A normal‐mode solution of the wave equation can be written asφ=e1ωl ∫0∞ J0(Kτ) F (Z,K)dK, whereF(Z,K) is a solution of(d2F/dz2) + [ω2/c2−K2] F=0. The specificF(Z,K) can be determined for a deep‐source shallow receiver by using the WKB approximation with the usual point source and surface‐boundary conditions. This solution can then be written as an infinite series of integrals, each of which is identifiable either as a real or a complex ray. This solution is not applicable in the immediate vicinity of the ray‐turning (horizontal) points. The first integral (the upcoming ray) is evaluated by the saddle‐point method. Where real rays exist, the usual ray equations are obtained, except for a slight correction to the intensity equation. It can be shown that this solution can be continued around the ray‐turning point to give an evaluation of the sound in the shadow zone. This solution will yield results similar to Pekeris' for his simple shadow case, and is similar in some respects to the work of Keller and Seckler. It justifies the use of ray optics after a caustic. It also justifies caustic‐intensity calculations based on ray optics. More important, it shows that the signal form is unchanged, if it is propagated by real rays, and is modified if it is propagated as a complex ray.