Title

Reflection in a Translation Invariant Surface

Authors

Brendan Guilfoyle, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow
Wilhelm Klingenberg, Department of Mathematical Sciences, University of Durham, DH1 3LE, Durham, United Kingdom

ORCID

0000-0002-7437-5046

Document Type

Preprint

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

Mathematical Physics, Analysis and Geometry. © 2007 Springer

Abstract

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. This is done by constructing explicitly the focal set of the reflected line congruence (2-parameter family of oriented lines in R 3) with the aid of the natural complex structure on the space of all oriented affine lines.

Recommended Citation

Guilfoyle, B., Klingenberg, W. Reflection in a Translation Invariant Surface. Math Phys Anal Geom 9, 225–231 (2006). https://doi.org/10.1007/s11040-007-9013-8