The generalized vectorial laws of reflection and refraction

Abstract

This paper discloses two important discoveries. These are: (i) discovery of ambiguity in the well-established laws of reflection and refraction of light which have been in regular use for many years, and (ii) discovery of generalized vectorial laws of reflection and refraction of light. The existing definitions of angle of incidence, angle of reflection and angle of refraction are considered first. Each of these definitions is found to be ambiguous, not in compliance with the fundamental definition of angle in geometry. Two typical questions (one in the case of reflection and the other for refraction) have been addressed, which cannot be dealt with by using the existing laws of reflection and refraction of light. Thus, the existing laws of reflection and refraction of light seem to be ambiguous in respect of generality and their validity in a broad sense is questionable. With a view to removing the ambiguities, proper definitions of the above three angles are given first and then the statement of the generalized vectorial law of reflection (as well as that of refraction) has been offered.