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A second-order theory is developed for the reflection and transmission of light by a slightly rough surface. The general results are discussed, especially for a rough interface between vacuum and a free-electron-like metal, where surface-plasma excitation can occur. The influence of the damping of the electron gas and of the shape of the roughness is discussed. Some different previous theories for reflection by a rough surface are shown to be limiting cases of the present theory.
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Kretschmann et al. (1975) studied this question.
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