In vacuum, the wavelength of an electromagnetic wave varies inversely with frequ

Question

In vacuum, the wavelength of an electromagnetic wave varies inversely with frequency. From equation (2.24), how does the wavelength of an electromagnetic wave penetrating a conductor vary with frequency? What is this wavelength if the skin depth at this frequency is 20 nm?

Explanation / Answer

( ilde{k} = 2pi/ ilde{lambda} = pm sqrt{i omega mu_o sigma}) ( ilde{lambda} =pm rac{2pi}{mu_o sigma omega} (1- i) ) =>(lambda = pm rac{2pi}{mu_o sigma omega} propto pm rac{1}{omega} ) so (lambda) decreases with increase in (omega). ( ilde{lambda} = pm sqrt{-2 pi^2 i} cdot S) ( ilde{lambda} = pm sqrt{2pi^2} cdot S cdot (1 - i) ) or (lambda = Re( ilde{lambda}) = pm sqrt{2pi^2} cdot S ) so (lambda) decreases with increase of the Skin depth. for S = 20 nm (lambda = 88.85766 nm )

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