the branch of optical technology dealing with the methods and means of measuring the refractive indexes of solid, liquid, and gaseous media in various regions of the optical-radiation, or light, spectrum. If the refractive index n and its dispersion (dependence on the wavelength of the light) D are known, it is possible to determine other quantities dependent on n and D.

The following types of refractometric methods can be distinguished: (1) methods of direct measurement of the angles of refraction when the light crosses the interface of two media; (2) methods based on the phenomenon of total internal reflection; (3) interference methods (seeINTERFERENCE OF LIGHT); (4) photometric methods, which make use of the Fresnel equations and are based on the dependence of the reflection coefficient or transmission coefficient of light at the interface of two media on the ratio of the refractive indexes of the media (seeREFLECTION OF LIGHT); and (5) other methods, such as measurement of the focal length of a lens and the curvature of its surfaces in order to determine the refractive index of the material of which the lens is made, measurement of the lateral displacement of a beam by a plane-parallel plate made of the material under study, and the immersion method. The first three types of methods are the most widely used.

In methods of the first type, the sample is given the form of a prism (seeDISPERSING PRISMS). To determine the refractive index, the prism is oriented so that the angle of deviation δ of the ray (Figure 1, a) is a minimum. Another way of measuring n is to position the sample under study in a specially made prism with a known refractive index N (Figure 1, b). In order to measure the refractive index of liquids, the liquid under study is poured

Figure 1. Determination of the refractive index n from the deviation of a ray in prismatic samples, (a) Path of ray through a prism with refracting angle α. The angle of deviation δ is a minimum when the path of the ray is symmetric-that is, when the angle of incidence i₁, is equal to the angle of emergence i₂. The value of n is given by the equation

(b) Path of ray through a prism whose refractive index n is to be measured. The prism is positioned in a right-angled recess in a prism with a known refractive index N. In the type shown, which is the most widely used type, the prism refracting angle α = 90° and the angles γ₁ = γ₂ = 45°. The relation between n and the measured angle of emergence β is given by the equation

into a hollow prismatic cell. The accuracy of the determination of the refractive index by these methods is ~ 10^-5; the difference between the refractive indexes of two substances can be determined with an accuracy of 10^-7.

Figure 2. Measurement of the refractive index n by means of the phenomenon of total internal reflection. (1-1ʹ) and (2-2ʹ) Paths of rays when illumination is from the direction of the sample under study (for the sake of simplicity, the reflected part of ray 2 is not shown); 1-1ʹ is the critical ray corresponding to the angle ɸ_1.tir in the material of the lower prism. (3-3ʹ), (4-4ʹ), and (5-5ʹ) Paths or rays when illumination is from below, that is, from the direction of the prism with known refractive index N; the ray 4-4ʹ, which is incident on the prism-sample interface at the angle ɸ_2.tir, is the critical ray for total internal reflection. (A) and (B) Schematic representations of the field of view of the instrument telescope when the rays 1ʹ and 4ʹ, respectively, pass through the telescope, (β) Angle between the direction of the critical ray and the normal to the prism. The relation between n and β, which is measured, is given by the equation

where α is the refracting angle of the prism with known refractive index.

Methods based on the phenomenon of total internal reflection are also often used. The sample whose refractive index is to be measured is brought into optical contact with a reference prism made of a material with a high refractive index N that has been accurately measured (Figure 2). The light rays may come from the direction of the sample or the prism. In either case, when a beam of light impinges on the sample-prism interface, for a very narrow range of angles of incidence there appears in the field of view of the instrument telescope a sharp boundary separating the dark and light regions of the field. One of the regions (the dark region when the illumination is from the direction of the sample, the light region when the illumination is from the direction of the prism) corresponds to the rays undergoing total internal reflection. The boundary of this region corresponds to the critical, or limiting, angle of incidence. The accuracy of the total internal reflection method is ~ 10^-5.

Figure 3. Operating principle of interference refractometer. A beam of light is divided so that its two parts pass through cells of length l filled with substances having different refractive indexes. The rays that emerge from the cells have a certain path difference; when these rays are brought together, they produce on a screen a pattern of interference maxima and minima with k orders (shown schematically at the right of the diagram). The difference between the refractive indexes is Δn = n₂ – n₁ = kλ/2, where λ is the wavelength of the light.

Interference methods are comparative in nature. In such methods, the difference between the refractive indexes of the media being compared is determined (Figure 3) from the number of orders of interference of the rays transmitted through these media. These methods, whose accuracy reaches 10^-7-10^-8, are used, for example, in measurements of indexes of gases and dilute solutions.

Instruments used to determine the refractive index by refractometric methods are called refractometers.

Refractometry has found broad application in physical chemistry in the determination of the composition and structure of substances. It is also used in monitoring the quality and composition of various products in, for example, the chemical, pharmaceutical, and food industries. The advantages of refractometric methods of quantitative chemical analysis are speed of measurement, low consumption of the substance, and high accuracy. If refractive-index gradients are known, density and concentration gradients can be calculated. In some cases, conclusions as to the character of the interaction of substances and the formation of compounds can be drawn from the shape of the refractive-index curves. Refractometric methods are used in testing the homogeneity of solid and liquid samples and in aerodynamic and hydrodynamic research. Refractometry plays a special role in the optical industry, since the refractive index and dispersion are very important characteristics of such optical materials as glass.