A lens system provides a zoom function (variable magnification) in a low profile camera (lens system height less than or equal to 6 mm), which may be in a cellular phone. The lens system includes at least three movable lens groups that are movable along a common optical axis. Each of the three movable lens groups is coupled to a corresponding actuator. Responsive to a request for a change in focal length or magnification, a controller sends a corresponding signal to each of the actuators that move the corresponding lens group by a corresponding distance in a corresponding direction. The various movable lens groups may be moved by different distances and in different directions of movement. An f-number of the lens system is less than f/3.0. Focusing of an image cast onto an image sensor is accomplished by adjusting the position along the optical axis of one of the movable lens groups.