In mathematics, Fresnel's wave surface , found by Augustin-Jean Fresnel in 1822, 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
a 2 x 2 x 2 + y 2 + z 2 − a 2 w 2 + b 2 y 2 x 2 + y 2 + z 2 − b 2 w 2 + c 2 z 2 x 2 + y 2 + z 2 − c 2 w 2 = 0 {\displaystyle {\frac {a^{2}x^{2}}{x^{2}+y^{2}+z^{2}-a^{2}w^{2}}}+{\frac {b^{2}y^{2}}{x^{2}+y^{2}+z^{2}-b^{2}w^{2}}}+{\frac {c^{2}z^{2}}{x^{2}+y^{2}+z^{2}-c^{2}w^{2}}}=0} They are used in the treatment of conical refractions .
Fresnel's Wave Surface, a quartic surface describing the propagation of light in an optically biaxial crystal, a = 1 , b = 0.5 , c = 1.5 , w = 1 {\displaystyle a=1,b=0.5,c=1.5,w=1} This page is based on this
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