The reciprocity theorem in colloid optics and its generalisation

Abstract

The reciprocity relation ρ_u = (1 + l/ρ_h )/(1 + l/ρ_v) connecting the three depolarisation factors ρ_u, ρ_v and ρ_h for the case of the transverse scattering is deduced theoretically. It is pointed out that this relation is valid, not for a single colloidal non-spherical particle with fixed orientation in space, but only for a solution containing a large number of particles which have no preferred orientation in the plane containing the incident and scattered beams. The same considerations are extended to the case of oblique directions of scattering and it is shown that the relation continues to be valid under the same conditions, ρ_u, ρ_v and ρ_h being now functions of the ang1e y of scattering and, of course, of the wave-length of the light used. These inferences have been tested out experimentally by the usual double double-image prism method and found valid. Direct measurements of the depolarisation factors ρ_u, ρ_v and ρ_h for oblique scattering for graphite and arsenic trisulphide sols are also found to satisfy the reciprocity relation. Curves representing ρ_u, ρ_v and ρ_h as a function of y, the angle of scattering, have been plotted and compared with the theoretical curves for the two cases of (a) large spherical particles and (b) small ellipsoidal particles. The experimental graphs exhibit characteristics which, in some respects, combine the feattlres exhibited by the theoretical curves and in other respects are intermediate betweel1 them. The values of ρ_v and ρ_h for the two sols examined show a maximttm and the valtte of ρ_u shows a minimum for a value of y intermediate between 0° and 180°. The curves for ρ_u, ρ_v and ρ_h are markedly unsymmetrical in shape, but both the maximum and the asymmetry of the curve for ρ_v are rather less pronounced than the corresponding curves for ρ_h and ρ_u.