Faster than light phenomenon

Originally posted by DragonsDemesne
The following is from my textbook "Optics" 4th edition by Eugene Hecht (which has the added bonus of being something I need to know for my final on Thursday, hehe)

...blah blah... some math derivations... we can arrive at an expression for n as a function of w, which is known as a dispersion equation:

n^2 = 1 + [(Nq^2)/(E*m)]*[1/(wo^2 - w^2)]

(gotta love trying to put formulas into a forum, lol)

n = index of refraction
q = elementary charge = 1.6*10^-19 C
E = permittivity of free space = 8.85*10^-12 F/m
m = mass of an electron
N = number of electrons in the volume being looked at
wo = resonant frequency
w = frequency of EM wave coming in (i.e. the light wave)

So at frequencies above resonance, (when w>wo) then the right hand side of the equation is going to be 1 + (something negative) = something smaller than 1.

Yes, I have only one question: why does wavelength not constitute a part of the formula or does it and I am just missing it? Not to say that I am surprised or anything, optics is way out of my league and something I may never go into. All that I know about light comes from my eduaction in chemistry. All we did were a few formulas like: frequency x wavelength = speed of wave. I am just currious.

Wavelength is involved in the formula in a kind of indirect way.

w = 2*pi*f
(w is frequency in radians, f is frequency in hertz)
v = f * L
(v= speed of wave, f = frequency Hz, and L = lambda=wavelength)

So it is there, it's just not immediately obvious.

[edit on 13-12-2005 by DragonsDemesne]