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In mathematics, Fresnel's '''wave surface''', found by [[Augustin-Jean Fresnel]] in 1821, is a [[quartic surface]] describing the [[propagation of light]] in an [[optically biaxial crystal]]. Wave surfaces are special cases of [[tetrahedroid]]s which are in turn special cases of  [[Kummer surface]]s.


In projective coordinates (''w'':''x'':''y'':''z'') the wave surface is given by
:<math>
\frac{a^2x^2}{x^2+y^2+z^2-a^2w^2} + \frac{b^2y^2}{x^2+y^2+z^2-b^2w^2} + \frac{c^2z^2}{x^2+y^2+z^2-c^2w^2} =0
</math>


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==References==
 
*{{Citation | last1=Bateman | first1=H. | title= Kummer's quartic surface as a wave surface. | doi=10.1112/plms/s2-8.1.375 | year=1910 | journal=[[Proceedings of the London Mathematical Society]] | issn=0024-6115 | volume=8 | issue=1 | pages=375–382}}
*{{Citation | last1=Cayley | first1=Arthur | author1-link=Arthur Cayley | title=Sur la surface des ondes | id=Collected papers vol 1 pages 302–305 | year=1846 | journal=Journal des Mathématiques Pures et Appliquées | volume=11 | pages=291–296}}
*{{Citation | last1=Knörrer | first1=H. | title=Arithmetik und Geometrie | publisher=Birkhäuser | location=Basel, Boston, Berlin | series=Math. Miniaturen | isbn=978-3-7643-1759-1  | id={{MR|879281}} | year=1986 | volume=3 | chapter=Die Fresnelsche Wellenfläche | pages=115–141}}
*{{Citation | last1=Love | first1=A. E. H. | title=A treatise on the Mathematical Theory of Elasticity | origyear=1927 | url=http://books.google.com/books?id=ViebCriF-ssC | publisher=Dover Publications, New York | isbn=978-0-486-60174-8 | id={{MR|0010851}} | year=2011}}
 
==External links==
 
*[http://enriques.mathematik.uni-mainz.de/csh/galeries/complexSurfaces/fresnel.html Fresnel wave surface]
 
[[Category:Algebraic surfaces]]
[[Category:Complex surfaces]]
[[Category:Waves]]

Revision as of 20:54, 17 September 2013

In mathematics, Fresnel's wave surface, found by Augustin-Jean Fresnel in 1821, is a quartic surface describing the propagation of light in an optically biaxial crystal. Wave surfaces are special cases of tetrahedroids which are in turn special cases of Kummer surfaces.

In projective coordinates (w:x:y:z) the wave surface is given by

References

  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

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