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Fermat's Principle is the statement that a ray will follow a minimum-time path between a point, A, to a point, B.

So, if I have a block of material of high refractive index, so that it slows the light considerably inside, the least-time path should avoid going through this block. In the picture below, in the topmost part a light ray going straight through the block is shown, in the bottommost the light ray goes around the object. Obviously, this situation does not occur and in reality, the ray goes straight through the block. Why does this not contradict Fermat's principle?

enter image description here

StefanH
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2 Answers2

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Well, Fermat's principle is really a principle of stationary time rather than least time. There is a stationary path through the block of high refractive index.

See this Phys.SE post for a related example.

Qmechanic
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To add to @Qmechanic's answer: The "shortest flight" formulation of Fermat's principle is true only "locally" for a sufficiently narrow angle bundle of rays. Take an elliptical reflector that can ideally image light from one of its focus to another. The direct straight line connection between them is the shortest path from one to another. The "shortest flight principle" here is applicable locally for those rays that are constrained to hit the elliptical wall before going reaching the other focal point.

hyportnex
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