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I Reflectance of metals at low frequencies

  1. May 29, 2016 #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?
     
  2. jcsd
  3. May 29, 2016 #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.
     
    Last edited: May 29, 2016
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