title: Reflection, refraction, and the Legendre transform.
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 magnification factor. The profiles of these optical surfaces are given by explicit formulas involving the Legendre transformation.
authors.affiliation: Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale, n 72 09124 Cagliari, Italy.
authors.forename: Cristian E
authors.initials: CE
authors.lastname: Gutiérrez