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Reflection, refraction, and the Legendre transform

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Abstract

We construct in dimension two a mirror that reflects collimated rays into a set of directions that amplify the image and an optical lens so that collimated rays are refracted into a set of directions with a prescribed magnifi cation factor. The profiles of these optical surfaces are given by explicit formulas involving the Legendre transformation.

© 2011 Optical Society of America

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