Translations:Fermat’s principle - book/16/en

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If the curvature of the reflecting surface is greater than that of the tangent elliptical surface, the reflected path ADB traversed by a ray then would be a relative minimum. At the other extreme, if the reflecting surface conforms to a surface lying within the ellipsoid, such as the dashed one shown, that same ray along ADB would negotiate a relative maximum transit time. This is true even though other unused paths (where ) would be shorter (i.e., apart from inadmissible curved paths). In all cases, the rays travel a path with either a minimum, maximum, or stationary transit time in accordance with Fermat’s principle. Note that because the principle speaks only about the path and not about the direction along it, a ray going from A to B will trace out the same route as one from B to A. This is the very useful principle of reciprocity.