The between- band chromatic dispersive power P is derived from the derivation of between- band chromatic aberration. A new achrothermal model considering the between-band chromatic aberration is prompted. Then, method of athermalized and multi-band zoom optical system is discussed. Based on this achrothermal model, a dual-band (MWIR/LWIR) dual-field of view optical system under the requirements of F=2, 150 mm/50 mm focal length, 3.7~4.8 mm and 7.7~10.3 mm waveband is designed with optical passive athermalization technology. The optical system, which consists of 8 lenses and 3 aspheric surfaces, has good image quality and Narcissus character at each field of view at -40 ℃~60 ℃.