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Durham University

Department of Mathematical Sciences


Publication details for Wilhelm Klingenberg

Klingenberg, Wilhelm & Guilfoyle, Brendan (2006). Reflection in a translation invariant surface. Mathematical Physics, Analysis and Geometry 9(3): 225-231.

Author(s) from Durham


We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while the focal surface is translation invariant. In addition, we show that the focal curve is not physically visible. This is done by constructing explicitly the focal set of the reflected line congruence (2-parameter family of oriented lines in R3R3) with the aid of the natural complex structure on the space of all oriented affine lines.