Asymptotic solution of some diffraction problems

Various diffraction problems are solved asymptotically in k * y (X wavelength) for k large (i.e., X small). These problems include diffraction of a plane wave by a parabolic cylinder, a paraboloid of revolution, a cylinder and a sphere; diffraction of a spherical wave by a paraboloid of revolution, a hyperboloid of revolution, and a plane interface; diffraction of a cylindrical wave by a parabolic cy- linder, a hyperbolic cylinder and a plane interface, etc. The boundary conditions considered are the vanishing of the function of its normal derivative and the impedance boundary condition. Formulas are obtained for reflection of any wave from any two dimensional surface, and certain formulas are deduced for three dimensional problems. The method employed is that devised by R.