Vol. 23, issue 07, article # 4

Abstract:

Based on the analysis of the Mie series terms contribution with the parameter x, equal to the ratio of the circumference length of the ball to the length of the light wave, it is shown that the central bright spot of a glory is governed by the light scattering at resonance frequencies of the ball with the harmonic numbers l_res exceeding x. The bright rings are generally formed by a group of harmonics with l from 0.9x to 0.95x. The process of formation of inner waves, generated due to the interconnection with the ball surface of the rays that passed through it, is substantiated as a mechanism of a glory bright rings formation. To describe the phase scattering function near the backward direction, averaged over the basic period of resonance oscillation dx, the approximation formula is proposed in the form of the Bessel function squares of the zero-th and the second orders and the geometric optics phase scattering function. The coefficients of this formula are given for the refraction index m= 4/3, for which dx = 0.82. For the range of m from 1.33 to 1.34 it was found that the product of the sum ( + 2) and the angular sizes of the first bright, the second dark and the subsequent alternating rings does not depend on m and is equal to 3.16; 5.13; 6.65; 8.31 and 9.86, respectively. These values are close to the alternating zeros of the first derivative and the second-order Bessel function.

Keywords:

glory, backward phase scattering function