Caustics Generated by Rolling Circles

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Light from a radiant point at infinity reflects off the blue curve. The envelope of the lines containing the rays of reflection is a caustic, which can be seen as the concentration of green lines. Boyle's theorem states that the blue curve has a corresponding red curve and a circle of varying radius that rolls along the red curve such that points on the rim of the circle sweep out the caustics produced from the radiant at various angles. For the parabola, the red curve degenerates to a single point located at the focus of the parabola. The multiple angles option shows the caustics generated from various angles, generated simultaneously.

Contributed by: Todd Will and Jeff Boyle (June 2013)
Open content licensed under CC BY-NC-SA


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