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<p>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.</p>

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Caustics by refraction of circles and lines

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月25日

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  • Felix Rydell

摘要

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.