Snell's law

Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index. Snell's law states that, for a given pair of media, the ratio of the sines of angle of incidence () and angle of refraction () is equal to the refractive index of the second medium w.r.t the first (n21) which is equal to the ratio of the refractive indices (n2/n1) of the two media, or equivalently, to the ratio of the phase velocities (v1/v2) in the two media. The law follows from Fermat's principle of least time, which in turn follows from the propagation of light as waves. Ptolemy, in Alexandria, Egypt, had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: confirmation bias). The law was eventually named after Snell, although it was first discovered by the Persian scientist Ibn Sahl, at the Baghdad court in 984. In the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberration. Alhazen, in his Book of Optics (1021), came close to rediscovering the law of refraction, but he did not take this step. The law was rediscovered by Thomas Harriot in 1602, who however did not publish his results although he had corresponded with Kepler on this very subject. In 1621, the Dutch astronomer Willebrord Snellius (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime.