Patent ID: 8693105

Claim:
A variable magnification optical system for projection consisting of: a first lens group having negative refractive power, and which is fixed when magnification of the variable magnification optical system is changed; a second lens group having negative refractive power, and which moves when magnification of the variable magnification optical system is changed; a third lens group having positive refractive power, and which moves when magnification of the variable magnification optical system is changed; and a fourth lens group having positive refractive power, and which is fixed when magnification of the variable magnification optical system is changed, the first lens group, the second lens group, the third lens group and the fourth lens group being arranged from the magnification side of the variable magnification optical system in the order mentioned above, wherein the reduction side of the variable magnification optical system is telecentric, and wherein the following formula (11) is satisfied: 1.5 <Bf/fw (11), where Bf: back focus in air of entire system at wide angle end, and fw: focal length of entire system at wide angle end.