In this article, we describe links between semi-conformality and geometric optics. In particular, we show the relation between Maxwell’s equation, the eikonal equation of geometric optics and the equation for a semi-conformal map into a surface. We exploit this to give a local existence theorem for semi-conformal map on an arbitrary Riemannian manifold.

Riemanian manifold, semi-conformality, harmonic morphism, geometric optics, Maxwell equations.