The law of refraction of light rays is derived from Fermat’s principle by means of the Weierstrass-Erdmann corner condition of the calculus of variations. In such a derivation the optical path need only be considered at the point of refraction, and the refraction principle follows from a differential equation rather than from an integral equation or geometric construction for a finite length of path. Likewise, the corner condition taken with Fermat’s principle is a differential equation which requires that an optical path be straight at all points where the velocity is unchanged.
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