Reflectance of metals at low frequencies

  • #1
When calculating the dielectric constant of metals using the Drude model, in the low frequency regime (infrared and beyond) one gets an approximately pure imaginary value:
$$\epsilon(\omega) \approx i\frac{4\pi n e^2\tau}{m_e\omega}$$
which gives an absorption coefficient:
$$\alpha(\omega) \approx \frac{\omega}{c}\sqrt{\frac{8\pi ne^2\tau}{m_e\omega}}$$
When looking at graphs of actual reflectivities of metals in the infrared, the reflectance is almost 100%. From this result however, I first thought that most of the incident light would be absorbed rather than reflected. Is there a physical reason for this difference, or is this a shortcoming of the Drude model?
 

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  • #2
Charles Link
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The reflectivity ## R ## at normal incidence is given by ## R=|(n-1)|^2/|(n+1)|^2 ##. When ## n ## is large and/or has a large imagninary part, the calculated ## R ## is very nearly 1.0. (The index ## n ## can be computed from ## \epsilon ## : ## n=\sqrt{\epsilon} ## ). Whatever gets inside the metal does not propagate very far, but very little gets inside. Most of it gets reflected.
 
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