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I am somewhat puzzled by a common formulation of the Fermat principle (light travel time), because it contains index of refraction related to phase velocity while light travel time through a slab of glass, for instance, should be IMO described by group velocity, at least in ordinary materials like water or glass (I know that sometimes even group velocity could be greater than light velocity in vacuum). Is usage of the phase velocity correct?

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up vote 4 down vote accepted

Phase velocity is the correct quantity, because Fermat's principle arises due to destructive interference between paths which are not extremal. The "principle of least time" is more accurately a "principle of extremal phase". However, if dispersion can be neglected then phase and group velocity are equal so they are somewhat interchangeable.

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Another (maybe more common?) term to search for (which means basically the same thing as what zephyr wrote) is the "principle of stationary phase". – Willie Wong Apr 27 '12 at 11:31
@zephyr Thanks a lot for the answer. I have still a subquestion. Let's suppose I have a perfect lens (without any aberration, that is one which focuses to a point, all paths having the same optical length), monochromatic light and a planar object. If I understand it correctly then light passing in different distances from the lens center would have different travel time so the resulting image in focal plane would be a superposition of individual images of the object in different time instants of time. – Leos Ondra Apr 27 '12 at 20:42
Leos: If the group and phase velocities are different, this can happen. That is one reason among many that if you have a very short (femtosecond) light pulse, and you pass it through any optical system, you can easily distort it in space and in time in many ways. It is certainly possible for different spatial parts of the beam to become delayed relative to each other if you're not careful. – Steve B Apr 27 '12 at 21:36

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