Wave surface

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title: "Wave surface" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["algebraic-surfaces", "complex-surfaces", "waves", "1822-in-science"] topic_path: "general/algebraic-surfaces" source: "https://en.wikipedia.org/wiki/Wave_surface" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

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 : \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 They are used in the treatment of conical refractions.[[File:Fresnel's Wave Surface.png|thumb|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.]]

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).

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