Let's do an experiment. Let us place a glass plate in the center of the optical disk and direct a beam of light at it. We will see that at the boundary of air with glass, light will not only be reflected, but will also penetrate inside the glass, changing the direction of its propagation (Fig. 84).

The change in the direction of light propagation as it passes through the interface between two media is called refraction of light.

Figure 84 shows: AO - incident beam; OB - reflected beam; OE - refracted beam.

Note that if we directed the beam in the direction EO, then due to the reversibility of light rays, it would exit the glass in the direction OA.

The refraction of light is explained by the change in the speed of propagation of light as it passes from one medium to another. For the first time such an explanation of this phenomenon was given in the middle of the 17th century. Father Menyan. According to Meignan, when light passes from one medium to another, the beam of light changes its direction in the same way as the direction of movement of the "soldier's front" changes when the meadow along which the soldiers are walking is blocked by arable land, the border of which runs at an angle to the front. Each of the soldiers who have reached the arable land slows down their movement, while those of the soldiers who have not yet reached it continue to move at the same speed. As a result of this, the soldiers who entered the arable land begin to lag behind those walking through the meadow, and the column of troops turns around (Fig. 85).

To determine in which direction a ray of light will deviate when it passes through the interface between two media, it is necessary to know in which of these media the speed of light is less and in which it is greater.

Light is electromagnetic waves. Therefore, everything that was said about the speed of propagation of electromagnetic waves (see § 28) applies equally to the speed of light. So, for example, the speed of light in vacuum is maximum and is equal to:

c = 299792 km/s ≈ 300000 km/s.

The speed of light in matter v is always less than in vacuum:

The values ​​of the speed of light in various media are given in Table 6.

Of the two media, the one in which the speed of light is less is called optically denser, and the one in which the speed of light is greater - optically less dense. For example, water is optically denser than air, and glass is optically denser than water.

Experience shows that, getting into a medium that is optically denser, a ray of light deviates from its original direction towards the perpendicular to the interface between two media (Fig. 86, a), and getting into a medium that is optically less dense, the ray of light deviates into reverse side (Fig. 86, b).

The angle between the refracted beam and the perpendicular to the interface between two media at the point of incidence of the beam is called angle of refraction. Figure 86

α - angle of incidence, β - angle of refraction.

Figure 86 shows that the angle of refraction can be either greater or less than the angle of incidence. Can these angles match? They can, but only when a beam of light falls on the interface at a right angle to it; in this case α = β = 0.

The ability to refract rays in different media is different. The more significantly the speeds of light in two media differ, the stronger the rays are refracted at the boundary between them.

One of the main parts of many optical instruments is a glass triangular prism (Fig. 87, a). Figure 87, b shows the path of the beam in such a prism: as a result of double refraction, the triangular prism deflects the beam incident on it to the side towards its base.

The refraction of light is the reason that the depth of a reservoir (river, pond, water bath) seems to us less than it really is. Indeed, in order to see any point S at the bottom of the reservoir, it is necessary that the rays of light coming out of it fall into the eye of the observer (Fig. 88). But after refraction at the border of water with air, the beam of light will be perceived by the eye as light coming from an imaginary image S 1 located higher than the corresponding point S at the bottom of the reservoir. It can be proved that the apparent depth h of a body of water is approximately ¾ of its true depth H.

This phenomenon was first described by Euclid. One of his books tells about the experience with the ring. The observer looks at the goblet with the ring lying at its bottom in such a way that the edges of the goblet do not allow him to be seen; then, without changing the position of the eyes, they begin to pour water into the goblet, and after a while the ring becomes visible.

The refraction of light also explains many other phenomena, for example, the apparent break of a spoon dipped into a glass of water; higher than the actual position of the stars and the Sun above the horizon, etc.

1. What is called the refraction of light? 2. What angle is called the angle of refraction? How is it designated? 3. What is the speed of light in vacuum? 4. Which medium is optically denser: ice or quartz? Why? 5. In what case is the angle of refraction of light less than the angle of incidence and in which more? 6. What is the angle of incidence of the beam if the refracted beam is perpendicular to the interface between the media? 7. Why does an observer looking down on the water, the depth of the reservoir seems less than it really is? What will the depth of the river appear to be if it is actually 2 m? 8. There are pieces of glass, quartz and diamond in the air. On which surface do light rays refract the most?

Experimental task. Repeat the experience of Euclid. Place a ring (or coin) on the bottom of a tea cup, then place it in front of you so that the edges of the cup cover its bottom. If, without changing the relative position of the cup and eyes, pour water into it, then the ring (or coin) becomes visible. Why?

At the boundary of the transition from one medium to another, if it is significantly longer than the wavelength, a change in the direction of the light rays is observed. In this case, part of the energy is reflected, that is, returned to the same medium, and part is refracted, penetrating into another medium. Using the laws of reflection and refraction of light, one can explain which direction the reflected and refracted rays have and what is the proportion of light energy that is reflected or transferred from one medium to another. In order for the phenomenon of reflection and refraction of light to occur, the body must be fairly smooth, not matte, and have a fairly uniform internal structure. An example of such a case would be the interface between water and air in a wide container. Polished metal bodies also have a mirror surface.

To understand the essence of these laws, you can conduct a simple experiment. A narrow stream of rays should be directed to water poured into a large vessel. It can be seen that part of the rays will be reflected on the surface, and the rest will go into the water. Moreover, we will see what happens refraction of light in water.

Law of reflection

The law of reflection determines the change in the direction of a beam of light when it meets a reflective surface. It consists in the fact that both the incident and the reflected beam are in the same plane with the perpendicular to the surface, and this perpendicular divides the angle between these rays into equal parts.

More often it is formulated as follows: the angle of incidence and light reflection angle are equal:

α=γ

This formulation is less accurate because it does not specify the exact direction of the beam reflection.

The law of reflection comes from the principles of wave optics. Experimentally, it was found by Euclid in the 3rd century BC. It can be considered a consequence of using Fermat's principle for a mirror surface.

Any medium has a certain degree of reflective and absorbing ability. The value that indicates the reflectivity of the surface is light reflectance. It determines what fraction of the energy brought to the surface is the energy that is carried away from it by reflected radiation. Its value depends on many factors, including the angle of incidence and the composition of the radiation.

As a result of the transition from a denser to a less optically dense medium (say, into air from glass), total reflection occurs, which means that the refracted beam disappears.

Total reflection is observed when rays fall on liquid mercury or silver deposited on glass.

This phenomenon occurs if the angle of incidence exceeds the limit angle of total light reflection αpr.

If a α = αpr, then sin β = 1, a sin αpr = n2/n1

When the second medium is air (i.e. n2 ≈ 1), this formula takes the following form:

sin αpr=1/n

The critical angle for the transition from glass to air is 42° (at n=1.5), for the transition from water to air - 48.7 ° (at n=1.33).

Total internal light reflection

In nature, examples of total reflection are various mirages and fata morgana. They arise as a result of reflection at the boundary of air layers with different temperatures. Besides, total reflection of light also explains the bright brilliance of precious stones, when each incoming ray forms many bright outgoing rays.

If, being under water, you look at the surface at a certain angle, you can see not what is in the air, but a mirror image of objects under water. This is another example of total internal reflection.

In the case when the angle of incidence on the boundary between two dielectric media is not equal to zero, both the reflected and refracted beams become partially polarized. Polarization of light upon reflection determined by its angle of incidence. The angle at which the reflected beam is completely polarized, and the refracted beam has the maximum possible degree of polarization, is called the Brewster angle.

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Laws of reflection and refraction of light photo

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• Incident angleα is the angle between the incident light beam and the perpendicular to the interface between two media, restored at the point of incidence (Fig. 1).

• Reflection angleβ is the angle between the reflected light beam and the perpendicular to the reflecting surface, restored at the point of incidence (see Fig. 1).

• refraction angleγ is the angle between the refracted beam of light and the perpendicular to the interface between two media, restored at the point of incidence (see Fig. 1).

• under the beam understand the line along which the energy of an electromagnetic wave is transferred. Let us agree to depict optical rays graphically using geometric rays with arrows. In geometric optics, the wave nature of light is not taken into account (see Fig. 1).

• Rays coming from one point are called divergent, and gathering at one point - converging. An example of divergent rays is the observed light of distant stars, and an example of converging rays is a set of rays that enter the pupil of our eye from various objects.

When studying the properties of light rays, four basic laws of geometric optics were experimentally established:

• the law of rectilinear propagation of light;
• the law of independence of light rays;
• law of reflection of light rays;
• law of refraction of light rays.

Light refraction

Measurements have shown that the speed of light in matter υ is always less than the speed of light in vacuum c.

• The ratio of the speed of light in vacuum c to its speed in a given medium υ is called absolute refractive index:

\(n=\frac(c)(\upsilon ).\)

The phrase " absolute refractive index of the medium" is often replaced by " refractive index of the medium».

Consider a beam incident on a flat interface between two transparent media with refractive indices n 1 and n 2 at some angle α (Fig. 2).

• The change in the direction of propagation of a beam of light when passing through the interface between two media is called refraction of light.

Laws of refraction:

• the ratio of the sine of the angle of incidence α to the sine of the angle of refraction γ is a constant value for two given media

\(\frac(sin \alpha )(sin \gamma )=\frac(n_2)(n_1).\)

• the rays, incident and refracted, lie in the same plane with the perpendicular drawn at the point of incidence of the ray to the plane of the interface between two media.

For refraction, principle of reversibility of light rays:

• a ray of light propagating along the path of a refracted ray, refracted at a point O at the interface between the media, propagates further along the path of the incident beam.

It follows from the law of refraction that if the second medium is optically denser through the first medium,

• those. n 2 > n 1 , then α > γ \(\left(\frac(n_2)(n_1) > 1, \;\;\; \frac(sin \alpha )(sin \gamma ) > 1 \right)\) (Fig. 3a);
• if n 2 < n 1 , then α< γ (рис. 3, б).

Rice. 3

The first mention of the refraction of light in water and glass is found in the work of Claudius Ptolemy "Optics", published in the II century AD. The law of light refraction was experimentally established in 1620 by the Dutch scientist Willebrod Snellius. Note that, independently of Snell, the law of refraction was also discovered by Rene Descartes.

The law of refraction of light allows you to calculate the path of rays in various optical systems.

At the interface between two transparent media, wave reflection is usually observed simultaneously with refraction. According to the law of conservation of energy, the sum of the energies of the reflected W o and refracted W np waves is equal to the energy of the incident wave W n:

W n = W np + W o.

total reflection

As mentioned above, when light passes from an optically denser medium to an optically less dense medium ( n 1 > n 2), the angle of refraction γ becomes larger than the angle of incidence α (see Fig. 3, b).

As the angle of incidence α increases (Fig. 4), at a certain value α 3 , the angle of refraction will become γ = 90°, i.e., the light will not enter the second medium. At angles large α 3 light will only be reflected. Refracted wave energy Wnp in this case, it will become equal to zero, and the energy of the reflected wave will be equal to the energy of the incident: W n = W o. Therefore, starting from this angle of incidence α 3 (hereinafter referred to as α 0), all light energy is reflected from the interface between these media.

This phenomenon is called total reflection (see Fig. 4).

• The angle α 0 at which total reflection begins is called limiting angle of total reflection.

The value of the angle α 0 is determined from the law of refraction, provided that the angle of refraction γ = 90°:

\(\sin \alpha_(0) = \frac(n_(2))(n_(1)) \;\;\; \left(n_(2)< n_{1} \right).\)

Literature

Zhilko, V.V. Physics: textbook. Allowance for grade 11 general education. school from Russian lang. training / V.V. Zhilko, L.G. Markovich. - Minsk: Nar. Asveta, 2009. - S. 91-96.

Laws of refraction of light.

The physical meaning of the refractive index. Light is refracted due to a change in the speed of its propagation when moving from one medium to another. The refractive index of the second medium relative to the first is numerically equal to the ratio of the speed of light in the first medium to the speed of light in the second medium:

Thus, the refractive index shows how many times the speed of light in the medium from which the beam exits is greater (less) than the speed of light in the medium into which it enters.

Since the speed of propagation of electromagnetic waves in vacuum is constant, it is advisable to determine the refractive indices of various media with respect to vacuum. Speed ​​ratio With propagation of light in a vacuum to the speed of its propagation in a given medium is called absolute refractive index given substance () and is the main characteristic of its optical properties,

,

those. the refractive index of the second medium relative to the first is equal to the ratio of the absolute indices of these media.

Usually, the optical properties of a substance are characterized by the refractive index n relative to air, which differs little from the absolute refractive index. In this case, the medium, in which the absolute index is greater, is called optically denser.

Limiting angle of refraction. If light passes from a medium with a lower refractive index to a medium with a higher refractive index ( n 1< n 2 ), then the angle of refraction is less than the angle of incidence

r< i (Fig. 3).

Rice. 3. Refraction of light during the transition

from optically less dense medium to medium

optically denser.

As the angle of incidence increases to i m = 90° (beam 3, Fig. 2) light in the second medium will propagate only within the angle r pr called limiting angle of refraction. In the region of the second medium within an angle additional to the limiting angle of refraction (90° - i pr ), no light penetrates (this area is shaded in Fig. 3).

Limit angle of refraction r pr

But sin i m = 1, therefore .

The phenomenon of total internal reflection. When light passes from a medium with a high refractive index n 1 > n 2 (Fig. 4), then the angle of refraction is greater than the angle of incidence. Light is refracted (passes into the second medium) only within the angle of incidence i pr , which corresponds to the angle of refraction rm = 90°.

Rice. 4. Refraction of light during the transition from an optically denser medium to a medium

less optically dense.

Light incident at a large angle is completely reflected from the boundary of the media (Fig. 4 beam 3). This phenomenon is called total internal reflection, and the angle of incidence i pr is the limiting angle of total internal reflection.

Limiting angle of total internal reflection i pr determined according to the condition:

, then sin r m =1, therefore, .

If light travels from any medium into a vacuum or into air, then

Due to the reversibility of the path of rays for these two media, the limiting angle of refraction in the transition from the first medium to the second is equal to the limiting angle of total internal reflection when the beam passes from the second medium to the first.

The limiting angle of total internal reflection for glass is less than 42°. Therefore, rays traveling through glass and incident on its surface at an angle of 45° are completely reflected. This property of glass is used in rotary (Fig. 5a) and reversible (Fig. 4b) prisms, which are often used in optical instruments.

Rice. 5: a – rotary prism; b - reverse prism.

fiber optics. Total internal reflection is used in the construction of flexible light guides. Light, getting inside a transparent fiber surrounded by a substance with a lower refractive index, is reflected many times and propagates along this fiber (Fig. 6).

Fig.6. The passage of light inside a transparent fiber surrounded by matter

with a lower refractive index.

To transmit high light fluxes and maintain the flexibility of the light guide system, individual fibers are assembled into bundles - light guides. The branch of optics that deals with the transmission of light and images through light guides is called fiber optics. The same term refers to the fiber-optic parts and devices themselves. In medicine, light guides are used to illuminate internal cavities with cold light and transmit images.

Practical part

Instruments for determining the refractive index of substances are called refractometers(Fig. 7).

Fig.7. Optical scheme of the refractometer.

1 - mirror, 2 - measuring head, 3 - system of prisms to eliminate dispersion, 4 - lens, 5 - rotary prism (beam rotation by 90 0), 6 - scale (in some refractometers

there are two scales: the scale of refractive indices and the scale of the concentration of solutions),

7 - eyepiece.

The main part of the refractometer is a measuring head, consisting of two prisms: an illuminating one, which is located in the folding part of the head, and a measuring one.

At the exit of the illuminating prism, its matte surface creates a scattered beam of light that passes through the test liquid (2-3 drops) between the prisms. Rays fall on the surface of the measuring prism at different angles, including at an angle of 90 0 . In the measuring prism, the rays are collected in the region of the limiting angle of refraction, which explains the formation of a light-shadow boundary on the device screen.

Fig.8. Beam path in the measuring head:

1 – illuminating prism, 2 – investigated liquid,

3 - measuring prism, 4 - screen.

DETERMINATION OF THE PERCENTAGE OF SUGAR IN SOLUTION

Natural and polarized light. visible light- this is electromagnetic waves with an oscillation frequency in the range from 4∙10 14 to 7.5∙10 14 Hz. Electromagnetic waves are transverse: the vectors E and H of the strengths of the electric and magnetic fields are mutually perpendicular and lie in a plane perpendicular to the wave propagation velocity vector.

Due to the fact that both the chemical and biological effects of light are mainly associated with the electrical component of the electromagnetic wave, the vector E the intensity of this field is called light vector, and the plane of oscillations of this vector is the plane of oscillation of the light wave.

In any light source, waves are emitted by many atoms and molecules, the light vectors of these waves are located in various planes, and the oscillations occur in different phases. Consequently, the plane of oscillations of the light vector of the resulting wave continuously changes its position in space (Fig. 1). This light is called natural, or unpolarized.

Rice. 1. Schematic representation of a beam and natural light.

If we choose two mutually perpendicular planes passing through a beam of natural light and project the vectors E on the plane, then on average these projections will be the same. Thus, it is convenient to depict a ray of natural light as a straight line on which the same number of both projections are located in the form of dashes and dots:

When light passes through crystals, it is possible to obtain light whose wave oscillation plane occupies a constant position in space. This light is called flat- or linearly polarized. Due to the orderly arrangement of atoms and molecules in a spatial lattice, the crystal transmits only light vector oscillations that occur in a certain plane characteristic of a given lattice.

A plane polarized light wave is conveniently depicted as follows:

The polarization of light can also be partial. In this case, the amplitude of oscillations of the light vector in any one plane significantly exceeds the amplitudes of oscillations in other planes.

Partially polarized light can be conventionally depicted as follows: , etc. The ratio of the number of dashes and dots determines the degree of light polarization.

In all methods of converting natural light into polarized light, components with a well-defined orientation of the polarization plane are completely or partially selected from natural light.

Methods for obtaining polarized light: a) reflection and refraction of light at the boundary of two dielectrics; b) transmission of light through optically anisotropic uniaxial crystals; c) the transmission of light through media, the optical anisotropy of which is artificially created by the action of an electric or magnetic field, as well as due to deformation. These methods are based on the phenomenon anisotropy.

Anisotropy is the dependence of a number of properties (mechanical, thermal, electrical, optical) on the direction. Bodies whose properties are the same in all directions are called isotropic.

Polarization is also observed during light scattering. The degree of polarization is the higher, the smaller the size of the particles on which scattering occurs.

Devices designed to produce polarized light are called polarizers.

Polarization of light during reflection and refraction at the interface between two dielectrics. When natural light is reflected and refracted at the interface between two isotropic dielectrics, its linear polarization occurs. At an arbitrary angle of incidence, the polarization of the reflected light is partial. The reflected beam is dominated by oscillations perpendicular to the plane of incidence, while the refracted beam is dominated by oscillations parallel to it (Fig. 2).

Rice. 2. Partial polarization of natural light during reflection and refraction

If the angle of incidence satisfies the condition tg i B = n 21, then the reflected light is completely polarized (Brewster's law), and the refracted beam is polarized not completely, but maximally (Fig. 3). In this case, the reflected and refracted rays are mutually perpendicular.

is the relative refractive index of the two media, i B is the Brewster angle.

Rice. 3. Total polarization of the reflected beam during reflection and refraction

at the interface between two isotropic dielectrics.

Double refraction. There are a number of crystals (calcite, quartz, etc.) in which a beam of light, being refracted, splits into two beams with different properties. Calcite (Icelandic spar) is a crystal with a hexagonal lattice. The axis of symmetry of the hexagonal prism that forms its cell is called the optical axis. The optical axis is not a line, but a direction in the crystal. Any line parallel to this direction is also an optical axis.

If a plate is cut out of a calcite crystal so that its faces are perpendicular to the optical axis, and a beam of light is directed along the optical axis, then no changes will occur in it. If, however, the beam is directed at an angle to the optical axis, then it will be divided into two beams (Fig. 4), of which one is called ordinary, the second - extraordinary.

Rice. 4. Birefringence when light passes through a plate of calcite.

MN is the optical axis.

An ordinary beam lies in the plane of incidence and has the usual refractive index for a given substance. The extraordinary beam lies in a plane passing through the incident beam and the optical axis of the crystal, drawn at the point of incidence of the beam. This plane is called principal plane of the crystal. The refractive indices for ordinary and extraordinary beams are different.

Both ordinary and extraordinary rays are polarized. The plane of oscillation of ordinary rays is perpendicular to the principal plane. The oscillations of the extraordinary rays occur in the main plane of the crystal.

The phenomenon of birefringence is due to the anisotropy of crystals. Along the optical axis, the speed of a light wave for ordinary and extraordinary rays is the same. In other directions, the velocity of an extraordinary wave in calcite is greater than that of an ordinary one. The greatest difference between the velocities of both waves occurs in the direction perpendicular to the optical axis.

According to the Huygens principle, with birefringence at each point of the surface of a wave reaching the crystal boundary, two elementary waves simultaneously arise (not one, as in ordinary media), which propagate in the crystal.

The propagation speed of one wave in all directions is the same, i.e. wave has a spherical shape and is called ordinary. The speed of propagation of another wave in the direction of the optical axis of the crystal is the same as the speed of an ordinary wave, and in the direction perpendicular to the optical axis, it differs from it. The wave has an ellipsoid shape and is called extraordinary(Fig.5).

Rice. 5. Propagation of an ordinary (o) and extraordinary (e) wave in a crystal

with double refraction.

Prism Nicholas. To obtain polarized light, a Nicol polarizing prism is used. A prism of a certain shape and size is cut out of calcite, then it is sawn along a diagonal plane and glued with Canadian balsam. When a light beam is incident on the upper face along the prism axis (Fig. 6), the extraordinary beam is incident on the gluing plane at a smaller angle and passes through almost without changing direction. An ordinary beam falls at an angle greater than the angle of total reflection for Canadian balsam, is reflected from the gluing plane and absorbed by the blackened face of the prism. The Nicol prism produces fully polarized light, the plane of oscillation of which lies in the principal plane of the prism.

Rice. 6. Nicolas prism. Scheme of the passage of an ordinary

and extraordinary rays.

Dichroism. There are crystals that absorb ordinary and extraordinary rays in different ways. So, if a natural light beam is directed to a tourmaline crystal perpendicular to the direction of the optical axis, then with a plate thickness of only a few millimeters, the ordinary beam will be completely absorbed, and only the extraordinary beam will come out of the crystal (Fig. 7).

Rice. 7. Passage of light through a tourmaline crystal.

The different nature of the absorption of ordinary and extraordinary rays is called absorption anisotropy, or dichroism. Thus, tourmaline crystals can also be used as polarizers.

Polaroids. Currently, polarizers are widely used. polaroids. To make a polaroid, a transparent film is glued between two plates of glass or plexiglass, which contains crystals of a dichroic substance polarizing light (for example, iodoquinone sulfate). During the film manufacturing process, the crystals are oriented so that their optical axes are parallel. The whole system is fixed in a frame.

The low cost of polaroids and the possibility of manufacturing plates with a large area ensured their wide application in practice.

Analysis of polarized light. To study the nature and degree of polarization of light, devices called analyzers. As analyzers, the same devices are used that serve to obtain linearly polarized light - polarizers, but adapted for rotation around the longitudinal axis. The analyzer passes only vibrations that coincide with its main plane. Otherwise, only the oscillation component that coincides with this plane passes through the analyzer.

If the light wave entering the analyzer is linearly polarized, then the intensity of the wave leaving the analyzer satisfies Malus' law:

,

where I 0 is the intensity of the incoming light, φ is the angle between the planes of the incoming light and the light transmitted by the analyzer.

The passage of light through the polarizer-analyzer system is shown schematically in fig. eight.

Rice. Fig. 8. Scheme of the passage of light through the polarizer-analyzer system (P - polarizer,

A - analyzer, E - screen):

a) the main planes of the polarizer and analyzer coincide;

b) the main planes of the polarizer and analyzer are located at a certain angle;

c) the main planes of the polarizer and analyzer are mutually perpendicular.

If the main planes of the polarizer and analyzer coincide, then the light completely passes through the analyzer and illuminates the screen (Fig. 7a). If they are located at a certain angle, the light passes through the analyzer, but is attenuated (Fig. 7b) the more, the closer this angle is to 90 0 . If these planes are mutually perpendicular, then the light is completely extinguished by the analyzer (Fig. 7c)

Rotation of the plane of oscillation of polarized light. Polarimetry. Some crystals, as well as solutions of organic substances, have the ability to rotate the plane of oscillations of polarized light passing through them. These substances are called optically a active. These include sugars, acids, alkaloids, etc.

For the majority of optically active substances, the existence of two modifications was found that rotates the plane of polarization clockwise and counterclockwise, respectively (for an observer looking towards the beam). The first modification is called dextrorotatory, or positive second - levorotary, or negative.

The natural optical activity of a substance in a non-crystalline state is due to the asymmetry of the molecules. In crystalline substances, optical activity can also be due to the peculiarities of the arrangement of molecules in the lattice.

In solids, the angle φ of rotation of the plane of polarization is directly proportional to the length d of the path of the light beam in the body:

where α is rotational ability (specific rotation), depending on the type of substance, temperature and wavelength. For left- and right-rotation modifications, the rotational abilities are the same in magnitude.

For solutions, the angle of rotation of the polarization plane

,

where α is the specific rotation, c is the concentration of the optically active substance in the solution. The value of α depends on the nature of the optically active substance and solvent, temperature and wavelength of light. Specific rotation- this is a 100 times increased rotation angle for a solution 1 dm thick at a substance concentration of 1 gram per 100 cm 3 of solution at a temperature of 20 0 C and at a wavelength of light λ=589 nm. A very sensitive method for determining the concentration c, based on this ratio, is called polarimetry (saccharimetry).

The dependence of the rotation of the polarization plane on the wavelength of light is called rotational dispersion. In the first approximation, there is Bio's Law:

where A is a coefficient depending on the nature of the substance and temperature.

In a clinical setting, the method polarimetry used to determine the concentration of sugar in the urine. The device used for this is called saccharimeter(Fig. 9).

Rice. 9. Optical layout of the saccharimeter:

And - a source of natural light;

C - light filter (monochromator), which ensures the coordination of the device operation

with Biot's law;

L is a converging lens that gives a parallel beam of light at the output;

P - polarizer;

K – tube with test solution;

A - analyzer mounted on a rotating disk D with divisions.

When conducting a study, the analyzer is first set to the maximum darkening of the field of view without the test solution. Then a tube with a solution is placed in the device and, rotating the analyzer, the field of view is darkened again. The smaller of the two angles through which the analyzer must be rotated is the angle of rotation for the analyte. The angle is used to calculate the concentration of sugar in the solution.

To simplify the calculations, the tube with the solution is made so long that the angle of rotation of the analyzer (in degrees) is numerically equal to the concentration With solution (in grams per 100 cm 3). The length of the tube for glucose is 19 cm.

polarizing microscopy. The method is based on anisotropy some components of cells and tissues that appear when they are observed in polarized light. Structures consisting of molecules arranged in parallel, or disks arranged in the form of a stack, when introduced into a medium with a refractive index that differs from the refractive index of the particles of the structure, exhibit the ability to double refraction. This means that the structure will only transmit polarized light if the plane of polarization is parallel to the long axes of the particles. This remains valid even when the particles do not have their own birefringence. Optical anisotropy observed in muscle, connective tissue (collagen) and nerve fibers.

The very name of skeletal muscle striated" due to the difference in the optical properties of individual sections of the muscle fiber. It consists of alternating darker and lighter areas of the tissue substance. This gives the fiber a transverse striation. The study of the muscle fiber in polarized light reveals that the darker areas are anisotropic and have properties birefringence, while the darker areas are isotropic. Collagen fibers are anisotropic, their optical axis is located along the fiber axis. Micelles in pulp neurofibrils are also anisotropic, but their optical axes are located in radial directions. A polarizing microscope is used for histological examination of these structures.

The most important component of a polarizing microscope is the polarizer, which is located between the light source and the capacitor. In addition, the microscope has a rotating stage or sample holder, an analyzer located between the objective and the eyepiece, which can be installed so that its axis is perpendicular to the polarizer axis, and a compensator.

When the polarizer and analyzer are crossed and the object is missing or isotropic the field appears uniformly dark. If there is an object with birefringence, and it is located so that its axis is at an angle to the plane of polarization, different from 0 0 or from 90 0 , it will divide the polarized light into two components - parallel and perpendicular to the plane of the analyzer. Consequently, some of the light will pass through the analyzer, resulting in a bright image of the object against a dark background. When the object rotates, the brightness of its image will change, reaching a maximum at an angle of 45 0 relative to the polarizer or analyzer.

Polarizing microscopy is used to study the orientation of molecules in biological structures (e.g. muscle cells), as well as during the observation of structures invisible by other methods (e.g. the mitotic spindle during cell division), identification of the helical structure.

Polarized light is used in model conditions to assess the mechanical stresses that occur in bone tissues. This method is based on the phenomenon of photoelasticity, which consists in the appearance of optical anisotropy in initially isotropic solids under the action of mechanical loads.

DETERMINATION OF THE LIGHT WAVE LENGTH USING A DIFFRACTION GRATING

Light interference. Light interference is a phenomenon that occurs when light waves are superimposed and is accompanied by their amplification or attenuation. A stable interference pattern arises when coherent waves are superimposed. Coherent waves are called waves with equal frequencies and the same phases or having a constant phase shift. Amplification of light waves during interference (maximum condition) occurs if Δ fits an even number of half-wavelengths:

where k – maximum order, k=0,±1,±2,±,…±n;

λ is the length of the light wave.

Weakening of light waves during interference (minimum condition) is observed if an odd number of half-wavelengths fit into the optical path difference Δ:

where k is the order of the minimum.

The optical path difference of two beams is the difference in distances from the sources to the point of observation of the interference pattern.

Interference in thin films. Interference in thin films can be observed in soap bubbles, in a spot of kerosene on the surface of water when illuminated by sunlight.

Let beam 1 fall on the surface of a thin film (see Fig. 2). The beam, refracted at the air-film interface, passes through the film, is reflected from its inner surface, approaches the outer surface of the film, is refracted at the film-air interface, and the beam emerges. We direct beam 2 to the beam exit point, which passes parallel to beam 1. Beam 2 is reflected from the surface of the film , superimposed on beam , and both beams interfere.

When illuminating the film with polychromatic light, we get a rainbow picture. This is due to the fact that the film is not uniform in thickness. Consequently, path differences of various magnitudes arise, which correspond to different wavelengths (colored soap films, iridescent colors of the wings of some insects and birds, films of oil or oils on the surface of water, etc.).

Light interference is used in devices - interferometers. Interferometers are optical devices that can be used to spatially separate two beams and create a certain path difference between them. Interferometers are used to determine the wavelength with a high degree of accuracy of small distances, the refractive indices of substances and determine the quality of optical surfaces.

For sanitary and hygienic purposes, the interferometer is used to determine the content of harmful gases.

The combination of an interferometer and a microscope (interference microscope) is used in biology to measure the refractive index, dry matter concentration, and thickness of transparent micro-objects.

Huygens-Fresnel principle. According to Huygens, each point of the medium, to which the primary wave reaches at a given moment, is a source of secondary waves. Fresnel refined this position of Huygens by adding that the secondary waves are coherent, i.e. when superimposed, they will give a stable interference pattern.

Diffraction of light. Diffraction of light is the phenomenon of deviation of light from rectilinear propagation.

Diffraction in parallel beams from one slit. Let on the target wide in a parallel beam of monochromatic light falls (see Fig. 3):

A lens is installed in the path of the rays L , in the focal plane of which the screen is located E . Most beams do not diffract; do not change their direction, and they are focused by the lens L in the center of the screen, forming a central maximum or zero-order maximum. Rays diffracting at equal diffraction angles φ , will form maxima on the screen 1,2,3,…, n - orders.

Thus, the diffraction pattern obtained from one slit in parallel beams when illuminated with monochromatic light is a bright stripe with maximum illumination in the center of the screen, then comes a dark stripe (minimum of the 1st order), then comes a bright stripe (maximum of the 1st order). order), dark band (minimum of the 2nd order), maximum of the 2nd order, etc. The diffraction pattern is symmetrical with respect to the central maximum. When the slit is illuminated with white light, a system of colored bands is formed on the screen, only the central maximum will retain the color of the incident light.

Terms max and min diffraction. If in the optical path difference Δ fit an odd number of segments equal to , then there is an increase in light intensity ( max diffraction):

where k is the order of the maximum; k =±1,±2,±…,± n;

λ is the wavelength.

If in the optical path difference Δ fit an even number of segments equal to , then there is a weakening of the light intensity ( min diffraction):

where k is the order of the minimum.

Diffraction grating. A diffraction grating consists of alternating bands that are opaque to the passage of light with bands (slits) that are transparent to light and of equal width.

The main characteristic of a diffraction grating is its period d . the period of the diffraction grating is the total width of the transparent and opaque bands:

A diffraction grating is used in optical instruments to enhance the resolution of the instrument. The resolution of a diffraction grating depends on the order of the spectrum k and on the number of strokes N :

where R - resolution.

Derivation of the diffraction grating formula. Let us direct two parallel beams onto the diffraction grating: 1 and 2 so that the distance between them is equal to the grating period d .

At points BUT and AT beams 1 and 2 diffract, deviating from the rectilinear direction at an angle φ is the diffraction angle.

Rays and focused by lens L onto a screen located in the focal plane of the lens (Fig. 5). Each slit of the grating can be considered as a source of secondary waves (the Huygens-Fresnel principle). On the screen at point D, we observe the maximum of the interference pattern.

From a point BUT on the path of the beam drop the perpendicular and get point C. consider a triangle ABC : right triangle РВАС=Рφ as angles with mutually perpendicular sides. From Δ ABC:

where AB=d (by construction),

SW = ∆ is the optical path difference.

Since at point D we observe max interference, then

where k is the order of the maximum,

λ is the length of the light wave.

Plugging in the values AB=d, into the formula for sinφ :

From here we get:

In general, the diffraction grating formula has the form:

The ± signs show that the interference pattern on the screen is symmetrical with respect to the central maximum.

Physical foundations of holography. Holography is a method of recording and reconstructing a wave field, which is based on the phenomena of wave diffraction and interference. If only the intensity of the waves reflected from the object is recorded on a regular photograph, then the phases of the waves are additionally recorded on the hologram, which provides additional information about the object and makes it possible to obtain a three-dimensional image of the object.