1. A variable magnification optical system, substantially consisting of a first lens group fixed with respect to the imaging plane and has a positive refractive power, a second lens group having a negative refractive power, a third lens group fixed with respect to the imaging plane and has a positive refractive power, and a fourth lens group having a positive refractive power, arranged in order from the object side, in which magnification is changed by moving the second lens group and focusing is performed by moving the fourth lens group, wherein: the first lens group substantially consists of a positive lens L 1 p and a cemented lens L 1 c substantially consists of a negative lens and a positive lens, and has a positive refractive power, arranged in order from the object side; the third lens group comprises a stop on the most object side; the fourth lens group substantially consists of a positive lens, a negative lens, and a positive lens, arranged in order from the object side, with at least one surface being an aspherical surface; and the variable magnification optical system satisfies conditional expressions given below: 
 3.1< f 1/ fw< 8.0  (1) 
 0.4< f 1 p/f 1 c< 2.0  (2) 
 0.3< R 1 c/fw< 0.7  (3) 
 1.0≦ FNt/FNw< 1.4  (4) 
 1.5< FNt< 2.3  (5) where: f1: focal length of the first lens group; fw: focal length of the entire system at the wide angle end; f1p: focal length of the positive lens L 1 p; f1c: focal length of the cemented lens L 1 c; R1c: radius of curvature of the cemented surface of the cemented lens; FNt: maximum aperture F-number of the entire system at the telephoto end; and FNw: maximum aperture F-number of the entire system at the wide angle end.