## Abstract

The light scattered by an infinite plane layer of suspended dielectric particles is discussed without consideration of the interference from different particles. Let the first-order quantity function (q.f.) be defined as that fractional part of the total incident light energy subject to one scattering process, the second-order q.f. as the fraction subject to two scattering processes, etc. Then the first-order q.f. and its angular distribution from a very dilute medium is given by Mie’s theory. The second- and higher order q.f. from a denser medium are derived in terms of elementary exponentials. Polar plots are presented showing that for a Rayleigh medium (*α*→0, where *α*=particle circumference/wave-length) second- as well as higher order light is of substantially uniform distribution whereas such uniformity is attained only for light of order greater than eight for a medium with a pronounced Mie primary distribution (*α*=5 in Fig. 6). The fractions of scattered light were calculated in two ways: (1) as forward progressive quantity functions for the several orders, to be multiplied by angular factors for any direction; (2) as separate forward and backward progressive half-space q.f. for the several orders, to be multiplied by angular factors taken in the corresponding half-spaces. Comparison of the ratio *r* of total backward to total forward light as obtained from both calculations, (1) and (2), gives similar results in most cases. *r* becomes smaller as both, *α* and the medium dilution increase (*r*=1 for *α*→0, *r*=~1/1000 for *α*=5). For very dense dispersions (still neglecting interference) *r* approaches unity for all *α* according to method (1), while it decreases slightly from *r*=1 for *α*=0 with increasing *α* according to the more detailed method (2). The latter method, however, proves to be the only one appropriate to trace the large backward reflection combined with the low forward transmission in some absorbing media.

Corrections are made for the q.f. of the several orders in terms of a slenderness factor where the medium is defined as a limited region of an infinite plane layer.

A specific numerical example is given for a low density medium for which this correction is negligible and method (1) is good enough. The weight of suspended material necessary for a barely photographable vapor trail is calculated for various sizes of dielectric particles.

© 1950 Optical Society of America

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