# Fermat - Fermat's Principle Before we embark upon an...

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Fermat's Principle Before we embark upon an analysis of reflection and refraction from the point of view of scattering light waves, it is worth exploring an alternative explanation for the propagation of light. Fermat's principle is a variational principle which states that: The path taken by light going between any two points is the one that is traversed in the least time. Indeed, by considering all possible paths for a light ray and choosing one which takes the least time, it is possible to determine how a light ray will move. Consider a situation where a particle moves from one medium to another. Figure %: Fermat's principle applied to refraction. If the point at which the light crosses the boundary is a distance x from the origin, and the speeds in the media are v A and v B respectively, then the time taken by the light is: t = + Minimizing time with respect to x : = + = 0 Rearranging this we find: = which is the law of refraction . In general, paths of minimum time are those paths which deviate

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Fermat - Fermat's Principle Before we embark upon an...

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