On Rayleigh and Mie scattering

Scattering described today as “Rayleigh scattering" represents something that is far short of what Rayleigh actually contributed to the topic in both optics and acoustics. This limited view seems to lie in a few papers in which he truncates series solutions for practical computations, thus leading to scattering of the form (ka)4 for ka≪ 1, where k is the wavenumber and a is the radius of the sphere and for selected limitations on index of refraction. These approximations led optical scientists to equating “Rayleigh scattering" to little more than “the blue sky.” In 1908, Gustav Mie developed a theory for plane-wave scattering from a sphere to which the names “Mie theory” and “Mie scattering” have been indelibly attached to many applications in optics. It is virtually unknown, especially in optics, that Rayleigh actually developed the full theory of plane-wave scattering from a sphere in 1878 (primarily Section 334, Vol. 2, The Theory of Sound, Macmillan), including original contributions in the concurrently developing mathematics of Bessel functions. The motivation of this presentation is to establish a means of treating weak scattering from bubbles based on their contribution as a distribution of spheres by combining Rayleigh and Mie.