Snell's law

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).

[4] The law was eventually named after Snell, although it was first discovered by the Persian scientist Ibn Sahl, at Baghdad court in 984.

[6][7][8] In the manuscript On Burning Mirrors and Lenses, Sahl used the law to derive lens shapes that focus light with no geometric aberration.

[9] Alhazen, in his Book of Optics (1021), came close to rediscovering the law of refraction, but he did not take this step.

[10] The law was rediscovered by Thomas Harriot in 1602,[11] 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the Dutch astronomer Willebrord Snellius (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime.

René Descartes independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay Dioptrique, and used it to solve a range of optical problems.

[12][13] Fermat's derivation also utilized his invention of adequality, a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.

[14][15] In his influential mathematics book Geometry, Descartes solves a problem that was worked on by Apollonius of Perga and Pappus of Alexandria.

When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves.

[16] According to Dijksterhuis,[17] "In De natura lucis et proprietate (1662) Isaac Vossius said that Descartes had seen Snell's paper and concocted his own proof.

In his 1678 Traité de la Lumière, Christiaan Huygens showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the Huygens–Fresnel principle.

With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage.

In 1962, Nicolaas Bloembergen showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.

[18] In 2008 and 2011, plasmonic metasurfaces were also demonstrated to change the reflection and refraction directions of light beam.

and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.

Refraction between two surfaces is also referred to as reversible because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.

Snell's law is generally true only for isotropic or specular media (such as glass).

When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media,

Snell's law can be derived from Fermat's principle, which states that the light travels the path which takes the least time.

(There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.)

In a classic analogy, the area of lower refractive index is replaced by a beach, the area of higher refractive index by the sea, and the fastest way for a rescuer on the beach to get to a drowning person in the sea is to run along a path that follows Snell's law.

Therefore, Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference Another way to derive Snell's Law involves an application of the general boundary conditions of Maxwell equations for electromagnetic radiation and induction.

Yet another way to derive Snell's law is based on translation symmetry considerations.

Using the well known dependence of the wavenumber on the refractive index of the medium, we derive Snell's law immediately.

is the normal vector that points from the surface toward the side where the light is coming from, the region with index

The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation which is impossible to satisfy.

Such dispersion of light in glass or water underlies the origin of rainbows and other optical phenomena, in which different wavelengths appear as different colors.

In optical instruments, dispersion leads to chromatic aberration; a color-dependent blurring that sometimes is the resolution-limiting effect.

This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself.