Summary: 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 \[ \mathrm {div}(s_\delta A \nabla u_{\delta }) + k^2 s_0 \Sigma u_{\delta } = s_0 f\text{ in } \Omega , \] where \( \Omega \) is a smooth connected bounded open subset of \( \mathbb{R}^d\) 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 \( s_\delta \) is a complex function whose real part takes the values \( 1\) and \( -1\) and whose imaginary part is positive and converges to 0 as \( \delta \) goes to 0. This is motivated from a result of N. A. Nicorovici, R. C. McPhedran, and G. W. Milton [“Optical and dielectric properties of partially resonant composites”, Phys. Rev. B 49, 8479–8482 (1994)]; another motivation is the concept of complementary media. 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.