Published online by Cambridge University Press: 16 October 2026
This chapter applies the plane-wave and dielectric-response formalisms to reflection and refraction at planar interfaces and to wave propagation in conducting media. Starting from a normally incident plane wave on a semi-infinite dielectric, it treats the material response with a polarization current, derives an integral equation for the field, and solves it to obtain incident, reflected, and transmitted waves. The result is expressed in terms of the susceptibility and refractive index, yielding normal-incidence Fresnel reflection and transmission coefficients and clarifying how boundary conditions emerge from the microscopic response. The chapter then turns to metals, modeling their response with a conduction current, J = σE. From the continuity equation and Gauss’s law it derives the dielectric relaxation time that governs charge screening, and from the wave equation with complex permittivity it finds plane-wave solutions with complex wave vector, strong attenuation, and a skin depth much smaller than a wavelength in good conductors. The discussion closes with qualitative implications for shielding and high-frequency signal transmission.
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