  This paper is devoted to the study of the behavior of the unique solution
$u_\delta \in H^{1}_{0}(\Omega)$, as $\delta \to 0$, to the equation
\begin{equation*} \dive(\epss_\delta A \nabla u_{\delta}) + k^2 \epss_0 \Sigma
u_{\delta} = \epss_0 f \mbox{in} \Omega, \end{equation*} where $\Omega$ is a
smooth connected bounded open subset of $\mR^d$ with $d=2$ or 3, $f \in
L^2(\Omega)$, $k$ is a non-negative constant, $A$ is a uniformly elliptic
matrix-valued function, $\Sigma$ is a real function bounded above and below by
positive constants, and $\epss_\delta$ is a complex function whose {\bf the
real part takes the value 1 and -1}, and the imaginary part is positive and
converges to 0 as $\delta$ goes to 0. This is motivated from a result in
\cite{NicoroviciMcPhedranMilton94} and the concept of complementary suggested
in \cite{LaiChenZhangChanComplementary, PendryNegative, PendryRamakrishna}.
After introducing the reflecting complementary media, complementary media
generated by reflections, we characterize $f$ for which
$\|u_\delta\|_{H^1(\Omega)}$ remains bounded as $\delta$ goes to 0. For such an
$f$, we also show that $u_\delta$ converges weakly in $H^1(\Omega)$ and provide
a formula to compute the limit.
