On the limitations of geometrical optics solutions for curved surfaces with variable impedance properties

In the preceding paper , t he authors have presented an asympto tic solution for t he fi eld in the illuminated region of a large circula r cylinder whose s urface impedance a round t he periph ery deviates from a constant value by a s inusoida l variation of small ampli t ude ." . T o 0 (.,,) , t he r eflected fi eld co mprises a specula rly reflected ray a nd two first-order diffracted rays ch aracteristic of a curved convex reflection grating. If the surface impeda nce varies " slowly," these t hree r ays can be combined in to a single spec ularly r eflected ray hav ing a reflection coeffi cien t which depends solely o n t he local impeda nce at the reflection point. The " slowness" co ndi t ions necessary for t he validity of th is local reflect ion prin ciple of geometrical optics a rc investigated a nd interprcted in ph ys ical term s. The resul ts a re presented in a ma nn er which suggests t heir appli cab ili ty to ge nera l, gently curved surfaces with slowly vary in g impedance propert ies.