In this paper, we present the equivalent medium theory by using the linear response theory. It is found that, under the condition of the linear response, a series of different media with different refractive indices $n_{i}(omega)$ and lengths $d_{i}$ can be equivalent to an effective medium with the volume-averaged refractive index $frac{1}{D}sum_{i=1}^{N}n_{i}(omega)d_{i}$ and the total length $D=sum_{i=1i}^{N}d_{i}$,where $N$ is the number of different media. Based on this equivalent theory, it is a simple but very useful method to design the effective medium with any desirable dispersion properties. As an example, we present a proposal to obtain the enhancement or reduction of the refractive index without absorption and the large dispersion without obvious absorption by assembling different linear dispersive gain and absorptive media.
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