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.

Although named after Dutch astronomer Willebrord Snellius (1580–1626), the law was first accurately described by the 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 aberrations.

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 ${\displaystyle \theta }$ as the angle measured from the normal of the boundary, ${\displaystyle v}$ as the velocity of light in the respective medium (SI units are meters per second, or m/s), ${\displaystyle \lambda }$ as the wavelength of light in the respective medium and ${\displaystyle n}$ as the refractive index (which is unitless) of the respective medium.

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