Microscopic approach to reflection, transmission, and the Ewald–Oseen extinction theorem

We describe how the reflection and transmission of light at a dielectric interface can be understood starting from the fact that dielectrics are collections of molecules. More precisely, we consider from the microscopic perspective the interpretation and significance of the Ewald–Oseen extinction theorem of classical optics. The usual interpretation of the theorem is that an incident field is extinguished by the dipoles on the boundary and replaced by transmitted and reflected fields consistent with the Maxwell equations for the media. However, the extinction theorem is more appropriately regarded simply as a boundary condition effected by all the molecular scatterers, not just those at the boundary. To demonstrate this we take a microscopic approach to three familiar problems: (1) the electrostatic interaction of a point charge with a dielectric wall; (2) the reflection of a monochromatic plane wave at a dielectric interface; and (3) diffraction by an aperture. We show that the extinction of the incident field cannot be attributed to any finite dipole boundary layer, and in particular it does not involve any ‘‘extinction theorem distance.’’