A direct proof of Malus' theorem using the symplectic structure of the set of oriented straight lines

TL;DR

This paper provides a direct proof of Malus' theorem in geometrical optics by leveraging the symplectic structure of the set of all oriented straight lines in Euclidean space.

Contribution

It introduces a novel proof of Malus' theorem based on symplectic geometry, offering a new perspective in geometrical optics.

Findings

Proof based on symplectic structure of oriented lines

Clarifies geometric foundations of Malus' theorem

Connects optics with symplectic geometry

Abstract

We present a direct proof of Malus' theorem in geometrical Optics founded on the symplectic structure of the set of all oriented straight lines in an Euclidean affine space. Nous pr\'esentens une preuve directe du th\'eor\`eme de Malus de l'optique g\'eom\'etrique bas\'ee sur la structure symplectique de l'ensemble des droites orient\'ees d'un espace affine euclidien.