Wavelength Change and Refractive index in a Conductor

[Calannon]

Homework Statement

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 :(

Homework Equations

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 I am = 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 :)

 

[ehild]

n and k must be huge in such a good conductor as the aluminium. I found data only for 200 micrometer: http://refractiveindex.info/?group=METALS&material=Aluminium

ehild