Refraction holodiagrams and Snell's law
Abstract:The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines.
Document Type: Research Article
Affiliations: Centro de Investigaciones Ópticas (CONICET-CIC), P.O. Box 124, 1900 La Plata, Argentina also with OPTIMO, Depto. de Fisicomatemáticas, Facultad de Ingeniería, Universidad Nacional de La Plata, Argentina
Publication date: May 1, 2003