ABSTRACT
A wave incident upon an interface separating two media gives rise (Section 22.1) to two waves, that is, a reflected (transmitted) wave propagating in the first (second) medium (Section 22.2). In the case of three media, for example, separated by two interfaces, waves incident from the two outer media can be reflected or transmitted once only, whereas waves propagating in the inner medium, between the two interfaces, can have multiple internal reflections. The calculation of the exact wave field, in the presence of multiple internal reflections, can be made by summing the reflections of all orders that lead to series (Section 22.6). The series will always converge provided that the process of transmission or reflection conserves or decreases energy, that is, the convergence is more rapid in the presence of adsorption at the interfaces, and/or absorption in the interior of the media (Section 22.5). The scattering of waves by a double interface, for example, a parallel-sided lens (Section 22.8), can also be studied by decomposing the wave field in the interior into two components propagating in opposite directions, orthogonal to the interfaces; the laws of reflection and transmission (Section 22.4) at the two interfaces then specify a system of algebraic equations, whose solution is the same as the sum of the series of multiple reflections. Both methods lead to global reflection and transmission coefficients for a lens consisting of two or more interfaces (Section 22.7), allowing it to be replaced by a single “equivalent” interface. These expressions include as particular instances the cases of transparent or opaque interfaces (Section 22.8), zones of darkness or of total reflection (Section 22.3), and constructive or destructive interference (Section 22.9). Multiple reflections occur for other geometries, and not only for light or electromagnetic waves, but also for acoustic, elastic, and other waves; in the case of elastic waves in solids, the reflections and/or focusing can lead to stress concentrations, crack formation and growth, and eventual structural failure or ejection of material (spalling).
