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The refractive index compares the phase velocity of light in a medium with the vacuum speed of light $c$. For a transparent, uniform medium with isotropy and a positive-index propagation branch,Here $\omega >0$ is the angular frequency, $k>0$ is the wavenumber, and $v_{\mathrm{ph}}=\omega /k$ is the speed of a surface of constant wave phase. The refractive index is a dimensionless quantity; it is a property of a specified material response at a specified frequency, rather than a universal number attached to the word “glass”. More general absorbing or negative-index media require the conventions discussed in refractive index and electromagnetic response. ^[ref]

For an original model example, choose $n=3/2$ at vacuum wavelength ${\lambda }_0=600\mathrm{nm}$. The phase velocity is $v_{\mathrm{ph}}=2c/3\simeq 1.999\times 10^{8}m/s$, the frequency is $f=c/{\lambda }_0\simeq 4.997\times 10^{14}\mathrm{Hz}$, and the medium wavelength is $400\mathrm{nm}$. These are stipulated model values, not measured properties of glass or water. A value at this single frequency does not determine a pulse's group velocity.

The usefulness of refractive index is that one measured response connects several different observations: Snell's law predicts refraction, optical path length predicts accumulated wave phase, and changes with frequency describe optical dispersion. Even at normal incidence, where a light ray does not bend, a changed refractive index changes wavelength and wave phase. The following comparison isolates that effect; the oblique geometry is developed in wavefront.