The dielectric constant K of a gas is related to its index of refraction by the relation K...

The dielectric constant K of a gas is related to its index of refraction by the relation K = n2.

a. Show that the group velocity for waves traveling in the gas may be expressed in terms of the dielectric constant by

 

where c is the speed of light in vacuum.

---

b. An empirical relation giving the variation of K with frequency is

 

where A and ω0 are constants for the gas. If the second term is very small compared to the first, show that