The Malus-Dupin theorem is a theorem in geometrical optics discovered by Étienne-Louis Malus in 1808[1] and clarified by Charles Dupin in 1822.[2] Hamilton proved it as a simple application of his Hamiltonian optics method.[3][4]
Consider a pencil of light rays in a homogenous medium that is perpendicular to some surface. Pass the pencil of rays through an arbitrary amount of reflections and refractions, then let it emerge in some other homogenous medium. The theorem states that the resulting pencil of light rays is still perpendicular to some other surface.
- ^ É. L. Malus, Journal de l’École Polytechnique 7, pp. 1–44 and 84–129.
- ^ C. Dupin, Applications de la géométrie, Mémoire présenté à l’Académie des Sciences en 1816, publié à Paris en 1822.
- ^ W. R. Hamilton, Theory of systems of rays, Part First and Part Second. Part first: Trans. Royal Irish Academy, 15, pp. 69–174. Part Second: manuscript. In Sir William Rowan Hamilton mathematical Works, vol. I, chapter I, Cambridge University Press, London, 1931
- ^ Marle, Charles-Michel (2016). "The works of William Rowan Hamilton in geometrical optics and the Malus-Dupin theorem". Banach Center Publications. 110: 177–191. arXiv:1702.05643. doi:10.4064/bc110-0-12. ISSN 0137-6934. S2CID 56427269.