The Structure of Caustics Formed by Reflection by Curves and Surfaces
Keywords:Caustic, Plane curve, Surface, Focal set, Singularities, Umbilics
In this paper we define a method for finding and plotting the caustics formed by reflection by curves. We then explicitly define the focal radius, ρ, and use it to make conclusions about the caustics of circles and ellipses. Some observations are made of the caustic’s cusps before shifting our attention to surfaces. There, a similar definition is made before showing some of the possible caustics of spheres and ellipsoids. We finish with a brief discussion on a potential analogue to umbilic points.
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Copyright (c) 2023 Josh Pearson
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