*(English)*Zbl 1219.35363

The paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium, which widely occur in practical applications. The case where the obstacle is buried in a two-layered piecewise homogeneous medium is considered but the results can be extended to the multi-layered case. The well-posedness of the corresponding direct problem is established by means of the integral equation method.

It was proved previously [see *X. Liu* and *B. Zang*, Appl. Anal. 88, No. 9, 1339–1355 (2009; Zbl 1176.78010)], under the condition that the wave numbers in the innermost and outmost homogeneous layers coincide and ${S}_{0}$ is known in advance, that the obstacle with its physical property can be uniquely determined from knowledge of the electric far-field pattern for incident plane waves. In the present paper this restriction is removed by establishing a new mixed reciprocity relation. It is proved that the penetrable interface between layers can also be uniquely determined.