Group velocity is the velocity of wave packet motion, vg=dw/dk.

The first formula is easy to understand. The electromagnetic plane wave is w=kc, and the speed of light is c = w/K.

The second formula is not very intuitive and can be understood from the sum-difference product formula of sin(a)+sin(b). The speed of wave packet is mainly determined by the difference frequency term. At this time, the phase velocity of the difference frequency term is the group velocity, and it is found that the group velocity of the difference frequency term is VG = (w1-w2)/(k1-k2), which is the limit case.