2010•Journal of OpticsOpen access

The caustics of two- and three-dimensional parabolic reflectors

Christopher G. Bell, H. Ockendon, J. R. Ockendon

Abstract

The caustic of a two-dimensional parabola illuminated off-axis is the Tschirnhausen cubic and does not contain any singular points. The caustic of a three-dimensional paraboloid of revolution similarly illuminated consists of two cusped sheets containing a hyperbolic umbilic singularity. We relate these two situations by considering a suitable sequence of illuminated elliptic paraboloids.

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Key concepts: Paraboloid, Caustic (mathematics), Parabola, Singularity, Optics, Physics, Parabolic reflector, Mathematical analysis