Refraction and reflexion according to the principle of general covariance

We show how the principle of general covariance introduced by Souriau in smoothly uniform contexts, can be extended to singular situations, considering the group of diffeomorphisms preserving the singular locus. As a proof of concept, we shall see how we get again, this way, the laws of reflection and refraction in geometric optics, by applying an extended general covariance principle to Riemannian metrics, discontinuous along a hypersurface. (C) 2019 Elsevier B.V. All rights reserved.