Size determination of spherical voids from the extrema of the Mie scattering intensities

Simple relations have been obtained, by numerical methods, between the diameter D of a spherical void (bubble) in a conducting medium of a given refractive index and the angular positions of the extrema of the Mie scattering intensities from the voids. The extrema are counted from the forward direction. These relations allow the determination of the positions of the extrema for a given diameter, or the reverse, without computational aids. The real part of the refractive index was varied from 1.25 to 15.00 and the imaginary part from 0.0 to 22.50. The size parameter α = πD/λ was varied in all cases from 4.00 to 24.00. The variable λ represents the wavelength of the incident radiation. These findings could thus be related to the scattering of microwaves by bubbles in water. Similar relations have also been obtained regarding the scattering of scalar waves by spherical voids. This corresponds to scattering of Schrödinger waves from complex spherical barrier potentials.