Definitions of Refractive index

The refractive index, n, of a medium is defined as the ratio of the velocity, c, of a wave phenomenon such as light or sound in a reference medium to the phase velocity, vp, in the medium itself:
It is most commonly used in the context of light with vacuum as a reference medium, although historically other reference media (e.g. air at a standardized pressure and temperature) have been common. It is usually given the symbol n. In the case of light, it equals
,
where εr is the material's relative permittivity, and μr is its relative permeability. For most materials, μr is very close to 1 at optical frequencies, therefore n is approximately . Contrary to a widespread misconception, n may be less than 1, for example for x-rays.[1] This has practical technical applications, such as effective mirrors for x-rays based on total external reflection. Another example is that the n of electromagnetic waves in plasmas is less than 1.
The phase velocity is defined as the rate at which the crests of the waveform propagate; that is, the rate at which the phase of the waveform is moving. The group velocity is the rate that the envelope of the waveform is propagating; that is, the rate of variation of the amplitude of the waveform. Provided the waveform is not distorted significantly during propagation, it is the group velocity that represents the rate that energy may be transmitted by the wave, for example the velocity at which a pulse of light travels down an optical fiber. Information travels at the front velocity.

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