PHYS 598 hw1 - 1 Fermat's principle According to Fermat's...

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Physics 498/MMA Handout 1 Fall 2007 Mathematical Methods in Physics I m-stone5 Prof. M. Stone 2117 ESB University of Illinois 1) Fermat’s principle : According to Fermat’s principle, the path taken by a ray of light between any two points makes stationary the travel time between those points. A medium is characterised optically by its refractive index n , such that the speed of light in the medium is c/n . In this problem we will assume that all light rays lie in the x - y plane. a) Use Fermat’s principle to show that light propagates along straight lines in homoge- neous media ( i.e. , media in which n is independent of position). b) Consider the propagation of light from one semi-infinite homogeneous medium of re- fractive index n 1 to another with refractive index n 2 . By examining paths that need not be differentiable at the interface, establish Snell’s law. c) A planar light ray propagates in an layered medium with refractive index n ( x ). Use
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