Snell's law
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Date: 14/03/2019

Snell's law, by Wikipedia https://en.wikipedia.org/wiki?curid=42964 / CC BY SA 3.0

#Geometrical_optics
Snell's law

Snell's law (also known as Snell–Descartes 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 metamaterials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.

Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the reciprocal of the ratio of the indices of refraction:

with each formula_2 as the angle measured from the normal of the boundary, formula_3 as the velocity of light in the respective medium (SI units are meters per second, or m/s), formula_4 as the wavelength of light in the respective medium and formula_5 as the refractive index (which is unitless) of the respective medium.

The law follows from Fermat's principle of least time, which in turn follows from the propagation of light as waves.

Ptolemy, a Greek living 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 fudging his data to fit theory (see: confirmation bias). Alhazen, in his "Book of Optics" (1021), came closer to discovering the law of refraction, though he did not take this step.

Although named after Dutch astronomer Willebrord Snellius (1580–1626), the law was first accurately described by the Persian scientist Ibn Sahl at the Baghdad court i...