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  1. Mathematical Physics, Analysis and Geometry
  2. Mathematical Physics, Analysis and Geometry : Volume 9
  3. Mathematical Physics, Analysis and Geometry : Volume 9, Issue 3, August 2006
  4. Reflection in a Translation Invariant Surface
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Mathematical Physics, Analysis and Geometry : Volume 20
Mathematical Physics, Analysis and Geometry : Volume 19
Mathematical Physics, Analysis and Geometry : Volume 18
Mathematical Physics, Analysis and Geometry : Volume 17
Mathematical Physics, Analysis and Geometry : Volume 16
Mathematical Physics, Analysis and Geometry : Volume 15
Mathematical Physics, Analysis and Geometry : Volume 14
Mathematical Physics, Analysis and Geometry : Volume 13
Mathematical Physics, Analysis and Geometry : Volume 12
Mathematical Physics, Analysis and Geometry : Volume 11
Mathematical Physics, Analysis and Geometry : Volume 10
Mathematical Physics, Analysis and Geometry : Volume 9
Mathematical Physics, Analysis and Geometry : Volume 9, Issue 4, November 2006
Mathematical Physics, Analysis and Geometry : Volume 9, Issue 3, August 2006
Gaussian Beam Construction for Adiabatic Perturbations
A Geometrical Interpretation of ‘Supergauge’ Transformations Using D-Differentiation
Reflection in a Translation Invariant Surface
On Separation of Variables for Homogeneous SL(r) Gaudin Systems
On the Two Spectra Inverse Problem for Semi-infinite Jacobi Matrices
Mathematical Physics, Analysis and Geometry : Volume 9, Issue 2, May 2006
Mathematical Physics, Analysis and Geometry : Volume 9, Issue 1, February 2006
Mathematical Physics, Analysis and Geometry : Volume 8
Mathematical Physics, Analysis and Geometry : Volume 7
Mathematical Physics, Analysis and Geometry : Volume 6
Mathematical Physics, Analysis and Geometry : Volume 5
Mathematical Physics, Analysis and Geometry : Volume 4
Mathematical Physics, Analysis and Geometry : Volume 3
Mathematical Physics, Analysis and Geometry : Volume 2
Mathematical Physics, Analysis and Geometry : Volume 1

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Reflection in a Translation Invariant Surface

Content Provider Springer Nature Link
Author Klingenberg, Wilhelm Guilfoyle, Brendan
Copyright Year 2007
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. 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 ${\Bbb{R}}^3$ ) with the aid of the natural complex structure on the space of all oriented affine lines.
Ending Page 231
Page Count 7
Starting Page 225
File Format PDF
ISSN 13850172
e-ISSN 15729656
Journal Mathematical Physics, Analysis and Geometry
Issue Number 3
Volume Number 9
Language English
Publisher Kluwer Academic Publishers
Publisher Date 2007-01-27
Publisher Place Dordrecht
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword focal set Geometry Differential line geometry reflection Analysis Mathematical and Computational Physics caustic Geometric optics Group Theory and Generalizations Applications of Mathematics line congruence Applications to physics
Content Type Text
Resource Type Article
Subject Mathematical Physics Geometry and Topology
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