  We study Maxwell's equations in time domain in an anisotropic medium. The
goal of the paper is to solve an inverse boundary value problem for
anisotropies characterized by scalar impedance $\alpha$. This means that the
material is conformal, i.e., the electric permittivity $\epsilon$ and magnetic
permeability $\mu$ are tensors satisfying $\mu =\alpha^2\epsilon$. This
condition is equivalent to a single propagation speed of waves with different
polarizations which uniquely defines an underlying Riemannian structure. The
analysis is based on an invariant formulation of the system of electrodynamics
as a Dirac type first order system on a Riemannian $3-$manifold with an
additional structure of the wave impedance, $(M,g,\alpha)$, where $g$ is the
travel-time metric. We study the properties of this system in the first part of
the paper. In the second part we consider the inverse problem, that is, the
determination of $(M,g,\alpha)$ from measurements done only on an open part of
the boundary and on a finite time interval. As an application, in the isotropic
case with $M\subset \R^3$, we prove that the boundary data given only on an
open part of the boundary determine uniquely the domain $M$ and the
coefficients $\epsilon$ and $\mu$.
