Geometrical Optics and the Theory of Multiple Small Angle Scattering

The theory of the small angle scattering of x-rays or thermal neutrons by particles of matter, in the case of particles large enough to produce large phase shifts, is re-examined. A theory based entirely on geometrical optics has been frequently employed in the past, and it is pointed out that, in the case of a single particle, this treatment gives an incomplete account of the scattering. A Huygen's principle approximational method (which is known to duplicate the results of wave theory in the single particle case), is applied to the many particle case, and it is shown that, here, the theory based entirely on geometrical optics is justified.