression (but dont try to solve it!) from which xmin could be found. c. Now, by using the geometry of the figure, derive Snells law from your answer to part b. Youve proven that Snells 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 Fermats pri