Séminaire Exceptionnel: Pierre Coullet

  • Culture scientifique
Publié le 18 octobre 2023 Mis à jour le 18 octobre 2023

le 23 octobre 2023

Institut de Physique de Nice

Points, Lines and Surfaces of Light

Seminars of the Institut de Physique de Nice,


The envelope of light rays coming from a point source, reflected on curved mirrors and refracted in dioptres, was one of the central subjects of differential geometry in the 19th century. The mathematical nature of "caustic" surfaces was elucidated by Gaspard Monge and his pupils Dupin and Malus. The history of optics has been
essentially geometrical since Euclid, up to and including Newton. We show in this seminar, as Gaspard Monge did in his famous article on "Les Déblais et les Remblais", that these phenomena are in no way specific to optics. It's simply the study of families of lines in dimension three that depend on two parameters, the
"congruence of lines". We will illustrate these questions with several elementary optical experiments and interactive simulations. We'll also show the impact of teaching geometry in secondary schools via optics, where only the compass and the ungraded ruler will be used by pupils. Finally, one of the aims of this seminar is to raise awareness among lINPHYNI researchers of an exhibition to be held from June 2024 to January 2025 at the Espace de l'Art Concret in Mouans-Sartoux on the theme of "Points,Lines and Surfaces of Light".