Optics of Inhomogeneous Media

the branch of optics concerned with phenomena accompanying the propagation of optical radiation in media whose index of refraction η is not constant but depends on the coordinates. The term “optical inhomogeneities” is applied to a medium’s surfaces or to regions within the medium where η varies. An inhomogeneity, regardless of its physical nature, always alters the direction of light. Reflection and refraction of light occur on surfaces separating regions of a medium with different n; scattering of light occurs in particles or other regions whose η differs from η for the surrounding medium. The interference of light between the scattered waves, reflected waves, refracted waves, and the initial, or incident, wave plays a significant role in the optics of inhomo-geneous media. The optics of thin layers is an important branch of the optics of inhomogeneous media.

Inclusions of other substances having a different n in a medium—such as aerosols, smokes, suspensions, or emulsions—can constitute optical inhomogeneities. The dimensions of these inclusions usually exceed the light wavelength λ. Such a medium is called a turbid medium. When the concentration of foreign particles is high, the particles’ scattering of incident light in all directions results in the turbid medium becoming opaque. When the inhomogeneity of the medium is due to the presence of finely divided colloidal particles, the medium seems to be completely transparent. The Tyndall effect, however, is manifested: observation at angles near 90° to the direction of the incident light reveals a luminosity of the medium because of intense scattering of light. Another class of turbid media is pure substances, or substances not containing foreign inclusions. Here light scattering results from changes in η in a large number of microregions. The changes are caused by fluctuations in the medium’s density because of the random thermal motion of the medium’s molecules or by the turbulence of the medium.

The intensity I of the light scattered by nonabsorbing dielectric particles is proportional to λ^–p, where ρ is a parameter dependent on the ratio of particle size to λ. For scattering by thermal fluctuations whose dimensions are much smaller than λ, Rayleigh’s law obtains: I∼ λ^–4. This strong dependence on λ explains the preferential scattering of shorter waves. The observed color of the sky in the daytime is thus azure even though the earth’s atmosphere is illuminated by white solar light, which is an aggregate of light waves of different wavelengths. For particles whose dimensions are ≫ λ, the parameter ρ is close to zero and scattering is determined by the geometric effects of light refraction at the particle surfaces. In this case I is independent of λ, as is in fact observed in the scattering of light in fog and clouds, which have a white color.

The methods of nephelometry and ultramicroscopy are based on the study of light scattering by inhomogeneities in gases, liquids, and solids. These methods permit scientists to determine concentrations and to study the nature of inhomogeneities. Nephelometry also permits determination of the inhomogeneities’ dimensions.