AbstractThe scattering of a ‘plane wave’ off a submerged body situated in an ocean of finite depth is investigated. The index of refraction is considered to be depth‐independent. It is shown that the far field is not unique; hence, the problem of determining the shape of an object from its far field is not well‐posed. If solutions are sought among a restricted class of problems the ‘dense set’ property implies that the problem can be made