A plane light wave propagates in a medium characterized by the law of dispersion: v = a + bλ, where a, b are positive constants, and v is the phase velocity. Show that the ratio of the path S traversed by the wave during the time interval t to the duration of this interval is equal to the group velocity.

A plane light wave propagates in a medium characterized by the law of dispersion: v = a + bλ, where a, b are positive constants, and v is the phase velocity. Show that the ratio of the path S traversed by the wave during the time interval t to the duration of this interval is equal to the group velocity.