Liquid-crystal cells shaped like a plano-convex lens or a plano-concave lens are prepared. The focal length can be varied from the value fe for an extraordinary ray, where the liquid-crystal cell takes a homogeneous alignment, to fo for an ordinary ray, where it takes a homeo-tropic alignment, by applying an electric field or a magnetic field across the lens-cell. The focal length in the lens-cell with the homogeneous alignment can also be switched between fe and fo. This is done by switching the direction of polarization of the incident light by applying a voltage across a TN cell sandwiched between the polarizer and the lens-cell. Since the thickness of the liquid-crystal layers increases in the lens-cells, the optical transmission properties are investigated as a function of the cell thickness.