PHYS 352, Spring 2013
Dispersion in Materials
1. Show that the imaginary part of the index of refraction for a single resonant gas where the
plasma frequency p is much smaller than optical frequencies is
Im(n)  
 p2

2o 4   2    2
where N is the number of dipoles per unit volume,  is the dissipation coefficient for the velocity
dependent drag force FD=mev, and =-o is the difference in frequency of the light wave
from the resonant frequency, o. Provide a qualitative hand sketch of Im(n) as a function of 
with your solution.
2. Show that the real and imaginary parts of the index of refraction are related by
no  1
2    

no

which is a form of the Kramers-Kronig relations, a set of relations that relate real and imaginary
parts of physical properties.