Advanced Topic The Color of Metals

The simple free electron model (the Drude model) developed in Section 4.4 for metals successfully explains some general properties, such as the filter action for UV radiation and their high reflectivity in the visible. However, in spite of the fact that metals are generally good mirrors, we perceive visually that gold has a yellowish color and copper has a reddish aspect, while silver does not present any particular color that is it has a similarly high reflectivity across the whole visible spectrum. In order to account for some of these spectral differences, we have to discuss the nature of interband transitions in metals. 

1 The sodium chloride (NaCl) crystal shows very high absorption and reflectivity in the infrared region, known as the Restrahlen region. The real and imaginary relative dielectric constants at 6000 nm are, respectively, ei = 16.8 and S2 = 91.4. At this wavelength, estimate (a) the refractive index and the extinction coefficient, and (b) the optical density and the reflectivity at normal incidence for a 1 mm thick NaCl sample, (c) If the previous sample is illuminated (at normal incidence) by a beam of intensity Iq at 6000 nm, estimate the intensity of this 

2 Sodium (Na) gas shows two well-defined absorption bands that peak at 589 nm and 589.6 nm. Consider this gas as a diluted medium (so that n 1), with a density of ions of N = 1 x 10 cm and a damping rate of F = 628 MHz. (a) Estimate the absorption coefficient at these two peaks, (b) Now estimate the power of a laser beam of 1 mW at 589.0 nm after it passes through a Na cell of thickness 5 cm. 

4 Zinc (Zn) is a divalent metal with an atomic density of 6.6 x 10 cm . Determine the wavelength region within the optical range for which you expect this metal to be a good mirror. 

5 Let us consider an ideal metal with 2 x 10 cm valence electrons. For such a metal, estimate (a) its plasma frequency, (b) the optical density at 400 nm for 

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