Wavelength Change and Refractive index in a Conductor

1. Feb 27, 2012

Calannon

1. The problem statement, all variables and given/known data
Hey guys, new to the forums so hopefully you can help. I have been given the frequency (and hence the wavelength) of a microwave of 10GHz, and the conductivity of Al which is 3.53x10^7 Siemens/m. From this I have worked out the skin depth. But it asks also what the wavelength of the microwaves in the Al are. It also asks to find the refractive index from this. I am completely lost :(

2. Relevant equations

3. The attempt at a solution
I tried using the following to find refractive index, but got ~14000....

η=n+ik=c*K/w where K^2=iwμσ.

Found the real and imaginary parts of K^2 (real = 0 and im = wσμ) then made the assumption that n≈k≈K(Im)/2=√σ/(2wε).

This resulted in huge n and k values and so huge η value so I think it is wrong..No idea about the wavelength change one...

Any help would be appreciated guys :)

2. Feb 27, 2012