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From my understanding of Fermat's Principle, you decide a start point and an end point for a light ray to travel between, and the light 'chooses' whichever path takes the least time (or technically whichever path the time is 'stationary' at).

So consider the following, you set up the start point, A, and the end point, B in different mediums. Of course the path of minimum time is that which obeys snells law.

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However if the light is coming from box which has only has a small hole in it (as shown in the diagram), the light is unable to follow this path of least time. But it is still the path of least time, so why is Fermat's principle no longer obeyed?

enter image description here

Does Fermat's Principle simply not apply for when there are objects that can block/absorb the light? Do we therefore assume that light is able to reach every point in space when using Fermat's Principle? If so, what is the point othe principle?


marked as duplicate by Qmechanic Mar 26 '16 at 23:42

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  • $\begingroup$ I don't understand the question. If you block the path that light would travel from point A to point B, then the observer at point B simply can't see the light emitted at point A. There are light sources on the other side of the Earth for which a stationary path to me is directly through the Earth, but, since the Earth is opaque, I can't see them. $\endgroup$ – Chris Mueller Aug 27 '15 at 15:12
  • $\begingroup$ @ChrisMueller Yes, my question is effectively 'how does Fermat's Principle deal with opaque objects?' Which path is taken by a light ray if the stationary path is blocked by an opaque object? $\endgroup$ – ToRQue Aug 27 '15 at 15:23
  • $\begingroup$ Fermat's principle doesn't deal with the intensity of the light, only the path. It doesn't know about attenuation in absorbing media for example. If all of the paths calculated using Fermat's principle go through opaque objects, then there is no way to see the object. $\endgroup$ – Chris Mueller Aug 27 '15 at 15:26
  • $\begingroup$ What if only some paths go through an opaque object? Is there a different stationary path that can be taken? (in the second diagram above, which path is taken from A to B since the expected path is blocked?) Also surely Fermat's principle does deal the intensity of light (at least to some extent), since light is more intense at points where there are more stationary paths to that point? (think of a convex lens) $\endgroup$ – ToRQue Aug 27 '15 at 15:29
  • $\begingroup$ Essentially a duplicate of physics.stackexchange.com/q/38348/2451 $\endgroup$ – Qmechanic Aug 28 '15 at 2:00