A new method is presented to determine the refractive index and the diameter of unclad optical fibers. The technique is based on an analysis of the back-scattered light when a beam from a cw laser impinges upon the fiber. A geometrical-optics analysis shows that the position of a sharp cutoff in the radiation pattern determines the refractive index, whereas the distance between certain successive minima gives the diameter. The theory is compared to experimental observations, with excellent agreement.