This paper aims to realize the miniaturization design of medium and long wavelength common optical path optical systems.An optical index allocation model for secondary imaging structures under size constraints based on Gaussian optics and primary aberration theory was established. Lens combinations of high, medium and low relative dispersion materials in the form of "-, +, -" structures are used as the primary mirror structure to correct the secondary spectrum; Meanwhile, field lenses and aspheric surfaces are used to correct spherical aberration to reduce the relay mirror. The light height is set to balance the residual aberration of the primary mirror.Because of the high edge light height and small optical power of the primary mirror, its spherical aberration, chromatic aberration and secondary spectrum are the main sources of aberrations in the system. To correct the secondary spectrum, the "-, +, -" structure can be used. A lens combination of high, medium and low relative dispersion materials is used as the main mirror structure. At this time, the residual aberration of the main mirror is small. Field lenses are used to reduce the light height of the relay lens group and aspherical surfaces are used to correct spherical aberration to balance the residual main mirror Aberration.Based on the above theory, a common optical path dual-wave infrared small optical system with a medium wave wavelength of 3.7-4.8 μm and a long wave band of 7.7-9.5 μm is designed. The total length of the system is no more than 135 mm, the structure is small and compact, the optical transfer function is close to the diffraction limit, and the operating temperature range covers -40-60 ℃ and is not sensitive to temperature. The analysis and design of a medium and long-wavelength common optical path miniaturized optical system based on the secondary imaging structure optical index distribution model are realized to meet the needs of a medium and long-wavelength common optical path miniaturized optical system.