Diffuse Reflexion due to the Multiple Reflexion within the Scattering Medium

[摘要] In spite of many experimental researches, no surfaces which strictly obey _??_ambert's cosine law have been found. On the other hand, no theory for the explanation of the diffuse reflexion phenomena, seems to have been successful. In such circumstances, Pokrowski(5), (6) proposed a theory and deduced a formula for the total reflecting power of a diffuse surface, where R means the amount of energy reflected back to the former space by the surface when the initial incident light of unit intensity hits the surface for the first time; and R1, the rate of reflexion of the surface for individual rays of light coming back outwards from the inner portion of a medium.After some analysis of his theory, we come to a conclusion that the procedure he took, is similar to that of computation for the reflexion of pile of plates which is sometimes used in order to obtain the polarized light in optics. Therefore, his computation should be able to be compared to the well-known formula for pile of transparent plates, when we assume the case of no absorption of energy in the scattering medium. Here, we can point out his calculation may need some revise; for, he took only the reflected rays I, II, ...... shown in the figure in our article, into consideration; but he did not consider those as i, that is reflected back inwards by any planes inside the medium.In fact, we can show that, under the assumption of no absorption, the procedure he took, gives a smaller value than that for pile of plates. The diffence between both is negligible when the medium is very thin. However, when the medium is sufficiently thick the value, obtained by his method, gives only half of the true value.In another article by the present author (Decrease of Radiation Intensity in the Diffusely Reflecting Medium) we showed Dietzius' relation for the scattering medium, which was obtained by solving Schuster's equation. In the present work, we have shown how Dietzius' relation corresponds to the pile of plates, and also have shown, it is much easier to solve the differential equation than to make calculations basing upon individual reflexion and transmission at each face within the medium. In the article cited above, through solving differential equations, we got already relations which hold for radiation in the medium, that has property of scattering as well as absorption.Applying those results, we get for the total reflective power of the medium, K=R+(1-R)(1-R1)β0/1-R1β0 where and R. R' have same meaning as Pokrowski's. when _??_ is large enough, we haveThe present author also suggests that, in treating the present problem, we have to consider in particular, not a surface, but a surface layer of some thickness, in which brightness is not expressed by scalar quantity, unless the initial incident rays are uniform for all directions. Backreturning rays, which arrive at the base of the surface layer from inside after they have travelled through the medium, may be considered perfectly diffuse, and may obey Lambert's law. Deviations from that law may be attributed to the nature of reflexion R o_??_ the surface layer. In other words, we may consider, as long as (1) the distribution of the particles in the surface layer, (2) the nature of incident light and (3) the reflective property of the particles, are quite unfavourable to give rise to regular reflexion in the surface layer, any reflected light from the substance, whose constituents are minute particles, obeys Lambert's law in approximate degree. On the other hand, according to this opinion by the author, there may be no surface in nature, which obeys Lambert's law strictly; and any effort to explain the law strictly theoretical way, by the irregular distribution of small mirror facets, will be unsuccessful.

[学科分类] 大气科学