Dispersion

DISPERSION, the change in the refractive index depending on the wavelength of light. The result of dispersion is, for example, the decomposition of white light into a spectrum when passing through a prism. For colorless substances transparent in the visible part of the spectrum, the change in the refractive index n can be represented with sufficient approximation by Cauchy's formula: n = A + B / \lambda² + C / \lambda⁴, where A, B, and C are constants that vary from substance to substance. Usually, the first two terms of the formula are sufficient, and the remaining terms are very small. As can be seen from the formula, n decreases with an increase in \lambda, i.e., as one moves into the red part of the spectrum. This is the case of so-called normal dispersion; it corresponds to the habitual rainbow alternation of colors in the spectrum. If, however, a substance possesses strong selective absorption in a given part of the spectrum, the course of dispersion is sharply disrupted, acquiring a character schematically depicted in the figure. The solid curve here represents the expression n - 1, and the dashed line represents the absorption band: it can be seen that in the region of the absorption band, the refractive index upon transition from the red part to the violet does not increase, but sharply decreases. Such anomalous dispersion is particularly pronounced in gases with sharp, thin absorption bands (e.g., in sodium vapors). In prisms made of a strongly absorbing substance (such as fuchsin), the alternation of colors in the spectrum is completely unusual, for example, green rays are refracted less than yellow ones. The phenomenon of anomalous and normal dispersion is fully explained theoretically if one assumes that the substance consists of elementary resonators driven by light waves. In that region where the natural period of atoms or molecules coincides with the period of the light wave, anomalous dispersion must be observed; maximum absorption must also occur in this same region. In the first approximation (if absorption is neglected) for a medium consisting of resonators of a single kind: n² - 1 = B / (\lambda² - \lambda₀²), where \lambda₀ is the natural wavelength of the resonators (the resonance region) and B is a constant. The above-mentioned formula of normal dispersion is a special case of this formula for waves far from the resonance region. From the theory of dispersion follows further the Lorentz-Lorenz formula (H. Lorentz, L. Lorenz), which is important for refractometric analysis: ((n² - 1) / (n² + 2)) * (1 / d) = R, where R is the so-called "specific refraction", n is the refractive index for a given wavelength, and d is the density of the substance; R turns out to be approximately constant for any aggregate state of the substance and in various chemical compounds that include this substance. The product of R and the atomic or molecular weight is called the atomic or, respectively, molecular refraction. Molecular dispersion is called the difference: ((n₁² - n₂²) / (n₁² + n₂² + 2)) * (M / d), where n₁ and n₂ denote the refractive indices for two different wavelengths, and M is the molecular weight.