Conventionally, a bright, very wide-angle optical system is designed as a floating type optical system that moves two or more lens groups composed of multiple lens in order to focus accurately. These have been widely used as phase detection auto focus (AF) methods within conventional digital single-lens reflex (DSLR) cameras. However, a phase detection AF optical system cannot be used when recording motion pictures. In contrast, a compact system camera (CSC) performs AF by the contrast method, where a stepper motor is used as the driving source for moving the optical lens. Nonetheless, to ensure that the focusing lens is lighter, these stepper motors should not have high torque and AF must be possible by moving only one lens. Yet, when focusing is performed with only one lens, aberration change due to focusing lens movement is magnified. Therefore, a very wide-angle optical system comprised of a half-angle of view more than 40 degrees and F of 1/4 has not been developed. Here, a very wide-angle optical system was designed with high resolving power that enables high speed AF, even in contrast mode, by moving only one lens while minimizing aberration change.