A geometric algebra reformulation of geometric optics

Abstract

This paper presents a geometric algebra reformulation of the laws of propagation, reflection, and refraction of light in geometrical optics. To transform an incident ray to a reflected or refracted ray, matrices are not used. Instead, rotations of vectors are expressed in terms of exponential rotation operators. The argument of these operators is a surface (bivector), which is a product of an oriented volume (trivector) and a ray (vector). The bivector and the trivector are two distinct types of 'imaginary numbers.'