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The absolute refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299 792 458 m/s, and the phase velocity v of light in the medium, =. Since c is constant, n is inversely proportional to v : n ∝ 1 v . {\displaystyle n\propto {\frac {1}{v}}.}
Refraction of light at the interface between two media of different refractive indices, with n 2 > n 1.Since the velocity is lower in the second medium (v 2 < v 1), the angle of refraction θ 2 is less than the angle of incidence θ 1; that is, the ray in the higher-index medium is closer to the normal.
For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200 000 km/s (124 000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than c.
In the context of electromagnetics and optics, the frequency is some function ω(k) of the wave number, so in general, the phase velocity and the group velocity depend on specific medium and frequency. The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n = c / v p = ck / ω.
It is possible to make the effective speed of light dependent on wavelength by making light pass through a material which has a non-constant index of refraction, or by using light in a non-uniform medium such as a waveguide. In this case, the waveform will spread over time, such that a narrow pulse will become an extended pulse, i.e., be dispersed.
The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n = c / v p = ck / ω. In this way, we can obtain another form for group velocity for electromagnetics. Writing n = n(ω), a quick way to derive this form is to observe
The index of refraction (n) is calculated from the change of angle of a collimated monochromatic beam of light from vacuum into liquid using Snell's law for refraction. Using the theory of light as an electromagnetic wave, [ 9 ] light takes a straight-line path through water at reduced speed ( v ) and wavelength ( λ ).
where d 1 and d 2 are the distances of the ray passing through medium 1 or 2, n 1 is the greater refractive index (e.g., glass) and n 2 is the smaller refractive index (e.g., air). See also [ edit ]