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$$\epsilon(\omega) \approx i\frac{4\pi n e^2\tau}{m_e\omega}$$

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?