Left-handed metamaterial (LHM) lenses allow the focusing of microwave radiation at specific positions within a medium, depending on its refractive index. A suitable approach needs to consider the reflections between the LHM lens and the adjacent media. This work faces the challenge of focusing the microwave radiation within a medium with arbitrary positive refractive index and characteristic impedance using LHM lenses as imaging-forming systems. To find a right lens formula, a full wave method is presented in theory. The results we achieved show that the characteristic flat shape of conformal-four lens configuration has a spot size of 0.53 x 0.34λeff2 at -3 dB if the different media are perfectly matched. Otherwise, a noteworthy aberration affects the focusing, but it can be mitigated using a conformal circular LHM lens with a spot size of ~0.4 x 0.4λeff2 at -3 dB.
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