# Snell's law

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In optics and physics, Snell's law (also known as Descartes' law, the Snellâ€“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 and glass. The law says that the ratio of the sines of the angles of incidence and of refraction is a constant that depends on the media. The refractive index can be calculated by rearranging the formula accordingly.

In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics and gemology to find the refractive index of a material.

Snell's law is also satisfied in metamaterials, which allow light to be bent "backward" at a negative angle of refraction (negative refractive index).

Named after Dutch mathematician Willebrord Snellius, one of its discoverers, Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of velocities in the two media, or equivalent to the opposite ratio of the indices of refraction:

with each Î¸ as the angle measured from the normal, v as the velocity of light in the respective medium (SI units are meters per second, or m/s) and n as the refractive index (which is unitless) of the respective medium.

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

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### History

Ptolemy, a Greek living in Alexandria,[1] 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).[2] Alhazen, in his Book of Optics (1021), came closer to discovering the law of refraction, though he did not take this step.[3]