Refractive Index

speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. Increasing refractive index corresponds to decreasing speed of light in the material.

$Illustration of the incidence and refraction angles$

Refraction of a light ray

The refractive index determines how much the path of light

The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n₁ sinθ₁ = n₂ sinθ₂, where θ₁ and θ₂ are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices n₁ and n₂. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel's equations) and Brewster's angle.^[1]

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ₀/n, where λ₀ is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and that the frequency (f = v/λ) of the wave is not affected by the refractive index. As a result, the perceived color of the refracted light to a human eye which depends on the frequency is not affected by the refraction or the refractive index of the medium.

The refractive index varies with wavelength, this c

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ₀/n, where λ₀ is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and that the frequency (f = v/λ) of the wave is not affected by the refractive index. As a result, the perceived color of the refracted light to a human eye which depends on the frequency is not affected by the refraction or the refractive index of the medium.

The refractive index varies with wavelength, this causes white light to split into constituent colors when refracted. This is called dispersion. It can be observed in prisms and rainbows, and as chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index.^[2] The imaginary part then handles the attenuation, while the real part accounts for refraction. For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Nevertheless, refractive indices for materials are commonly reported using a single value for n, typically measured at 633 nm.

The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves. It can also be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.^[3]

The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, and the phase velocity v of light in the medium,^[1]

n={\frac {c}{v}}.

The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves.

The definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used.^[1] Historically air at a standardized pressure and temperature has been common as a reference medium.

History

Thomas Young coined the term index of refraction.

Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in 1807.^[4] At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water).^[5] Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9" (for urine).^[6] Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water).^[7]

Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, and µ.^[8]^[9]^[10] The symbol n gradually prevailed.

Typical values

phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves.

The definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used.^[1] Historically air at a standardized pressure and temperature has been common as a reference medium.

History

[1] Historically air at a standardized pressure and temperature has been common as a reference medium.

Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in 1807.^[4] At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water).^[5] Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9" (for urine).^[6] Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water).^[7]

Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, and µ.^[8]^[9]^[10] The symbol n gradually prevailed.