The focal length of neutron lenses using capillary optics

Capillary-fiber optics have been shown to be a useful technique for guiding and focusing both X-rays and neutrons by means of multiple reflection in hollow glass tubes and the principles of X-ray and neutron lenses have been demonstrated. An optimum condition is derived for such a device. The focal length L of the focusing lens, the average critical angle _c of the material of the fibers and the radius R of the fibers that comprise the lens are related by the simple equation L = xR/_c, where the factor x depends on the particular optimization required and the source of radiation used. The value of _c depends on the spectrum of the radiation transmitted by the lens.