The generalized vectorial laws of reflection and refraction leading to the development of novel equations involving the coordinates of the source point, point of observation, and the point of incidence

Abstract

This paper considers the derivation of novel equations involving the coordinates of a pair of points lying respectively on the incident ray and the reflected (refracted) ray as well as those of the point of incidence by making use of the generalized vectorial laws of reflection and refraction developed by the author in 2005. The novel equations developed will be applicable irrespective of the positions of the pair of points lying on the incident ray and the reflected (refracted) ray respectively. If, however, one of the pair of points considered is supposed to be the source point and the other one is considered as the point of observation, then such novel equations will effectively represent the relation(s) between the coordinates of the source point, point of observation and the point of incidence. The problem addressed is novel and interesting and the development of such novel equations increases the range of applicability of the generalized vectorial laws of reflection and refraction, there by enhancing the traditional optical physics literature as well.