The reciprocity theorem in colloid optics

Abstract

A simple method of deriving the following algebraic relation betweenρ _u,ρ _v and ρ_h is given, ρ_u=(1+1/ρ _h)/(1+1/ρ _h) applying the general dynamical Principle of Reciprocity formulated by Helmholtz and Rayleigh, where ρ _u, ρ _v and ρ _h are the measures of the depolarisation of the Tyndall scattering when the incident light is respectively (1) unpolarised, (2) polarised with its electric vector vertical, and (3) polarised with its electric vector horizontal. The conclusions derived from the reciprocity principle admit of a very simple and direct experimental test which has been carried out and found to be satisfied by all kinds of colloidal solutions, emulsions, suspensions, protein solutions, etc., irrespective of size, shape or structure of the particles contained in them or of their non-uniformity. The principle of the experimental method employed to test the relation consists of splitting the incident unpolarised light by means of a double-image prism into two beams of equal intensity but polarised perpendicularly. The scattered light is also viewed through another doubleimage prism. The four images of the tracks corresponding to the components V _v , H _v , V _h and H _h can be viewed at the same time and their intensities compared. In all the cases studied, H _v is found to be equal to V _h which is equivalent to the relations stated above. The relative intensity of the four track-images furnishes useful indications of the size and shape of the particles in the dispersing medium.