In Chapters 9 to 11, the discussion of Mie scattering was restricted to N > 1. We now consider a new type of semiclassical diffraction effect, not included in the classification given in Chapter 1, that takes place, for N < 1, near the critical angle for total reflection. It occurs, for example, in the scattering of light by air bubbles in water.

In the geometrical-optic limit, the new effect, near-critical scattering, does not correspond to a caustic singularity in the light intensity, which remains continuous: there is a limiting singularity, but only in the gradient of the intensity. We refer to it as a weak caustic.

The penetration of light incident beyond the critical angle into the optically rarer medium is the earliest example of tunneling in physics. It was discovered, amazingly enough, by Newton, who observed frustrated total reflection in his experiments on Newton's rings (see the above quotation).

According to Newton's ideas, a light ray would follow a parabolic path within the rarer medium before returning to the denser one. This would produce a lateral displacement of the reflected beam. Although our views about paths differ from Newton's, the displacement does exist: it is known as the Goos–Hänchen shift (Goos & Hänchen 1947). In near-critical scattering from a curved interface, it is modified by the dynamical effects of curvature.