Scalar diffraction by prolate spheroids whose eccentricities are almost one

The pressure distribution on the surface of a long, thin prolate spheroid is found under the conditions: (1) The spheroid is illuminated by a harmonic point source of wavelength λ located on the axis of the spheroid. (2) If a and b are the semi-major and semi-minor axes of the spheroid, then (3) The boundary conditions on the spheroid are either the Neumann or the Dirichlet conditions. The distribution is found from the asymptotic solutions of the Helmholtz equation using the inequalities in (2). The distribution is interpreted on certain regions of the surface in terms of travelling waves.