The optical model of scattering by a composite cylinder

The optical approximation to scattering by a composite cylinder includes two classes of rays: those which are reflected by the core and those which are not. It is shown here that members of the latter set may arise whenever a certain integral has a stationary phase point in a restricted parameter regime. Consideration of the restrictions in the case of forward scattering shows that relatively few core-independent rays of low order will satisfy the geometrical requirements even when a stationary phase point exists.