The refractive index of a medium relative to vacuum, i.e., for the case of the transition of light rays from vacuum to a medium, is called absolute and is determined by formula (27.10): n=c/v.

In calculations, the absolute refractive indices are taken from the tables, since their value is determined quite accurately using experiments. Since c is greater than v, then the absolute refractive index is always greater than unity.

If light radiation passes from vacuum to a medium, then the formula for the second law of refraction is written as:

sin i/sin β = n. (29.6)

Formula (29.6) is also often used in practice when rays pass from air to a medium, since the speed of light propagation in air differs very little from c. This can be seen from the fact that the absolute refractive index of air is 1.0029.

When the beam goes from the medium to vacuum (to air), then the formula for the second law of refraction takes the form:

sin i/sin β = 1/n. (29.7)

In this case, the rays, when leaving the medium, necessarily move away from the perpendicular to the interface between the medium and the vacuum.

Let's find out how you can find the relative refractive index n21 from the absolute refractive indices. Let the light pass from the medium with absolute indicator n1 into the environment with absolute index n2. Then n1 = c/V1 andn2 = s/v2, from where:

n2/n1=v1/v2=n21. (29.8)

The formula for the second law of refraction for such a case is often written as follows:

sini/sinβ = n2/n1. (29.9)

Let us remember that by Maxwell's theory absolute exponent refraction can be found from the relation: n = √(με). Since for substances transparent to light radiation, μ is practically equal to unity, we can assume that:

n = √ε. (29.10)

Since the frequency of oscillations in light radiation is of the order of 10 14 Hz, neither dipoles nor ions in a dielectric, which have a relatively large mass, have time to change their position with such a frequency, and the dielectric properties of a substance under these conditions are determined only by the electronic polarization of its atoms. This explains the difference between the value ε=n 2 from (29.10) and ε st in electrostatics. So, for water ε \u003d n 2 \u003d 1.77, and ε st \u003d 81; the ionic solid dielectric NaCl ε=2.25, and ε st =5.6. When a substance consists of homogeneous atoms or non-polar molecules, i.e., it has neither ions nor natural dipoles, then its polarization can only be electronic. For similar substances, ε from (29.10) and ε st coincide. An example of such a substance is diamond, which consists of only carbon atoms.

Note that the value of the absolute refractive index, in addition to the type of substance, also depends on the oscillation frequency, or on the radiation wavelength . As the wavelength decreases, as a rule, the refractive index increases.

In the 8th grade physics course, you got acquainted with the phenomenon of light refraction. Now you know that light is electromagnetic waves of a certain frequency range. Based on knowledge about the nature of light, you will be able to understand the physical cause of refraction and explain many other light phenomena associated with it.

Rice. 141. Passing from one medium to another, the beam is refracted, i.e., changes the direction of propagation

According to the law of light refraction (Fig. 141):

  • rays incident, refracted and perpendicular drawn to the interface between two media at the point of incidence of the beam lie in the same plane; the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media

where n 21 is the relative refractive index of the second medium relative to the first.

If the beam passes into any medium from a vacuum, then

where n is the absolute refractive index (or simply refractive index) of the second medium. In this case, the first "environment" is vacuum, the absolute index of which is taken as one.

The law of light refraction was discovered empirically by the Dutch scientist Willebord Snellius in 1621. The law was formulated in a treatise on optics, which was found in the scientist's papers after his death.

After the discovery of Snell, several scientists put forward a hypothesis that the refraction of light is due to a change in its speed when it passes through the boundary of two media. The validity of this hypothesis was confirmed by theoretical proofs carried out independently by the French mathematician Pierre Fermat (in 1662) and the Dutch physicist Christian Huygens (in 1690). By different paths they arrived at the same result, proving that

  • the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media, equal to the ratio of the speeds of light in these media:

(3)

From equation (3) it follows that if the angle of refraction β is less than the angle of incidence a, then the light of a given frequency in the second medium propagates more slowly than in the first, i.e. V 2

The relationship of the quantities included in equation (3) served as a good reason for the appearance of another formulation of the definition of the relative refractive index:

  • the relative refractive index of the second medium relative to the first is a physical quantity equal to the ratio of the speeds of light in these media:

n 21 \u003d v 1 / v 2 (4)

Let a beam of light pass from vacuum to some medium. Replacing v1 in equation (4) with the speed of light in vacuum c, and v 2 with the speed of light in a medium v, we obtain equation (5), which is the definition of the absolute refractive index:

  • the absolute refractive index of a medium is a physical quantity equal to the ratio of the speed of light in vacuum to the speed of light in a given medium:

According to equations (4) and (5), n 21 shows how many times the speed of light changes when it passes from one medium to another, and n - when it passes from vacuum to a medium. This is physical meaning refractive indices.

The value of the absolute refractive index n of any substance is greater than unity (this is confirmed by the data contained in the tables of physical reference books). Then, according to equation (5), c/v > 1 and c > v, i.e., the speed of light in any substance is less than the speed of light in vacuum.

Without giving rigorous justifications (they are complex and cumbersome), we note that the reason for the decrease in the speed of light during its transition from vacuum to matter is the interaction of a light wave with atoms and molecules of matter. The greater the optical density of the substance, the stronger this interaction, the lower the speed of light and the greater the refractive index. Thus, the speed of light in a medium and the absolute refractive index are determined by the properties of this medium.

According to the numerical values ​​of the refractive indices of substances, one can compare their optical densities. For example, the refractive index different varieties glasses lie in the range from 1.470 to 2.040, and the refractive index of water is 1.333. This means that glass is an optically denser medium than water.

Let us turn to Figure 142, with the help of which we can explain why, at the boundary of two media, with a change in speed, the direction of propagation of a light wave also changes.

Rice. 142. When light waves pass from air to water, the speed of light decreases, the front of the wave, and with it its speed, change direction

The figure shows a light wave passing from air into water and incident on the interface between these media at an angle a. In air, light propagates at a speed v 1 , and in water at a slower speed v 2 .

Point A of the wave reaches the boundary first. Over a period of time Δt, point B, moving in the air at the same speed v 1, will reach point B. "During the same time, point A, moving in water at a lower speed v 2, will cover a shorter distance, reaching only point A". In this case, the so-called wave front A "B" in the water will be rotated at a certain angle with respect to the front of the AB wave in the air. And the velocity vector (which is always perpendicular to the wave front and coincides with the direction of its propagation) rotates, approaching the straight line OO", perpendicular to the interface between the media. In this case, the angle of refraction β is less than the angle of incidence α. This is how the refraction of light occurs.

It can also be seen from the figure that upon transition to another medium and rotation of the wave front, the wavelength also changes: upon transition to an optically denser medium, the velocity decreases, the wavelength also decreases (λ 2< λ 1). Это согласуется и с известной вам формулой λ = V/v, из которой следует, что при неизменной частоте v (которая не зависит от плотности среды и поэтому не меняется при переходе луча из одной среды в другую) уменьшение скорости распространения волны сопровождается пропорциональным уменьшением длины волны.

Questions

  1. Which of the two substances is optically denser?
  2. How are refractive indices determined in terms of the speed of light in media?
  3. Where does light travel the fastest?
  4. What is the physical reason for the decrease in the speed of light when it passes from vacuum to a medium or from a medium with less optical density Wednesday with more?
  5. What determines (i.e., what do they depend on) the absolute refractive index of the medium and the speed of light in it?
  6. Explain what Figure 142 illustrates.

Exercise

Light refraction- a phenomenon in which a beam of light, passing from one medium to another, changes direction at the boundary of these media.

The refraction of light occurs according to the following law:
The incident and refracted rays and the perpendicular drawn to the interface between two media at the point of incidence of the beam lie in the same plane. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for two media:
,
Where α - angle of incidence,
β - angle of refraction
n - a constant value independent of the angle of incidence.

When the angle of incidence changes, the angle of refraction also changes. The larger the angle of incidence, the larger the angle of refraction.
If light goes from an optically less dense medium to a denser medium, then the angle of refraction is always less than the angle of incidence: β < α.
A beam of light directed perpendicular to the interface between two media passes from one medium to another without breaking.

absolute refractive index of a substance- a value equal to the ratio of the phase velocities of light (electromagnetic waves) in vacuum and in a given medium n=c/v
The value n included in the law of refraction is called the relative refractive index for a pair of media.

The value n is the relative refractive index of medium B with respect to medium A, and n" = 1/n is the relative refractive index of medium A with respect to medium B.
This value, ceteris paribus, is greater than unity when the beam passes from a denser medium to a less dense medium, and less 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.
A beam falling from airless space onto the surface of some medium B is refracted more strongly than when falling on it from another medium A; The refractive index of a ray incident on a medium from airless space is called its absolute refractive index.

(Absolute - relative to vacuum.
Relative - relative to any other substance (the same air, for example).
The relative index of two substances is the ratio of their absolute indices.)

Complete internal reflection - internal reflection, provided that the angle of incidence exceeds a certain critical angle. In this case, the incident wave is completely reflected, and the value of the reflection coefficient exceeds its most big values for polished surfaces. The reflection coefficient for total internal reflection does not depend on the wavelength.

In optics, this phenomenon is observed for a wide range electromagnetic radiation, including the x-ray range.

In geometric optics, the phenomenon is explained in terms of Snell's law. Considering that the angle of refraction cannot exceed 90°, we obtain that at an angle of incidence whose sine is greater than the ratio of the smaller refractive index to the larger index, electromagnetic wave should be fully reflected on the first Wednesday.

In accordance with the wave theory of the phenomenon, the electromagnetic wave nevertheless penetrates into the second medium - the so-called “non-uniform wave” propagates there, which decays exponentially and does not carry away energy with it. The characteristic depth of penetration of an inhomogeneous wave into the second medium is of the order of the wavelength.

Laws of refraction of light.

From all that has been said, we conclude:
1 . At the interface between two media of different optical density, a beam of light changes its direction when passing from one medium to another.
2. When a light beam passes into a medium with a higher optical density, the angle of refraction is less than the angle of incidence; when a light beam passes from an optically denser medium to a less dense medium, the angle of refraction is greater than the angle of incidence.
The refraction of light is accompanied by reflection, and with an increase in the angle of incidence, the brightness of the reflected beam increases, while the refracted one weakens. This can be seen by conducting the experiment shown in the figure. Consequently, the reflected beam carries away with it the more light energy, the greater the angle of incidence.

Let MN- the interface between two transparent media, for example, air and water, JSC- falling beam OV- refracted beam, - angle of incidence, - angle of refraction, - speed of light propagation in the first medium, - speed of light propagation in the second medium.

Laboratory work

Light refraction. Measurement of the refractive index of a liquid

with a refractometer

Goal of the work: deepening of ideas about the phenomenon of light refraction; study of methods for measuring the refractive index of liquid media; study of the principle of operation with a refractometer.

Equipment: refractometer, solutions table salt, pipette, soft cloth for wiping the optical parts of devices.

Theory

Laws of reflection and refraction of light. refractive index.

At the interface between media, light changes the direction of its propagation. Part of the light energy returns to the first medium, i.e. light is reflected. If the second medium is transparent, then part of the light, under certain conditions, passes through the interface between the media, changing, as a rule, the direction of propagation. This phenomenon is called refraction of light. (Fig. 1).

Rice. 1. Reflection and refraction of light on a flat interface between two media.

The direction of the reflected and refracted rays during the passage of light through a flat interface between two transparent media is determined by the laws of reflection and refraction of light.

The law of reflection of light. The reflected ray lies in the same plane as the incident ray and the normal restored to the interface plane at the point of incidence. Angle of incidence equal to the angle of reflection
.

The law of refraction of light. The refracted beam lies in the same plane as the incident beam and the normal restored to the interface plane at the point of incidence. The ratio of the sine of the angle of incidence α to the sine of the angle of refraction β there is a constant value for these two media, called the relative refractive index of the second medium with respect to the first:

Relative refractive index two media is equal to the ratio of the speed of light in the first medium v ​​1 to the speed of light in the second medium v ​​2:

If light goes from vacuum to a medium, then the refractive index of the medium relative to vacuum is called the absolute refractive index of this medium and is equal to the ratio of the speed of light in vacuum With to the speed of light in a given medium v:

Absolute refractive indices are always greater than one; for air n taken as a unit.

The relative refractive index of two media can be expressed in terms of their absolute indices n 1 And n 2 :

Determination of the refractive index of a liquid

For quick and convenient determination of the refractive index of liquids, there are special optical instruments - refractometers, the main part of which are two prisms (Fig. 2): auxiliary Etc. 1 and measuring Ex 2. The test liquid is poured into the gap between the prisms.

When measuring indicators, two methods can be used: the grazing beam method (for transparent liquids) and the total internal reflection method (for dark, cloudy and colored solutions). In this work, the first of them is used.

In the gliding beam method, the light from external source goes over the edge AB prisms Ex 1, diffuses on its matte surface AC and then through the layer of the investigated liquid penetrates into the prism Ex 2. The matte surface becomes a source of rays from all directions, so it can be observed through the face EF prisms Ex 2. However, the line AC can be seen through EF only at an angle greater than some limiting minimum angle i. The value of this angle is uniquely related to the refractive index of the liquid located between the prisms, which will happen to be the main idea of ​​the refractometer design.

Consider the passage of light through a face EF lower measuring prism Ex 2. As can be seen from fig. 2, applying twice the law of refraction of light, we can obtain two relationships:

(1)

(2)

Solving this system of equations, it is easy to come to the conclusion that the refractive index of the liquid

(3)

depends on four quantities: Q, r, r 1 And i. However, not all of them are independent. For example,

r+ s= R , (4)

Where R - refractive angle of a prism Ex 2. In addition, by setting the angle Q the maximum value is 90°, from equation (1) we get:

(5)

But the maximum value of the angle r , as it can be seen from fig. 2 and relations (3) and (4), correspond to the minimum values ​​of the angles i And r 1 , those. i min And r min .

Thus, the refractive index of a liquid for the case of "gliding" rays is related only to the angle i. In this case, there is a minimum value of the angle i, when the edge AC is still observed, i.e., in the field of view, it appears to be mirror white. For smaller viewing angles, the edge is not visible, and in the field of view this place appears black. Since the instrument's telescope captures a relatively wide angular zone, light and black areas are simultaneously observed in the field of view, the boundary between which corresponds to the minimum observation angle and is unambiguously related to the refractive index of the liquid. Using the final calculation formula:

(its conclusion is omitted) and a number of liquids with known refractive indices, it is possible to calibrate the device, i.e., establish a one-to-one correspondence between the refractive indices of liquids and angles i min . All the above formulas are derived for rays of any one wavelength.

Light of different wavelengths will be refracted, taking into account the dispersion of the prism. Thus, when the prism is illuminated with white light, the interface will be blurred and colored in different colors due to dispersion. Therefore, each refractometer has a compensator that allows you to eliminate the result of dispersion. It can consist of one or two direct vision prisms - Amici prisms. Each Amici prism consists of three glass prisms with different refractive indices and different dispersions, for example, the outer prisms are made of crown glass, and the middle prism is made of flint glass (crown glass and flint glass are types of glass). By turning the compensator prism with the help of a special device, a sharp, colorless image of the interface is achieved, the position of which corresponds to the refractive index value for the yellow sodium line λ \u003d 5893 Å (prisms are designed so that rays with a wavelength of 5893 Å do not experience deviations in them).

The rays that have passed through the compensator enter the objective of the telescope, then pass through the reversing prism through the eyepiece of the telescope into the observer's eye. The schematic course of rays is shown in fig. 3.

The refractometer scale is calibrated in terms of the refractive index and the concentration of the sucrose solution in water and is located in the focal plane of the eyepiece.

experimental part

Task 1. Checking the refractometer.

Point the light with a mirror at the auxiliary prism of the refractometer. With the auxiliary prism raised, pipette a few drops of distilled water onto the measuring prism. Lowering the secondary prism, achieve the best illumination of the field of view and set the eyepiece so that the crosshairs and refractive index scale can be clearly seen. Turning the camera of the measuring prism, get the border of light and shadow in the field of view. By rotating the compensator head, achieve the elimination of the coloration of the border of light and shadow. Align the border of light and shadow with the crosshair point and measure the refractive index of water n ism . If the refractometer is working, then for distilled water the value should be n 0 = 1.333, if the readings differ from this value, you need to determine the correction Δn= n ism - 1.333, which should then be taken into account in further work with the refractometer. Make corrections in table 1.

Table 1.

n 0

n ism

Δ n

H 2 ABOUT

Task 2. Determination of the refractive index of a liquid.

    Determine the refractive indices of solutions of known concentrations, taking into account the correction found.

Table 2.

C, about. %

n ism

n ist

    Plot the dependence of the refractive index of sodium chloride solutions on the concentration according to the results obtained. Make a conclusion about the dependence of n on C; draw conclusions about the accuracy of measurements on a refractometer.

    Take a salt solution of unknown concentration WITH x , determine its refractive index and find the concentration of the solution from the graph.

    take away workplace, gently wipe the prisms of the refractometers with a damp, clean cloth.

Control questions

    Reflection and refraction of light.

    Absolute and relative performance refraction of the medium.

    The principle of operation of the refractometer. Sliding beam method.

    Schematic course of rays in a prism. Why are compensator prisms needed?

Propagation, reflection and refraction of light

The nature of light is electromagnetic. One proof of this is the coincidence of the velocities of electromagnetic waves and light in vacuum.

In a homogeneous medium, light propagates in a straight line. This statement is called the law of rectilinear propagation of light. An experimental proof of this law is the sharp shadows given by point sources of light.

A geometric line indicating the direction of light propagation is called a light beam. In an isotropic medium, light rays are directed perpendicular to the wave front.

The locus of points of the medium oscillating in the same phase is called the wave surface, and the set of points to which the oscillation has reached a given point in time is called the wave front. Depending on the type of wave front, plane and spherical waves are distinguished.

To explain the process of light propagation, use general principle wave theory about the movement of the wave front in space, proposed by the Dutch physicist H. Huygens. According to the Huygens principle, each point of the medium, to which light excitation reaches, is the center of spherical secondary waves, which also propagate at the speed of light. The surface envelope of the fronts of these secondary waves gives the position of the front of the actually propagating wave at that moment in time.

It is necessary to distinguish between light beams and light rays. A light beam is a part of a light wave that carries light energy in a given direction. When replacing a light beam with a light beam describing it, the latter must be taken to coincide with the axis of a rather narrow, but having a finite width (the dimensions of the cross section are much larger than the wavelength), light beam.

There are divergent, converging and quasi-parallel light beams. The terms beam of light rays or simply light rays are often used, meaning by this a set of light rays that describe a real light beam.

The speed of light in vacuum c = 3 108 m/s is a universal constant and does not depend on frequency. For the first time, the speed of light was experimentally determined by the astronomical method by the Danish scientist O. Römer. A. Michelson measured the speed of light more accurately.

The speed of light in matter is less than in vacuum. The ratio of the speed of light in vacuum to its speed in a given medium is called the absolute refractive index of the medium:

where c is the speed of light in vacuum, v is the speed of light in a given medium. The absolute refractive indices of all substances are greater than unity.

When light propagates in a medium, it is absorbed and scattered, and at the interface between the media it is reflected and refracted.

The law of reflection of light: the incident beam, the reflected beam and the perpendicular to the interface between two media, restored at the point of incidence of the beam, lie in the same plane; the angle of reflection g is equal to the angle of incidence a (Fig. 1). This law coincides with the law of reflection for waves of any nature and can be obtained as a consequence of the Huygens principle.

The law of refraction of light: the incident beam, the refracted beam and the perpendicular to the interface between two media, restored at the point of incidence of the beam, lie in the same plane; the ratio of the sine of the angle of incidence to the sine of the angle of refraction for a given frequency of light is a constant value, called the relative refractive index of the second medium relative to the first:

The experimentally established law of light refraction is explained on the basis of the Huygens principle. According to wave concepts, refraction is a consequence of a change in the speed of wave propagation during the transition from one medium to another, and the physical meaning of the relative refractive index is the ratio of the wave propagation velocity in the first medium v1 to the velocity of their propagation in the second medium

For media with absolute refractive indices n1 and n2, the relative refractive index of the second medium relative to the first is equal to the ratio of the absolute refractive index of the second medium to the absolute refractive index of the first medium:

The medium that has a higher refractive index is called optically denser, the speed of light propagation in it is lower. If light passes from an optically denser medium to an optically less dense one, then at a certain angle of incidence a0 the angle of refraction should become equal to p/2. The intensity of the refracted beam in this case becomes equal to zero. Light incident on the interface between two media is completely reflected from it.

The angle of incidence a0 at which total internal reflection of light occurs is called the limiting angle of total internal reflection. At all angles of incidence equal to or greater than a0, total reflection of light occurs.

The value of the limiting angle is found from the relation If n2 = 1 (vacuum), then

2 The refractive index of a substance is a value equal to the ratio of the phase velocities of light (electromagnetic waves) in vacuum and in a given medium. They also talk about the refractive index for any other waves, for example, sound

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 when the frequency of electromagnetic waves changes from low frequencies to optical and beyond, and can also change even more sharply in certain areas of the frequency scale. The default is usually the optical range, or the range determined by the context.

There are optically anisotropic substances in which the refractive index depends on the direction and polarization of the light. Such substances are quite common, in particular, these are all crystals with a sufficiently low symmetry of the crystal lattice, as well as substances subjected to mechanical deformation.

The refractive index can be expressed as the root of the product of the magnetic and permittivities of the medium

(it must be taken into account that the values ​​of the magnetic permeability and the absolute permittivity index for the frequency range of interest - for example, the optical one, can be very different from the static value of these values).

To measure the refractive index, manual and automatic refractometers are used. When using a refractometer to determine the concentration of sugar in an aqueous solution, the device is called a saccharimeter.

The ratio of the sine of the angle of incidence () of the beam to the sine of the angle of refraction () during the transition of the beam from medium A to medium B is called the relative refractive index for this pair of media.

The quantity n is the relative refractive index of the medium B with respect to the medium A, an" = 1/n is the relative refractive index of the medium A with respect to the medium B.

This value, 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 a medium).

A beam falling from airless space onto the surface of some medium B is refracted more strongly than when falling on it from another medium A; the refractive index of a ray incident on a medium from airless space is called its absolute refractive index or simply the refractive index of this medium, this is the refractive index, the definition of which is given at the beginning of the article. The refractive index of any gas, including air, under normal conditions is much less than the refractive indices of liquids or solids, therefore, approximately (and with relatively good accuracy) the absolute refractive index can be judged from the refractive index relative to air.

Rice. 3. The principle of operation of the interference refractometer. A beam of light is divided so that its two parts pass through cuvettes of length l filled with substances with different refractive indices. At the exit from the cell, the rays acquire a certain path difference and, being brought together, give on the screen a picture of interference maxima and minima with k orders (shown schematically on the right). The difference in refractive indices Dn=n2 –n1 =kl/2, where l is the wavelength of light.

Refractometers are devices used to measure the refractive index of substances. The principle of operation of a refractometer is based on the phenomenon of total reflection. If a scattered beam of light falls on the interface of two media with refractive indices and from a more optically dense medium, then starting from a certain angle of incidence, the rays do not enter the second medium, but are completely reflected from the interface in the first medium. This angle is called the limiting angle of total reflection. Figure 1 shows the behavior of the rays when they fall into a certain current of this surface. The beam goes at a limiting angle. From the law of refraction, you can determine:, (because).

The limiting angle depends on the relative refractive index of the two media. If the rays reflected from the surface are directed to a converging lens, then in the focal plane of the lens one can see the border of light and penumbra, and the position of this border depends on the value of the limiting angle, and, consequently, on the refractive index. A change in the refractive index of one of the media entails a change in the position of the interface. The boundary between light and shadow can serve as an indicator in determining the refractive index, which is used in refractometers. This method of determining the refractive index is called the total reflection method.

In addition to the total reflection method, refractometers use the grazing beam method. In this method, a scattered light beam hits the boundary from a less optically dense medium at all possible angles (Fig. 2). The beam sliding on the surface (), corresponds to -- limit angle refraction (beam in Fig. 2). If we put a lens in the path of the rays () refracted on the surface, then in the focal plane of the lens we will also see a sharp border between light and shadow.

Rice. 2

Since the conditions that determine the value of the limiting angle are the same in both methods, the position of the interface is the same. Both methods are equivalent, but the total reflection method allows you to measure the refractive index of opaque substances

The path of rays in a triangular prism

Figure 9 shows a section of a glass prism with a plane perpendicular to its side edges. The beam in the prism deviates to the base, refracting on the faces OA and 0B. The angle j between these faces is called the refractive angle of the prism. The deflection angle q of the beam depends on the refractive angle of the prism j, the refractive index n of the prism material and the angle of incidence a. It can be calculated using the law of refraction (1.4).

The refractometer uses a white light source 3. Due to dispersion when light passes through prisms 1 and 2, the boundary between light and shadow turns out to be colored. To avoid this, a compensator 4 is placed in front of the telescope lens. It consists of two identical prisms, each of which is glued together from three prisms with a different refractive index. Prisms are selected so that a monochromatic beam with a wavelength= 589.3 µm. (wavelength of the yellow sodium line) was not tested after passing the deflection compensator. Rays with other wavelengths are deflected by prisms in different directions. By moving the compensator prisms with the help of a special handle, the border between light and darkness becomes as clear as possible.

Rays of light, having passed the compensator, fall into the lens 6 of the telescope. The image of the light-shadow interface is viewed through the eyepiece 7 of the telescope. At the same time, scale 8 is viewed through the eyepiece. Since the limiting angle of refraction and the limiting angle of total reflection depend on the refractive index of the liquid, the values ​​​​of this refractive index are immediately plotted on the scale of the refractometer.

The optical system of the refractometer also contains a rotary prism 5. It allows you to position the axis of the telescope perpendicular to the prisms 1 and 2, which makes observation more convenient.

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