Chapter 33: Reflection & Transmission from Surfaces

Reflection & Transmission from Surfaces , titled "Reflection from Surfaces," provides the rigorous theoretical derivation of how electromagnetic waves, particularly light, behave when encountering the boundary between two different materials, building upon geometric optics principles like the equivalence of the angle of incidence and the angle of reflection, and Snell's law for refraction. The primary focus shifts from simple rules to the dependency of reflection and transmission on the wave's polarization, leading to the derivation of the Fresnel's equations, which relate the amplitudes of the incident, reflected, and transmitted waves based on whether the electric field (E vector) is polarized perpendicular or parallel to the plane of incidence. This derivation requires applying Maxwell’s equations and solving the boundary conditions that must be satisfied by the electric (E) and magnetic (B) fields across the interface. The treatment utilizes the representation of a plane wave using the wave vector (k) within dense materials. Finally, the chapter applies these theoretical results to two key phenomena: reflection from metals, which requires using a complex index of refraction to account for the material’s absorption of light, and total internal reflection, which is shown to result in an evanescent wave that penetrates the second medium for a short, exponentially decreasing distance beyond the interface.