The Structure of Caustics Formed by Reflection by Curves and Surfaces

Authors

  • Josh Pearson University of Portsmouth

DOI:

https://doi.org/10.59973/emjsr.35

Keywords:

Caustic, Plane curve, Surface, Focal set, Singularities, Umbilics

Abstract

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.

References

https://www.gregegan.net/SCIENCE/Catacaustics/Catacaustics.html

William Ford, Numerical Linear Algebra with Applications: Using Matlab (2015)

Thomas Waters and Matthew Cherrie, The normal map as a vector field, Balkan Journal of Geometry and Its Applications,

Vol.27, No.2, pp. 145-157, (2022)

Andrew Pressley, Elementary Differential Geometry, Second Edition (2010) DOI: https://doi.org/10.1007/978-1-84882-891-9

https://en.wikipedia.org/wiki/Apollonius of Perga

I.R. Porteus, Geometric Differentiation: For the Intelligence of Curves and Surfaces, Second Edition (2001)

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Published

2023-11-09

How to Cite

Pearson, J. (2023). The Structure of Caustics Formed by Reflection by Curves and Surfaces. Emerging Minds Journal for Student Research, 1, 109–119. https://doi.org/10.59973/emjsr.35