Assume that a low-density gas has only one resonant frequency, ?0, and show that n ? Nq^2 / (2?0me(?0^2-?^2) ) starting with n^2 = Nq^2 / (2?0me(?0^2-?^2) ). Fully justify any mathematical expansion you employ. Assume the resonance occurs at a wavelength (corresponding with ?0) of 800nm, near the red limit of what the eye can see, and use a number density of 1 amagat to numerically plot the index vs. wavelength of the range from 400nm to 780nm. Breifly explain the general shape of the plot.