REFRACTIVE INDICATOR(refractive index) - optical. environmental characteristic associated with refraction of light at the interface between two transparent optically homogeneous and isotropic media during its transition from one medium to another and due to the difference in the phase velocities of light propagation in the media. The value of P. p., equal to the ratio of these speeds. relative

P. p. of these environments. If light falls on the second or first medium from (where the speed of light propagation With), then the quantities are absolute P. p. of these environments. In this case, the law of refraction can be written in the form where and are the angles of incidence and refraction.

The magnitude of the absolute P. p. depends on the nature and structure of the substance, its state of aggregation, temperatures, pressures, etc. At high intensities, the P. p. depends on the light intensity (see. non-linear optics). In a number of substances, P. p. changes under the influence of external. electric fields ( Kerr effect- in liquids and gases; electro-optical Pockels effect- in crystals).

For a given medium, the absorption band depends on the wavelength l of light, and in the region of absorption bands this dependence is anomalous (see Fig. Light dispersion). For almost all media, the absorption band is close to 1; in the visible region for liquids and solids, it is about 1.5; in the IR region for a number of transparent media 4.0 (for Ge).

They are characterized by two parametric phenomena: ordinary (similar to isotropic media) and extraordinary, the magnitude of which depends on the angle of incidence of the beam and, consequently, the direction of propagation of light in the medium (see Fig. Crystal optics). For media with absorption (in particular, for metals), the absorption coefficient is a complex quantity and can be represented as where n is the usual absorption coefficient, is the absorption index (see. Light absorption, metal optics).

P. p. is macroscopic. characteristic of the environment and is associated with its permittivity n magn. permeability Classic electronic theory (cf. Light dispersion) allows you to associate the value of P. p. with microscopic. characteristics of the environment - electronic polarizability atom (or molecule) depending on the nature of the atoms and the frequency of light, and the medium: where N is the number of atoms per unit volume. Acting on an atom (molecule) electric. field of the light wave causes a shift of the optical. an electron from an equilibrium position; the atom becomes induced. dipole moment changing in time with the frequency of the incident light, and is a source of secondary coherent waves, to-rye. interfering with the wave incident on the medium, they form the resulting light wave propagating in the medium with phase velocity, and therefore

The intensity of conventional (non-laser) light sources is relatively low; the field of a light wave acting on an atom is much smaller than intra-atomic electric. fields, and an electron in an atom can be considered as harmonic. oscillator. In this approximation, the value of and P. p.

They are constant values ​​(at a given frequency), independent of light intensity. In intense light fluxes created by powerful lasers, the magnitude of the electric. the field of a light wave can be commensurate with the intra-atomic electric-rich. fields and the harmony model, the oscillator turns out to be unacceptable. Accounting for the anharmonicity of forces in the electron-atom system leads to the dependence of the polarizability of the atom, and hence the polarization coefficient, on the light intensity. The connection between and turns out to be non-linear; P. p. can be represented in the form

Where - P. p. at low light intensities; (usually accepted designation) - non-linear addition to P. p., or coefficient. non-linearity. P. p. depends on the nature of the environment, for example. for silicate glass

P. p. is also affected by high intensity as a result of the effect electrostriction, changing the density of the medium, high-frequency for anisotropic molecules (in a liquid), as well as as a result of an increase in temperature caused by absorption

Let us turn to a more detailed consideration of the refractive index introduced by us in § 81 when formulating the law of refraction.

The refractive index depends on the optical properties and the medium from which the beam falls and the medium into which it penetrates. The refractive index obtained when light from a vacuum falls on a medium is called the absolute refractive index of this medium.

Rice. 184. Relative refractive index of two media:

Let the absolute refractive index the first environment is and the second environment - . Considering the refraction at the boundary of the first and second media, we make sure that the refractive index during the transition from the first medium to the second, the so-called relative refractive index, is equal to the ratio of the absolute refractive indices of the second and first media:

(Fig. 184). On the contrary, when passing from the second medium to the first, we have a relative refractive index

The established connection between the relative refractive index of two media and their absolute refractive indices could also be derived theoretically, without new experiments, just as it can be done for the law of reversibility (§82),

A medium with a higher refractive index is said to be optically denser. The refractive index is usually measured various environments relative to air. The absolute refractive index of air is . Thus, the absolute refractive index of any medium is related to its refractive index relative to air by the formula

Table 6. Refractive index of various substances relative to air

Liquids

Solids

Substance

Substance

Ethanol

carbon disulfide

Glycerol

Glass (light crown)

liquid hydrogen

Glass (heavy flint)

liquid helium

The refractive index depends on the wavelength of light, that is, on its color. Different colors correspond to different refractive indices. This phenomenon, called dispersion, plays important role in optics. We will deal with this phenomenon repeatedly in later chapters. The data given in table. 6, refer to yellow light.

It is interesting to note that the law of reflection can be formally written in the same form as the law of refraction. Recall that we agreed to always measure the angles from the perpendicular to the corresponding ray. Therefore, we must consider the angle of incidence and the angle of reflection to have opposite signs, i.e. the law of reflection can be written as

Comparing (83.4) with the law of refraction, we see that the law of reflection can be viewed as special case the law of refraction at . This formal similarity between the laws of reflection and refraction is of great use in solving practical problems.

In the previous presentation, the refractive index had the meaning of a constant of the medium, independent of the intensity of the light passing through it. Such an interpretation of the refractive index is quite natural; however, in the case of high radiation intensities achievable using modern lasers, it is not justified. The properties of the medium through which strong light radiation passes, in this case, depend on its intensity. As they say, the medium becomes non-linear. The nonlinearity of the medium manifests itself, in particular, in the fact that a light wave of high intensity changes the refractive index. The dependence of the refractive index on the radiation intensity has the form

Here, is the usual refractive index, a is the non-linear refractive index, and is the proportionality factor. The additional term in this formula can be either positive or negative.

The relative changes in the refractive index are relatively small. At non-linear refractive index. However, even such small changes in the refractive index are noticeable: they manifest themselves in a peculiar phenomenon of self-focusing of light.

Consider a medium with a positive nonlinear refractive index. In this case, the areas of increased light intensity are simultaneous areas of increased refractive index. Usually in real laser radiation the intensity distribution over the cross section of the ray beam is nonuniform: the intensity is maximum along the axis and gradually decreases towards the edges of the beam, as shown in Fig. 185 solid curves. A similar distribution also describes the change in the refractive index over the cross section of a cell with a nonlinear medium, along the axis of which the laser beam propagates. The refractive index, which is greatest along the cell axis, gradually decreases towards its walls (dashed curves in Fig. 185).

A beam of rays leaving the laser parallel to the axis, falling into a medium with a variable refractive index, is deflected in the direction where it is greater. Therefore, an increased intensity in the vicinity of the OSP cell leads to a concentration of light rays in this region, which is shown schematically in cross sections and in Fig. 185, and this leads to a further increase in . Ultimately, the effective cross section of a light beam passing through a nonlinear medium decreases significantly. Light passes as if through a narrow channel with an increased refractive index. Thus, the laser beam narrows, and the nonlinear medium acts as a converging lens under the action of intense radiation. This phenomenon is called self-focusing. It can be observed, for example, in liquid nitrobenzene.

Rice. 185. Distribution of radiation intensity and refractive index over the cross section of the laser beam at the entrance to the cuvette (a), near the input end (), in the middle (), near the output end of the cuvette ()

There is nothing else than the ratio of the sine of the angle of incidence to the sine of the angle of refraction

The refractive index depends on the properties of the substance and the wavelength of the radiation, for some substances the refractive index changes quite strongly with a change in frequency electromagnetic waves from low frequencies to optical and beyond, and can also change even more dramatically in certain areas of the frequency scale. The default is usually the optical range, or the range determined by the context.

The value of n, ceteris paribus, is usually less than unity when the beam passes from a denser medium to a less dense medium, and more than unity when the beam passes from a less dense medium to a denser medium (for example, from a gas or from vacuum to a liquid or solid ). There are exceptions to this rule, and therefore it is customary to call a medium optically more or less dense than another (not to be confused with optical density as a measure of the opacity of the medium).

The table shows some refractive index values ​​for some media:

A medium with a higher refractive index is said to be optically denser. The refractive index of various media relative to air is usually measured. The absolute refractive index of air is . Thus, the absolute refractive index of any medium is related to its refractive index relative to air by the formula:

The refractive index depends on the wavelength of light, that is, on its color. Different colors correspond to different refractive indices. This phenomenon, called dispersion, plays an important role in optics.

Fields of application of refractometry.

The device and principle of operation of the IRF-22 refractometer.

The concept of the refractive index.

Plan

Refractometry. Characteristics and essence of the method.

To identify substances and check their purity, use

refractor.

Refractive index of a substance- a value equal to the ratio of the phase velocities of light (electromagnetic waves) in vacuum and the seen medium.

The refractive index depends on the properties of the substance and the wavelength

electromagnetic radiation. The ratio of the sine of the angle of incidence relative to

the normal drawn to the plane of refraction (α) of the beam to the sine of the angle of refraction

refraction (β) during the transition of the beam from medium A to medium B is called the relative refractive index for this pair of media.

The value n is the relative refractive index of the medium B according to

in relation to environment A, and

The relative refractive index of the medium A with respect to

The refractive index of a beam incident on a medium from an airless

th space is called absolute indicator refraction or

simply the refractive index of a given medium (Table 1).

Table 1 - Refractive indices of various media

Liquids have a refractive index in the range of 1.2-1.9. Solid

substances 1.3-4.0. Some minerals do not exact value show-

for refraction. Its value is in a certain "fork" and determines

due to the presence of impurities in the crystal structure, which determines the color

crystal.

Identification of the mineral by "color" is difficult. So, the mineral corundum exists in the form of ruby, sapphire, leucosapphire, differing in

refractive index and color. Red corundums are called rubies

(chromium admixture), colorless blue, light blue, pink, yellow, green,

violet - sapphires (impurities of cobalt, titanium, etc.). Light-colored

nye sapphires or colorless corundum is called leucosapphire (widely

used in optics as a light filter). The refractive index of these crystals

stall lies in the range of 1.757-1.778 and is the basis for identifying

Figure 3.1 - Ruby Figure 3.2 - Sapphire blue

Organic and inorganic liquids also have characteristic refractive index values ​​that characterize them as chemical

nye compounds and the quality of their synthesis (table 2):

Table 2 - Refractive indices of some liquids at 20 °C

4.2. Refractometry: concept, principle.

Method for the study of substances based on the determination of the indicator



(coefficient) of refraction (refraction) is called refractometry (from

lat. refractus - refracted and Greek. metreo - I measure). Refractometry

(refractometric method) is used to identify chemical

compounds, quantitative and structural analysis, determination of physico-

chemical parameters of substances. Refractometry principle implemented

in Abbe refractometers, illustrated by Figure 1.

Figure 1 - The principle of refractometry

The Abbe prism block consists of two rectangular prisms: illuminating

body and measuring, folded by hypotenuse faces. Illuminator-

prism has a rough (matte) hypotenuse face and is intended

chena for illuminating a liquid sample placed between the prisms.

Scattered light passes through a plane-parallel layer of the investigated liquid and, being refracted in the liquid, falls on the measuring prism. The measuring prism is made of optically dense glass (heavy flint) and has a refractive index greater than 1.7. For this reason, the Abbe refractometer measures n values ​​less than 1.7. An increase in the measuring range of the refractive index can only be achieved by changing the measuring prism.

The test sample is poured onto the hypotenuse face of the measuring prism and pressed against the illuminating prism. In this case, a gap of 0.1-0.2 mm remains between the prisms in which the sample is located, and through

which passes by refracting light. To measure the refractive index

use the phenomenon of complete internal reflection. It consists in

next.

If rays 1, 2, 3 fall on the interface between two media, then depending on

the angle of incidence when observing them in a refractive medium will be

the presence of a transition of areas of different illumination is observed. It's connected

with the incidence of some part of the light on the boundary of refraction at an angle of approx.

kim to 90° with respect to the normal (beam 3). (Figure 2).

Figure 2 - Image of refracted rays

This part of the rays is not reflected and therefore forms a lighter object.

refraction. Rays with smaller angles experience and reflect

and refraction. Therefore, an area of ​​less illumination is formed. In volume

the boundary line of total internal reflection is visible on the lens, the position

which depends on the refractive properties of the sample.

The elimination of the phenomenon of dispersion (colouring the interface between two areas of illumination in the colors of the rainbow due to the use of complex white light in Abbe refractometers) is achieved by using two Amici prisms in the compensator, which are mounted in the telescope. At the same time, a scale is projected into the lens (Figure 3). 0.05 ml of liquid is sufficient for analysis.

Figure 3 - View through the eyepiece of the refractometer. (The right scale reflects

concentration of the measured component in ppm)

In addition to the analysis of single-component samples, there are widely analyzed

two-component systems (aqueous solutions, solutions of substances in which

or solvent). In ideal two-component systems (forming-

without changing the volume and polarizability of the components), the dependence is shown

refractive index on the composition is close to linear if the composition is expressed in terms of

volume fractions (percentage)

where: n, n1, n2 - refractive indices of the mixture and components,

V1 and V2 are the volume fractions of the components (V1 + V2 = 1).

The effect of temperature on the refractive index is determined by two

factors: a change in the number of liquid particles per unit volume and

dependence of the polarizability of molecules on temperature. The second factor became

becomes significant only at very large temperature changes.

The temperature coefficient of the refractive index is proportional to the temperature coefficient of the density. Since all liquids expand when heated, their refractive indices decrease as the temperature rises. The temperature coefficient depends on the temperature of the liquid, but in small temperature intervals it can be considered constant. For this reason, most refractometers do not have temperature control, however, some designs provide

water temperature control.

Linear extrapolation of the refractive index with temperature changes is acceptable for small temperature differences (10 - 20°C).

Precise definition the refractive index in wide temperature ranges is produced according to empirical formulas of the form:

nt=n0+at+bt2+…

For solution refractometry over wide concentration ranges

use tables or empirical formulas. Display dependency-

refractive index of aqueous solutions of certain substances on concentration

is close to linear and makes it possible to determine the concentrations of these substances in

water in a wide range of concentrations (Figure 4) using refraction

tometers.

Figure 4 - Refractive index of some aqueous solutions

Usually, n liquid and solid bodies are determined by refractometers with precision

up to 0.0001. The most common are Abbe refractometers (Figure 5) with prism blocks and dispersion compensators, which make it possible to determine nD in "white" light on a scale or digital indicator.

Figure 5 - Abbe refractometer (IRF-454; IRF-22)