Phase velocity and group velocity
The phase velocity and group velocity are speed in terms of an expression which are directly equal to each other.
A single (infinite) wave is described by the expression or equivalent. The pattern travels with a velocity (actually a speed)vp is what matters with interference. The refractive index n is deﬁned as c/v and this means c/vp.
An inﬁnite wave is unrealistic. A real wave has to have beginning and end. The overall shape is called the envelope. Various shapes are possible - abrupt or gentle.
Relation between group velocity and phase velocity: