  In this paper we study an inverse boundary value problem for Maxwell's
equations. The goal is to reconstruct perturbations in the refractive index of
the medium inside an object from the knowledge of the tangential trace of an
electric field on a part of the boundary of the domain. We first provide a
uniqueness result for this inverse problem. Then, we propose a complete
procedure to reconstruct numerically the perturbations, based on the
minimization of a cost functional involving an iterated sensitivity equation.
