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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.
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| In projective coordinates (''w'':''x'':''y'':''z'') the wave surface is given by
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| :<math>
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| \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
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| </math> | |
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| ==References==
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| *{{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}}
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| *{{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}}
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| *{{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}}
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| *{{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}}
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| ==External links==
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| *[http://enriques.mathematik.uni-mainz.de/csh/galeries/complexSurfaces/fresnel.html Fresnel wave surface]
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| [[Category:Algebraic surfaces]]
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| [[Category:Complex surfaces]]
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| [[Category:Waves]]
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Latest revision as of 04:23, 12 April 2014
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