Refractive index

The refractive index of a material is the factor by which the phase velocity of electromagnetic radiation is slowed relative to vacuum. It is given by:

Related Topics:
Phase velocity - Electromagnetic radiation

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:: n=sqrt{epsilon_rmu_r}

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where εr is the material's relative permittivity, and μr is its relative permeability. For a non-magnetic material, μr is very close to 1, therefore n is approximately sqrt{epsilon_r}.

Related Topics:
Permittivity - Permeability

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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. It is the group velocity that (almost always) represents the rate that information (and energy) may be transmitted by the wave, for example the velocity at which a pulse of light travels down an optical fibre.

Related Topics:
Phase - Amplitude - Optical fibre

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The speed of all electromagnetic radiation in vacuum is the same, approximately 3×108 meters per second, and is denoted by c.

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Therefore, if v is the phase velocity of radiation of a specific frequency in a specific material, the refractive index is given by

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::n =rac{c}{v}

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This number is typically bigger than one: the denser the material, the more the light is slowed down. However, at certain frequencies (e.g. near absorption resonances, and for x-rays), n will actually be smaller than one. This does not contradict the theory of relativity, which holds that no information-carrying signal can ever propagate faster than c, because the phase velocity is not the same as the group velocity or the signal velocity.

Related Topics:
Absorption - X-ray - Theory of relativity - Phase velocity - Group velocity - Signal velocity

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Sometimes, a "group velocity refractive index", usually called the group index is defined:

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::n_g=rac{c}{v_g},

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:where vg is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity.

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At the microscale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the permittivity. The charges will, in general, oscillate slightly out of phase with respect to the driving electric field. The charges thus radiate their own electromagnetic wave that is at the same frequency but with a phase delay. The macroscopic sum of all such contributions in the material is a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions (see scattering).

Related Topics:
Electric field - Electron - Phase - Scattering

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If the refractive indices of two materials are known for a given frequency, then one can compute the angle by which radiation of that frequency will be refracted as it moves from the first into the second material from Snell's law.

Related Topics:
Refracted - Snell's law

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Recent research has also demonstrated the existence of negative refractive index which can occur if ε and μ are simultaneously negative. Not thought to occur naturally, this can be achieved with so called metamaterials and offers the possibility of perfect lenses and other exotic phenomena such as a reversal of Snell's law.

Related Topics:
Metamaterial - Snell's law

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