Exploring Reflection: Designing Light Reflectors for Uniform Illumination

Many students first learn of the law of reflection when they are told about the reflective properties of conics. Typically students are exposed to a curve or surface, and then its reflective properties are derived or verified. In this paper we explore reflection by starting from a desired property of an unknown reflector and proceeding to find a reflector with those properties. This is done in the context of finding a reflector that produces uniform illumination of nearby objects. The reflectors considered are those whose analysis can be reduced to studying curves in two dimensions.