A dynamically variable lens is made from actively tunable electromagnetic metamaterial cells. The lens operates on electromagnetic radiation including: radio frequency waves, microwaves, teraherz waves, near infrared waves, infrared waves and visible waves. The focal length of the lens is changed at a selected frequency. In the alternative, the frequency of radiation operated on is changed as a function of time. A third alternative provides precise control of the index of refraction of the lens. The index of refraction is varied progressively across the lens from one edge to the opposite edge causing the radiation to be directed at an angle.