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Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, [1] 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.
This phenomenon, known as total internal reflection, occurs at incidence angles for which Snell's law predicts that the sine of the angle of refraction would exceed unity (whereas in fact sin θ ≤ 1 for all real θ). For glass with n = 1.5 surrounded by air, the critical angle is approximately 42°.
For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence and angle of refraction is equal to the ratio of phase velocities in the two media, or equivalently, to the refractive indices of the two media: [2]
[47]: 229 The refractive index is used for optics in Fresnel equations and Snell's law; while the relative permittivity and permeability are used in Maxwell's equations and electronics. Most naturally occurring materials are non-magnetic at optical frequencies, that is μ r is very close to 1, therefore n is approximately √ ε r. [48]
Refraction of a thin planoconvex lens. Consider a thin lens with a first surface of radius and a flat rear surface, made of material with index of refraction .. Applying Snell's law, light entering the first surface is refracted according to = , where is the angle of incidence on the interface and is the angle of refraction.
Ibn Sahl dealt with the optical properties of curved mirrors and lenses and has been described as the discoverer of the law of refraction (Snell's law). [9] [10] [11] Ibn Sahl uses this law to derive lens shapes that focus light with no geometric aberrations, known as anaclastic lenses.
Snell's Law can be used to predict the deflection of light rays as they pass through "linear media" as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism.
Snell's law for refraction requires that these terms be equal. As this calculation demonstrates, Snell's law is equivalent to vanishing of the first variation of the optical path length. As this calculation demonstrates, Snell's law is equivalent to vanishing of the first variation of the optical path length.