The angular distribution of intensity of light scattered from a collimated beam incident upon a spherical air bubble in water is determined for any bubble with radius greater than a few wavelengths of the incident light. The computations are for wavelength 5893 A and n = 1.3334, the relative index of refraction of water at 15°C. One external reflection, five internal reflections, and six refractions are considered. A general equation for the geometric attenuation factor is developed, with special forms for external reflection and for zero angle of incidence. The limits of accuracy of the equations for angles of scattering in the neighborhood of 0° and 180° are evaluated. The effects of diffraction and interference are assumed to be negligible. The fractions of the incident light scattered from each of the six “surfaces” (successive points of incidence of any ray on the spherical surface) are shown by accurate curves for all angles of deviation. The corresponding geometric attenutation factors are similarly shown. Final intensity values are tabulated and are plotted both with rectangular and with polar coordinates.
GEORGE E. DAVIS, "Scattering of Light by an Air Bubble in Water," J. Opt. Soc. Am. 45, 572-572 (1955)