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A theory is developed for the p-polarized optical properties of a semi-infinite electron gas with a surface that scatters the electrons din'usely. The electron gas response is described by the Soltzmann equation. An important ingredient of the theory is the use of a legitimate distribution function for electrons leaving the surface, one which permits the normal component of the current density to vanish at the surface. It is found that the optical absorptance below the plasma frequency is an order of magnitude too large if this boundary condition on the normal component of the current is ignored by simply using the unperturbed distribution function for electrons leaving the surface. The calculated absorptance is compared for diffusely and specularly scattering surfaces. Below the plasma frequency the absorptance is higher for diffuse scattering, as is also true for s polarization, while above the plasma frequency the absorptance is essentially the same for diffuse and specular scattering. Interesting structure occurs in the vicinity of the plasma frequency.

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