Wavelength Change and Refractive index in a Conductor

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SUMMARY

The discussion centers on calculating the wavelength of microwaves in aluminum (Al) at a frequency of 10 GHz and determining the refractive index based on its conductivity of 3.53x107 Siemens/m. The user attempted to use the equation η=n+ik=c*K/w, where K2=iwμσ, but encountered unrealistic values for the refractive index and wave vector. The user seeks clarification on the wavelength change in a conductor and the correct approach to calculating the refractive index for aluminum.

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  • Understanding of electromagnetic wave propagation in conductors
  • Familiarity with complex refractive index calculations
  • Knowledge of skin depth in conductive materials
  • Basic principles of microwave frequency and wavelength relationships
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Calannon
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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 :)
 
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