The dielectric constant K of a gas is related to its index of refraction by the relation K = n. a. Show that the group velocity for waves traveling in the gas may be expressed in terms of the dielectric constant by Ug C VK w dK 1 2K dw where c is the speed of light in vacuum. b. An empirical relation giving the variation of K with fre- quency is K = 1 + [A/(w - w)] where A and wo are constants for the gas. If the second term is very small compared to the first, show that wA Ug - -(w/ w)]