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For crystals or glasses, the group index in the visible or near-infrared spectral range is typically larger than the ordinary refractive index, which determines the phase velocity.
This implies that the group velocity is often (but not always) lower than the phase velocity.
Refractive index (solid lines) and group index (dotted lines) of silica versus wavelength at temperatures of 0 °C (blue), 100 °C (black) and 200 °C (red).
Note that for optical fibers and other waveguides, one uses the so-called effective refractive index instead of the ordinary refractive index in order to calculate the group velocity, since waveguide dispersion has to be taken into account.
Based on that, an effective group index of a fiber could be calculated.