Caustics by Refraction of Circles and Lines
Algebraic Geometry
2025-07-15 v2
Abstract
This short note revisits the classical result that the complete caustic by refraction of a circle is the evolute of Cartesian ovals. We provide additional details to the statement and geometric proof of this fact, as presented in G. Salmon's 1879 book `Higher Plane Curves'. We observe that as the circle tends to a line, the Cartesian ovals collapse into an ellipse or a branch of a hyperbola. Further, we derive a general formula for caustics by refraction of circles using a computer algebra system, providing a modern computational perspective on this classical problem.
Cite
@article{arxiv.2402.00475,
title = {Caustics by Refraction of Circles and Lines},
author = {Felix Rydell},
journal= {arXiv preprint arXiv:2402.00475},
year = {2025}
}