In mathematics, Fresnel's wave surface, found by

Augustin-Jean Fresnel Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theo ...

in 1822, is a

quartic surface In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An ''affine'' 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 surface In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian vari ...

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

\frac + \frac + \frac =0

References

* * * Fresnel, A. (1822), "Second supplément au mémoire sur la double réfraction" (signed 31 March 1822, submitted 1 April 1822), in H. de Sénarmont, É. Verdet, and L. Fresnel (eds.), ''Oeuvres complètes d'Augustin Fresnel'', Paris: Imprimerie Impériale (3 vols., 1866–70)
vol.2 (1868)
pp.369–442, especially pp. 369 (date ''présenté''), 386–8 (eq.4), 442 (signature and date). * *{{Citation , last1=Love , first1=A. E. H. , title=A treatise on the Mathematical Theory of Elasticity , orig-year=1927 , url=https://books.google.com/books?id=ViebCriF-ssC , publisher=Dover Publications, New York , isbn=978-0-486-60174-8 , mr=0010851 , year=2011

External links

Algebraic surfaces Complex surfaces Waves