For an infinite plane elastic wave which strikes the plane interface separating two semiinfinite isotropic media, the calculation of the complex reflection coefficient,R*, for varying angles of incidence, θ, is not difficult. In the past, calculations have been made for a number of lossless media and, consequently, an important facet of theR*−θ curve for real materials has been overlooked. The total reflection, |R*|=1, which occurs at the longitudinal‐ and shear‐wave critical angles is well known, but the appearance of a minimum (sometimes a zero) inR* is not and its existence defines a third critical angle, sometimes inappropriately called the Rayleigh‐wave angle, at which a wave with large surface components is generated. During experiments with beams of acoustic waves, there is an apparent lateral displacement of the reflected beam at the third critical angle which manifests itself markedly only when there is a near‐zero in |R*|. Notwithstanding the calculations of Schoch [Ergeb. Exakt. Naturw.23, 127–234 (1950)] and the experimental measurements of others apparently to the contrary, it is strongly suggested that no actual lateral displacement occurs and that re‐radiation from the region outside that ensonified by the incident beam gives rise to the apparent lateral displacement. Some outcomes of the investigation are discussed and of these the more important are: (1) Rayleigh and other interface and surface waves in real media are degenerate; (2) no interface wave can exist independently at the junction of two nonideal media; (3) Huyghens's principle in its elementary secondary‐wavelet form does not apply to lossy media; (4) the usefulness of the sensitivity ofR* to minute changes in elastic parameters at the Rayleigh angle as a measuring tool has a wide application; (5) elliptical polarization of both shear and longitudinal waves can occur, owing to boundary influences in lossy refracting media. The real part of the propagation vector lies in the plane of the ellipse.