Back-scattering cross section of a thin, dielectric, spherical shell

The back-scattering cross section of a thin dielectric, spherical shell is calculated on the basis of simplified boundary conditions at the shell. These conditions approximate the correct conditions at the shell better, the higher the dielectric constant of the shell, and the less the variation of the normal component of the electric field along the surface of the shell. Numerical results are added for a shell, whose electrical radius <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kr₁<5</tex> , and whose thickness <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> and dielectric constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kₑ</tex> obey the relation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(Kₑ-1)kd = 0.4</tex> . A comparison is made, with the results obtained, by applying Rayleigh's scattering law to objects that are small as compared to the wavelength.