Debye theory analysis of the scattering intensity and refractive index measurement for glass beads

When investigating the scattering intensity distribution produced by a glass bead which is illuminated by a collimated beam with single length, Debye theory can be used to simulate and discuss the scattering properties. It is found that the intensity distribution of the k-order rainbow recorded by a detector which is on the left of a spherical particle is the superposition of the diffracted rays, the external reflected rays and the k time internal reflected rays primarily. The intensity distribution of the k-order rainbow on the right of the spherical particle is the superposition of the diffracted rays, the transmitting rays and the k time internal reflected rays mostly. When the wavelength of incident light is constant, the refractive index of the glass beads will change the degrees of the minimum deviation angle in the scattered light intensity distribution on the detector, and their diameters have no effect on the position of minimum deviation angle. Experimentally, the scattered intensity distribution of the first and the second rainbows of the glass beads with different refractive indices and radius are analyzed, and are compared with the geometrical method, which agrees with the result of simulation in Debye theory. This result shows that the proposed assumptions are reasonable, which can be used to measure the refractive index of the glass beads through testing the minimum deviation angle formed by the light scattering.