The beamwidth of a reflector antenna may be varied by defocusing the feed. The radiation characteristics are studied for both axisymmetric and offset single reflector antennas using both geometric optics for understanding the operation and physical optics for a parametric study. The beamwidth may be increased by over 200% compared to the focused reflector before the main beam bifurcates, but the on-axis gain is reduced. Better performance is obtained with an offset reflector antenna. The study quantifies the limits of beam broadening which can be achieved. Measurements on a 30 GHz experimental antenna show good agreement with theory.