# REFRACTOMETRY

REFRACTOMETRY (late lat. refractio refraction + Greek metreo to measure, measure) — set of the optical techniques of the analysis of substance based on measurement of index of refraction of light in the studied environment.

Thanks to high precision, speed and simplicity of measurements methods of refractometry found broad application in medicine. In a wedge., fiziol. and biochemical laboratories determine by methods P. the content of proteins (albumine, globulins and fibrinogen) in blood serum, hemoglobin in erythrocytes, nonprotein ph. P. use for definition of purity of drugs, the analysis of solutions for injections, powders of medicinal mixes, definitions of concentration of alcohol in tinctures. Methods P. use during the definition refractions of an eye (see). Determine humidity of various foodstuff, content of proteins in milk and dairy products, seeds of oily plants, cakes, cakes and pod by index of refraction. By means of methods P. it is possible to watch purity of a distilled water, and also impurity level in drinking and sea water.

Fig. 1. Refraction of light rays on border of two transparent n1 and n2 environments: i1 and i2 — hades of beams 1 and 2, a1 and a2 — the angles of refraction, a2 — the limit angle of refraction (a2 = 90 °). At the opposite direction of a path of rays (from the n2 environment in the n1 environment) the corner a2 is called the angle of total internal reflection (at corners, big a2, light will not pass in the n1 environment).

The index of refraction (n) is the relation of velocity of light in vacuum to velocity of light in the environment, from a cut light falls on limit of the section; it is expressed by the relation of a sine of the angle of falling of a ray of light (i) to a sine of the angle of refraction (a) (fig. 1).

For each environment n — the constant which is not depending on a hade. In practice p usually define during the falling of light on the refracting environment from air. As size n depends on the wavelength of light and temperature, at p usually specify the wavelength of light or designation of a spectrum line, at a cut measurement, e.g., of n was performed 20 D means that n is measured at the wavelength of 589,3 nanometers (the yellow line of sodium) and temperature equal 20 °. In practice often use the size which is function of index of refraction and called by a refraction. The refraction carried to one gram of substance is called specific refraction (r):

r = [(n 2 - 1) / (n 2 +2)] * (1/d)

the Refraction carried to one mole of a substance is called molecular refraction (R):

R = [(n 2 - 1) / (n 2 +2)] * (M/d)

to a tda of d — the specific weight of substance, M — molecular weight.

Molecular refraction consists of the refractions entering a molecule of atoms is characteristic of each substance and allows to identify, in particular, composition of liquids (with an accuracy of 0,01%), to carry out quantification (at a consumption of substance 0,001 — 0,1 g), to study a structure of molecules, to define concentration gradients of substance at sedimentation, an electrophoresis, diffusion.

On a way of measurement of n distinguish several methods P., the main of to-rykh are: 1) methods of direct measurement of corners during the passing of a ray of light through limit of the section of two environments; 2) interferential methods; 3) immersion methods.

Fig. 2. A path of rays through a prism with the refracting corner f: the angle of deviation δ has the smallest size at a hade of a ray of light i equal to the angle of refraction on escaping of a prism β.

In one of options of the first method the studied liquid pour in hollow prismatic to a ditch with the refracting corner φ (fig. 2). The prism is lit with a parallel beam of light from one side and measure the smallest angle of deviation of a ray of light δ, to-ry corresponds to a symmetric path of rays through a prism. Size of index of refraction of n x it is calculated on a formula:

n x = sin ([φ + δ]/2) / sin(φ/2).

Fig. 3. Schematic diagram of measurement of index of refraction by method of a limit angle of refraction: and — the beams (1 and 2) falling on a prism through a sample under different corners after refraction remain in the limit angle of refraction and, limited to a beam 2 for which the hade is equal 90 °; on escaping of a prism the sharp border between light area (I) and a shadow (II) observed in the telescope is formed; — the beams (1, 2 and 3) falling on limit of the section from one of sides of a prism completely are reflected at a hade of a ray of light more limit corner of i (a beam 3) and partially are reflected at a hade less, than i (a beam 2); on escaping of a prism the border between light area (I) and a half-shade (III) observed in the telescope is formed; φ — the refracting corner of a prism; β — the angle of refraction on escaping of a prism.

Bigger distribution was gained by a method of determination of index of refraction (nx) of a sample by measurement of a limit angle of refraction or the angle of total internal reflection on border of a sample and prism with precisely known index of refraction (n 0 ), big, than n x (fig. 3). The studied liquid is poured in the transparent vessel installed on a surface of a prism (in case of a solid its one surface is polished on the plane, and between this plane and a surface of a prism place a drop of liquid, edges spreads in a thin plane-parallel coat).

In one option of a method (fig. 3, a) the border of contact of the studied sample is lit with a wide beam of light from a sample, and in another — from one of sides of a prism (fig. 3, b). Calculation is made on

a formula n x = n 0 sin (a),

where and — the limit angle of refraction corresponding to a hade of a ray of light of i = 90 °, n 0 — known value of an angle of refraction of a prism, n x — required value of index of refraction.

In practice usually measure not the limit angle of refraction, but an angle of emergence of a limit beam from a prism in air β. In this case

n x = sinφ √ (n 0 2 - sin 2 β) ± cosφsinβ,

where φ — the angle of refraction of a prism (the same other designations).

The most sensitive is the interferential method of measurement of indices of refraction. If to divide a ray of light of a certain wavelength from one light source into two parallel beams and then to reduce them together, then in the presence of a constant difference of phases between fluctuations of electromagnetic waves in one beam concerning another in the plane of crossing of beams the interference will be observed. The placement on ways of one beam ditches with the studied substance, and on the way of another same ditches with reference substance (i.e. index of refraction of n e to-rogo it is precisely known) leads to the shift of an interference pattern on m of strips in comparison with a case when both ditches are filled with the same substance. In this case nx value is calculated by a formula:

n x = n e ± mλ/l,

where λ — the wavelength of light, l — length ditches.

This method gained the greatest distribution at R. of gaseous and liquid transparent substances, determination of amount of impurity, concentration of dilute solutions etc.

At R. of refraction of the solids which do not have a certain form (e.g., powders, pieces of glass, etc.), the immersion method based on selection of reference immersion liquid with the index of refraction equal to index of refraction of the studied sample is used (n e — n x ). During the placing of the studied sample in this liquid it becomes «invisible».

At an immersion method a set of reference liquids prepares in advance, in to-rye the studied sample is consistently entered. At achievement of optical homogeneity of the environment measure index of refraction of liquid by means of one of the methods described above. As a rule, by means of an immersion method it is observed under a microscope.

Pulfrikh's refractometers, ABBA, submersible refractometers belong to the refractometers working by the principle of measurement of a limit angle of refraction. Sensitivity of these devices about 10 - 4 . In Pulfrikh's refractometer the measuring prism with the refracting corner and — 90 ° is used, the refractometer to ABBA — the measuring prism has a corner and = 60 °. Because the index of refraction depends on temperature, refractometers are supplied with the thermostatic device (water jacket) which allows to measure the angle of refraction at a certain temperature or to define temperature dependence of index of refraction of a sample.

Fig. 4. Elementary optical diagram of the submersible refractometer: 1 — a ray of light from the lighting device; 2 — a mirror; 3 — the studied liquid; 4 — a measuring prism; 5 — the compensator for elimination of dispersion of a prism and the studied liquid; 6 — a lens; 7 — the microscrew; 8, 9 — lenses of an eyepiece; 10 — the picture observed in an eyepiece.

In practice for measurement of index of refraction of liquids the submersible refractometer (fig. 4) was widely adopted. The measuring prism in operating time plunges directly into the studied liquid, is poured edge in a transparent glass. Rays of light from the lighting device are reflected a mirror, pass through a sample and get on a measuring prism. Counting is conducted on the scale applied on a lens of an eyepiece.

Also refractometers of a special purpose, e.g., RPL refractometers (are used to definition of sugar in aqueous solutions), by RZh (to definition of fats), etc. In production technological processes for continuous control of quality of products and automatic control of the course of process the automatic registering and regulating devices with photoelectronic determination of size of index of refraction of n are created. Transition to photoelectronic registration allows to increase sensitivity of refractometers to 1•10 - 6 .

Fig. 5. Elementary optical diagram of the interferometer of Zhamen: 1 — a ray of light from the lighting device; 2 — the reflecting plates; 5 — a standard sample; 4 — the studied sample; 5 — the telescope.

For measurement of indices of refraction with use of an interference of waves interference refractometers serve, among to-rykh the greatest distribution received Zhamen's (fig. 5) interferometers, Christmas and Rayleigh. The principle of operation of these interferometers is identical, they differ only with methods of receiving coherent bunches, to-rye pass through the reference and studied samples and then come down together. The index of refraction of the studied sample is determined by the shift of an interference pattern, testing length (ditches) and the size of index of refraction of a standard. In the interferometer Christmas beams are divided by means of translucent plates, in Rayleigh's interferometer — by means of two slit diaphragms. Sensitivity of interference refractometers 10 - 7 — 10 - 8 .

See also Optical techniques of a research .

Bibliography: Boky G. B. Immersion method, M., 1948; Ioffe of B. V. Refraktometricheskiye methods of chemistry, L., 1974, bibliogr.; JI jolly boats Yu. Page and Klyachko Yu. A. Theoretical bases of modern qualitative analysis, M., 1978; Methods of the analysis of food, agricultural products and medical supplies, the lane with English, under the editorship of A. F. Namestnikov, M., 1974.

V. N. Verkhoturov.