Abstract: This paper mainly investigates the theoretical problem of all-symmetric system with respect to its magnification change ratio,ideal optical formulas and computational techniques of reduction and enlargment ratio.Half of the all-symmetric system is a three-element structure with the arrangment of"-.+.-".The commutative principle of the object and image is adopted in the variable magnification lens group.This theory is applicable to the design of the zoom for the all-symmetric type and apochromatic reproduction camera objective lens,the transversal magnification of which is -1x.This paper mainly discusses the distribution of power and gives a numerical example of power distribution of the apochromatic reproduction camera objective lens with second-order zoom,which can satisfy the field-flattening and apochromatism,and in the meantime meet the requirements of the end values of both long and short focal lengths ranging from 600 to 450 mm.