1. The frequency-dependent dielectric constant in an insulator is approximately given by Ne Zb 1 r (w) = 1 + meo j=1 w} - w - ixjw" where N is the number density of molecules, Ze is the number of bound electrons per molecule, e and m are the electron charge and mass, {w} is the set of resonant frequencies which have widths (w), and wis the frequency of the electromagnetic wave. (a) Calculate the real and imaginary parts of the dielectric constant = & + ". (b) Sketch the real and imaginary parts of the dielectric constant for two well- separated resonances wi w2, say one in the far infrared and one in the far ultraviolet. (c) Show that at frequencies far below all of the resonances, the real and imaginary parts of the dielectric constant are given by 1+ Ne/(meon) + (Ne/(meon))w, Find 1 and 2. 0.