In this article, the electromagnetic waves scattered by an inhomogeneous medium are studied when the electromagnetic waves are polarized in the case of transverse electric. Using the Rellich lemma, the uniqueness of the solution of the direct problem is proved. In order to show the existence of the solution of this problem, the operator equations are constructed and the Riesz theory is used. In addition, the uniqueness and the existence of the solution of the interior boundary value problem are proved. (c) 2004 Elsevier Inc. All rights reserved.