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Full-Text Articles in Physical Sciences and Mathematics
Reflection Of A Wave Off A Surface, Brendan Guilfoyle, Wilhelm Klingenberg
Reflection Of A Wave Off A Surface, Brendan Guilfoyle, Wilhelm Klingenberg
Preprints
Recent advances in twistor theory are applied to geometric optics in R 3 . The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecting surface is a plane, when the incoming wave is a plane and when the incoming wave is spherical. In each case particular examples are computed exactly and the results plotted to illustrate the outgoing wavefront.
On Hamilton’S Characteristic Functions For Reflection, Brendan Guilfoyle, Wilhelm Klingenberg
On Hamilton’S Characteristic Functions For Reflection, Brendan Guilfoyle, Wilhelm Klingenberg
Publications
We review the complex differential geometry of the space of oriented affine lines in R3 and give a description of Hamilton’s characteristic functions for reflection in an oriented C1 surface in terms of this geometry.