Editing Group velocity (section)

=== Other expressions ===
For light, the refractive index {{math|''n''}}, vacuum wavelength  {{math|''λ<sub>0</sub>''}}, and wavelength in the medium  {{math|''λ''}}, are related by
:<math>\lambda_0 = \frac{2\pi c}{\omega}, \;\; \lambda = \frac{2\pi}{k} = \frac{2\pi v_{\rm p}}{\omega}, \;\; n = \frac{c}{v_{\rm p}} = \frac{\lambda_0}{\lambda},</math>
with  {{math|''v''<sub>p</sub>&nbsp;{{=}}&nbsp;''ω''/''k''}} the [[phase velocity]].

The group velocity, therefore, can be calculated by any of the following formulas,
:<math> \begin{align}
  v_{\rm g} &= \frac{c}{n + \omega \frac{\partial n}{\partial \omega}}
       = \frac{c}{n - \lambda_0 \frac{\partial n}{\partial \lambda_0}}\\
      &= v_{\rm p} \left(1 + \frac{\lambda}{n} \frac{\partial n}{\partial \lambda}\right)
       = v_{\rm p} - \lambda \frac{\partial v_{\rm p}}{\partial \lambda} = v_{\rm p} + k \frac{\partial v_{\rm p}}{\partial k}.
\end{align}</math>