User:Germendax
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Group and phase velocity
Another consequence of dispersion manifests itself as a temporal effect. The formula above, v = c / n calculates the phase velocity of a wave; this is the velocity at which the phase of any one frequency component of the wave will propagate. This is not the same as the group velocity of the wave, which is the rate that changes in amplitude (known as the envelope of the wave) will progagate. The group velocity vg is given by:
![v_g = c \left[ n - \lambda \frac{dn}{d\lambda} \right]^{-1}](../../../../math/a/5/e/a5e93458bcb765cba9facf704fd696b0.png)
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The group velocity vg is often thought of as the velocity at which energy or information is conveyed along the wave. In most cases this is true, and the group velocity can be thought of as the signal velocity of the waveform. In some unusual circumstances, where the wavelength of the light is close to an absorption resonance of the medium, it is possible for the group velocity to exceed the speed of light (vg > c), leading to the conclusion that superluminal (faster than light) communication is possible. In practice, in such situations the distortion and absorption of the wave is such that the value of the group velocity essentially becomes meaningless, and does not represent the true signal velocity of the wave, which stays less than c.
