The Geometry of Light Paths for Equiangular Spirals

Abstract

First geometric calculus alongside its description of equiangular spirals, reflections and rotations is introduced briefly. Then single and double reflections at such a spiral are investigated. It proves suitable to distinguish incidence from the \textit{right} and \textit{left} relative to the radial direction. The properties of geometric light propagation inside the equiangular spiral are discussed, as well as escape conditions and characteristics. Finally the dependence of right and left incidence from the source locations are examined, revealing a well defined inner \textit{critical} curve, which delimits the area of purely right incident propagation. This critical curve is self similar to the original equiangular spiral.