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Note on Krishnan's Reciprocity Relation in Light Scattering
1.R. S. Krishnan, Proc. Indian Acad. Sci. A, 1, 782 (1935).
2.R. S. Krishnan, Proc. Indian Acad. Sci. A, 7, 21 (1938).
3.Rayleigh, Theory of Sound (The Macmillan Company, London, 1926), Vol. 1, p. 93.
4.This assumption is not essential, but simplifies the statement of the result.
5.A. Sommerfeld, in Frank‐von Mises, Differentialgleichungen der Physik (Friedrich Vieweg & Sohn, Braunschweig, Germany, 1927), 7th edition, p. 580.
6.For the extension to the anisotropic case, see A. F. Stevenson, Quart. Appl. Math. 5, 369 (1948). In this paper, an error in Sommerfeld’s proof is also pointed out, which does not, however, invalidate the result.
7.The argument used here is identical with that of Krishnan (reference 2), except that we consider scattering by a single particle instead of by a number of particles. Krishnan’s argument applies rigorously only when multiple scattering and the effect of the container walls are neglected, or a symmetry condition is satisfied, as discussed in Sec. 3.
8.It is not sufficient to consider only those particles which are in the original primary beam, since particles outside this beam receive scattered light.
9.A slight complication arises from the fact that, experimentally, the primary beam has a finite cross section and is not a plane wave of infinite extent as assumed theoretically. Such a primary beam can, however, be regarded as the superposition of plane waves of different directions of propagation and different polarizations. Since all these waves will have a direction of propagation and a polarization differing but little from that ascribed to the primary beam, it is seen that the above conclusions remain valid to a high degree of approximation.
10.See, for instance, R. S. Krishnan, reference 2;
10.M. A. Boutaric and J. Breton, J. Chim. Phys. 36, 193 (1936);
10.Hoover, Putnam, and Wittenberg, J. Phys. Chem. 46, 81 (1942).
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