Finding the Cut Locus of Reflected Rays by the Wavefronts

In this paper, we will study the relation between the caustics produced by the wavefronts of rays reflected in plane curves and the cut locus, as the self-intersection points of the wavefronts will generate the cut locus of the caustic. This is related to the study of caustics in general and their cusps, as other authors have made in [1, 2, 3]. Firstly, we will define the wavefronts and other related elements to analyse this statement, then we will use two different methods for evaluating the self-intersection points of the wavefronts, which are useful for determining self-intersections of curves in general. In the end, we will use the results obtained and see their relationship with the confocal conics when the reflection curve is an ellipse.