Geometric optics and the “hairy ball theorem”

Abstract

Applications of the hairy ball theorem to the geometrical optics are discussed. When the ideal mirror, topologically equivalent to a sphere, is illuminated at every point, the “hairy ball theorem” prescribes the existence of at least one point at which the incident light will be normally reflected. For the more general case of the surface, topologically equivalent to a sphere, which is both reflecting and refracting the “hairy ball theorem” predicts the existence of at least one point, at which the incident light will be normally reflected and also normally refracted. Keywords: Hairy ball theorem, Reflection of light, Refraction of light, Topology, Optics