INTERFERENCE OF POLARIZED RAYS- a phenomenon that occurs when adding coherent polarized light vibrations (see. Light polarization).AND. p. l. studied in the classical experiments of O. Fresnel (A. Fresnel) and D. F. Arago (D. F. Arago) (1816). Naib, interference contrast. The pattern is observed when adding coherent oscillations of one type of polarization (linear, circular, elliptical) with coinciding azimuths. Interference is never observed if the waves are polarized in mutually perpendicular planes. When two linearly polarized mutually perpendicular oscillations are added, in the general case, an elliptically polarized oscillation arises, the intensity of which is equal to the sum of the intensities of the initial oscillations. I. p. l. can be observed, for example, when linearly polarized light passes through anisotropic media. Passing through such a medium, the polarized oscillation is divided into two coherent elementary orthogonal oscillations propagating with decomp. speed. Next, one of these oscillations is converted to orthogonal (in order to obtain coinciding azimuths) or components of the same type of polarization with coinciding azimuths are separated from both oscillations. Scheme of observation I. p. l. in parallel beams is given in fig. one, a. A beam of parallel rays leaves the polarizer N 1 linearly polarized in the direction N 1 N 1 (Fig. 1, b). In a record To, cut from a birefringent uniaxial crystal parallel to its optical. axes OO and located perpendicular to the incident rays, the oscillations are separated N 1 N 1 into components A e, parallel to the optical axis (extraordinary), and A 0 perpendicular to the optical. axis (ordinary). To increase the contrast of interference. pattern angle between N 1 N 1 and BUT 0 is set equal to 45°, due to which the oscillation amplitudes A e and BUT 0 are equal. The refractive indices n e and n 0 for these two beams are different, and therefore their velocities are also different.
Rice. 1. Observation of the interference of polarized beams in parallel beams: a - diagram; b- determination of the oscillation amplitudes corresponding to the scheme a.
distribution in To, as a result of which at the exit of the plate To between them there is a phase difference d=(2p/l)(n 0 -n e), where l is the thickness of the plate, l is the wavelength of the incident light. Analyzer N 2 from each beam A e and BUT 0 transmits only components with vibrations parallel to its direction of transmission N 2 N 2. If Ch. the cross sections of the polarizer and analyzer are crossed ( N 1 ^N 2 ) , then the amplitudes of the terms BUT 1 and BUT 2 are equal, and the phase difference between them is D=d+p. Because these components are coherent and linearly polarized in the same direction, they interfere. Depending on the value of D per to-l. section of the plate, the observer sees this section as dark or light (d \u003d 2kpl) in monochromatic. light and differently colored in white light (the so-called chromatic polarization). If the plate is inhomogeneous in thickness or refractive index, then its places with the same these parameters will be respectively equally dark or equally light (or equally colored in white light). Curves of the same color are called. isochromes. An example of an observation scheme I. p. l. in converging moons is shown in Fig. 2. A converging plane-polarized beam of rays from a lens L 1 falls on a plate cut from a uniaxial crystal perpendicular to its optical. axes. In this case, rays of different inclinations pass different paths in the plate, and the ordinary and extraordinary rays acquire a path difference D=(2p l/lcosy)(n 0 -n e), where y is the angle between the direction of propagation of rays and the normal to the surface of the crystal. The interference observed in this case. the picture is given in fig. 1, and to Art. conoscopic figures. Points corresponding to the same phase differences D,
Rice. 2. Scheme for observing the interference of polarized beams in converging beams: N 1 - polarizer; N 2, - analyzer, To- plate thickness l, cut from a uniaxial birefringent crystal; L 1 , L 2 - lenses.
arranged in a concentric circle (dark or light, depending on D). Rays included in To with fluctuations parallel to Ch. plane or perpendicular to it, are not divided into two components and for N 2 ^N 1 will not be missed by the analyzer N 2. In these planes you get a dark cross. If a N 2 ||N 1 , the cross will be light. I. p. l. applied in
If the crystal is positive, then the front of the ordinary wave is ahead of the front of the extraordinary wave. As a result, a certain path difference arises between them. At the output of the plate, the phase difference is equal to: 
, where is the phase difference between the ordinary and extraordinary waves at the moment of incidence on the plate. Consider. some of the most interesting cases by setting=0. 1. Ra the difference between the ordinary and extraordinary waves, created by the plate, satisfies the condition - the plate is a quarter of the wavelength. At the output of the plate, the phase difference (up to) is equal. Let the vector E be directed at an angle a to one of the ch. directions parallel to the optical axis of the plate 00". If the amplitude of the incident wave E, then it can be decomposed into two components: ordinary and extraordinary. The amplitude of the ordinary wave: extraordinary. After leaving the plate, two waves, adding up in the case, give elliptical polarization. The ratio of the axes will be depend on the angle α In particular, if α = 45 and the amplitude of the ordinary and extraordinary waves is the same, then the light will be circularly polarized at the exit from the plate. Using a plate of 0.25λ, you can also perform the inverse operation: turn elliptically or circularly polarized light into linearly polarized.If the optical axis of the plate coincides with one of the axes of the polarization ellipse, then at the moment the light hits the plate, the phase difference (up to a value that is a multiple of 2π) is equal to zero or π. In this case, the ordinary and extraordinary waves add up to give linearly polarized light. 2.
The thickness of the plate is such that the path difference and the phase shift created by it will be respectively equal to and 
. In this case, the light leaving the plate remains linearly polarized, but the polarization plane rotates counterclockwise by an angle of 2α, if you look towards the beam. 3.
for a plate of a whole wavelength, the path difference The emerging light in this case remains linearly polarized, and the oscillation plane does not change its direction for any orientation of the plate. Analysis polarization states. Polarizers and crystal plates are also used to analyze the state of polarization. Light of any polarization can always be represented as a superposition of two light streams, one of which is polarized elliptically (in a particular case, linearly or circularly), and the other is natural. Analysis of the state of polarization is reduced to revealing the relationship between the intensities of the polarized and non-polarized components and determining the semi-axes of the ellipse. At the first stage, the analysis is carried out using a single polarizer. As it rotates, the intensity changes from some maximum I max to a minimum value I min . Since, in accordance with the Malus law, light does not pass through a polarizer if the transmission plane of the latter is perpendicular to the light vector, then, if I min = 0, we can conclude that the light has a linear polarization. At I max = I min (regardless of the position, the analyzer transmits half of the light flux incident on it), the light is natural or circularly polarized, and when 
it is partially or elliptically polarized. The positions of the analyzer corresponding to the maximum or minimum of the transmission differ by 90° and determine the position of the semi-axes of the ellipse of the polarized component of the light flux. The second stage of analysis is carried out using a plate and analyzer. The plate is positioned so that the polarized component of the light flux at its output has a linear polarization. To do this, the optical axis of the plate is oriented in the direction of one of the axes of the ellipse of the polarized component. (For I max, the orientation of the optical axis of the plate does not matter). Since natural light does not change the state of polarization when passing through the plate, a mixture of linearly polarized and natural light generally leaves the plate. Then this light is analyzed, as in the first stage, using an analyzer.
6,10 Propagation of light in an optically inhomogeneous medium. The nature of scattering processes. Rayleigh and Mie scattering, Raman scattering of light. Scattering of light consists in the fact that a light wave passing through a substance causes oscillations of electrons in atoms (molecules). These electrons excite secondary waves propagating in all directions. In this case, the secondary waves turn out to be coherent with each other and therefore interfere. Theoretical calculation: in the case of a homogeneous medium, the secondary waves completely cancel each other in all directions, except for the direction of propagation of the primary wave. By virtue of this redistribution of light in directions, i.e., light scattering in a homogeneous medium, does not occur. In the case of an inhomogeneous medium, light waves, diffracting on small inhomogeneities of the medium, give a diffraction pattern in the form of a fairly uniform intensity distribution in all directions. This phenomenon is called light scattering. The trick of these media: the content of small particles, the refractive index of which differs from the environment. In light passing through a thick layer of a turbid medium, the long-wavelength part of the spectrum predominates, and the medium appears reddish short-wavelength and the medium appears blue. Reason: electrons making forced oscillations in atoms of an electrically isotropic particle of small size () are equivalent to one oscillating dipole. This dipole oscillates with the frequency of the light wave incident on it and the intensity of the light emitted by it. - Mr. Rayleigh. That is, the short-wave part of the spectrum is scattered much more intensively than the long-wave part. Blue light, which is about 1.5 times the frequency of red light, scatters about 5 times more intensely than red light. This explains the blue color of scattered light and the reddish color of transmitted light. Mi Scattering. Rayleigh's theory correctly describes the basic patterns of light scattering by molecules and also by small particles, the size of which is much smaller than the wavelength (and<λ/15). При рассеянии света на более крупных частицах наблюдаются значительные расхождения с рассмотренной теорией. Строгое описание рассеяния света малыми частицами произвольной формы, размеров и диэлектрических свойств представляет сложную математическую задачу. В соответствии с теорией Ми характер рассеяния зависит от приведенного радиуса частицы . Интенсивность рассеяния зависит от флуктуаций величины ε, которые будут особенно большими в разреженных газах. В жидкостях флуктуации заметными вблизи фазовых переходов. Причиной сильного рассеяния света являются флуктуации плотности, которые из-за неограниченного возрастания сжимаемости веществавблизи критической точки становятся большими.Raman scattering of light. - inelastic scattering. Raman scattering is caused by a change in the dipole moment of the molecules of the medium under the action of the field of the incident wave E. The induced dipole moment of the molecules is determined by the polarizability of the molecules and the strength of the wave.
The phenomena of interference of polarized rays were studied in the classical experiments of Fresnel and Argo (1816), who proved the transverse nature of light vibrations. Their essence depends on the result of interference on the angle between the planes of light vibrations: the bands are most contrasting with parallel planes and disappear if the waves are polarized orthogonally. The difficulty in obtaining interference of polarized waves lies in the fact that when two coherent beams polarized in mutually perpendicular directions are superimposed, no interference pattern with intensity maxima and minima can be obtained. Interference occurs only if the oscillations in the interacting beams occur along the same direction. Oscillations in two beams, initially polarized in mutually perpendicular directions, can be reduced to one plane by passing these beams through a polarizing crystal plate.
Consider the scheme for obtaining the interference of polarized rays (Fig. 11.13).
Rice. 11.13
The radiation of a point source S that has passed through the polarizer P falls on a half-wave crystal plate Q, which allows you to change the angle between the polarization planes of the interfering rays: its rotation by an angle α rotates the vector by 2α. If the interference fringes are observed through the analyzer A, then when it is rotated by π/2, the picture observed on the screen E is inverted: due to the additional phase difference π, the dark fringes become light and vice versa. The analyzer is also needed here in order to bring the oscillations of two differently polarized beams into one plane.
when polarized light passes through a crystal plate, the path difference between the two polarization components depends on the thickness of the plate, the average angle of refraction, and the difference between the indices and . Obviously, the resulting phase difference
Rotation of the plane of polarization.
Rotation of the plane of polarization transverse wave - a physical phenomenon consisting in the rotation of the polarization vector of a linearly polarized transverse wave around its wave vector when the wave passes through an anisotropic medium. The wave can be electromagnetic, acoustic, gravitational, etc.
A linearly polarized shear wave can be described as a superposition of two circularly polarized waves with the same wave vector and amplitude. In an isotropic medium, the projections of the field vector of these two waves onto the plane of polarization oscillate in phase, their sum is equal to the field vector of the total linearly polarized wave. If the phase velocity of circularly polarized waves in the medium is different (circular anisotropy of the medium, see also double refraction), then one of the waves lags behind the other, which leads to the appearance of a phase difference between the oscillations of the indicated projections on the selected plane. This phase difference changes as the wave propagates (in a homogeneous medium, it grows linearly). If you rotate the plane of polarization around the wave vector by an angle equal to half the phase difference, then the oscillations of the projections of the field vectors on it will again be in phase - the rotated plane will be the plane of polarization at a given moment.
Rotation of the plane of polarization of an electromagnetic wave in a plasma when a magnetic field is applied (Faraday effect).
Thus, the direct cause of the rotation of the polarization plane is the incursion of the phase difference between the circularly polarized components of a linearly polarized wave as it propagates in a circularly anisotropic medium. For electromagnetic oscillations, such a medium is called optically active (or gyrotropic).
), for elastic transverse waves - acoustically active. There is also a rotation of the plane of polarization at reflection from an anisotropic medium (see, for example, magneto-optical Kerr effect).The circular anisotropy of a medium (and, accordingly, the rotation of the plane of polarization of a wave propagating in it) may depend on external fields (electric, magnetic) imposed on the medium and on mechanical stresses (see Photoelasticity
). In addition, the degree of anisotropy and the phase shift, generally speaking, can depend on the wavelength (dispersion). The angle of rotation of the polarization plane depends linearly, other things being equal, on the wavelength in the active medium. An optically active medium, consisting of a mixture of active and inactive molecules, rotates the plane of polarization in proportion to the concentration of an optically active substance, on which the polarimetric method for measuring the concentration of such substances in solutions is based; the proportionality coefficient relating the rotation of the polarization plane to the beam length and the concentration of the substance is called the specific rotation of the given substance.
In the case of acoustic vibrations, the rotation of the plane of polarization is observed only for transverse elastic waves (since the plane of polarization is not defined for longitudinal waves) and, therefore, can occur only in solids, but not in liquids or gases.
The general theory of relativity predicts the rotation of the plane of polarization of a light wave in a vacuum during the propagation of a light wave in space with certain types of metrics due to the parallel transfer of the polarization vector along the zero geodesic - the trajectory of the light beam (the gravitational Faraday effect, or the Rytov-Skrotsky effect)
The effect of rotation of the plane of polarization of light is used
§ to determine the concentration of optically active substances in solutions (see, for example, Saccharimetry
§ to study mechanical stresses in transparent bodies;
§ to manage transparency liquid crystal layer in liquid crystal indicators(the circular anisotropy of the LC depends on the applied electric field).
An important case I. s. - interference of polarized rays (see Polarization of light). In the general case, when two differently polarized coherent light waves are added, their amplitudes are vector-added, which leads to elliptical polarization. This phenomenon is observed, for example, when linearly polarized light passes through anisotropic media. Getting into such a medium, a linearly polarized beam is divided into 2 coherent, polarized in mutually perpendicular beam planes. Due to the different state of polarization, the speed of their propagation in this medium is different and a phase difference arises between them, depending on the distance traveled in the substance. The value of will determine the state of elliptical polarization; in particular, at equal to an integer number of half-waves, the polarization will be linear.
The interference of polarized rays is widely used in crystal optics to determine the structure and orientation of crystal axes, in mineralogy to determine minerals and rocks, to detect and study stresses and strains in solids, to create very narrow-band optical filters, etc.
The optical axis of the crystal.
Optical axis of a crystal, the direction in a crystal in which light propagates without undergoing birefringence.
The main section of the crystal.
The main section of the crystal is a plane formed by the direction of propagation of the incident light and the direction of the optical axis of the crystal.
Optically active substances.
Optically active substances, media with natural optical activity. O.-a. in. are divided into 2 types. Related to the 1st of them are optically active in any state of aggregation (sugar, camphor, tartaric acid), to the 2nd - they are active only in the crystalline phase (quartz, cinnabar). In substances of the 1st type, optical activity is due to the asymmetric structure of their molecules, of the 2nd type - by the specific orientation of molecules (ions) in the unit cells of the crystal (the asymmetry of the field of forces that bind particles in the crystal lattice). O.'s crystals - and. in. always exist in two forms - right and left; in this case, the lattice of the right crystal is mirror-symmetric to the lattice of the left one and cannot be spatially combined with it (the so-called enantiomorphic forms, see Enantiomorphism). Optical activity of the right and left forms of O. - and. in. Type 2 crystals have different signs (and are equal in absolute value under the same external conditions), so they are called optical antipodes (sometimes type 1 OA crystals are also called so).
Molecules of the right and left O. - and. in. Type 1 are optical isomers (see Isomerism, Stereochemistry), i.e. That is, in their structure they are mirror images of each other. They can be distinguished one from the other, while particles of optical antipodes (O.-a. v. 1st type) are simply indistinguishable (identical). The physical and chemical properties of pure optical isomers are exactly the same in the absence of any asymmetric agent that reacts to the mirror asymmetry of the molecules. The product of a chemical reaction without the participation of such an agent is always a mixture of optical isomers in equal amounts, the so-called. racemate. The physical properties of the racemate and pure optical isomers are often different. For example, the melting point of the racemate is somewhat lower than that of the pure isomer. The racemate is separated into pure isomers either by selection of enantiomorphic crystals, or in a chemical reaction involving an asymmetric agent - a pure isomer or an asymmetric catalyst, or microbiologically. The latter indicates the presence of asymmetric agents in biological processes and is associated with a specific property of living nature that has not yet found a satisfactory explanation to build proteins from left-handed optical isomers of amino acids - 19 out of 20 vital amino acids are optically active. (In relation to O.-a. century of the 1st type, the terms "left" and "right" - L and D- are conditional in the sense that they do not directly correspond to the direction of rotation of the plane of polarization in them, in contrast to the same terms - l and d - for O.-a. in. 2nd type or the terms "left-handed" and "right-handed".) The physiological and biochemical effects of optical isomers are often completely different. For example, art-synthesized proteins from D-amino acids are not absorbed by the body; bacteria ferment only one of the isomers without affecting the other; L-nicotine is several times more poisonous D-nicotine. The amazing phenomenon of the predominant role of only one of the forms of optical isomers in biological processes can be of fundamental importance for elucidating the ways of the origin and evolution of life on Earth.
When two coherent beams polarized in mutually perpendicular directions are superimposed, no interference pattern, with its characteristic alternation of intensity maxima and minima, is observed. Interference occurs only if the oscillations in the interacting beams occur along the same direction. The directions of oscillations in two beams, initially polarized in mutually perpendicular directions, can be reduced to one plane by passing these beams through a polarizing device installed so that its plane does not coincide with the plane of oscillation of either of the beams.
Let us consider what is obtained by superimposing the ordinary and extraordinary rays emerging from the crystal plate. Under normal incidence of light
on a crystal face parallel to the optical axis, the ordinary and extraordinary rays propagate without separating, but at different speeds. As a result, there is a difference between them
or phase difference
where d- the path traveled by the rays in the crystal, λ 0 - the wavelength in vacuum [see. formulas (17.3) and (17.4)].
Thus, if natural light is passed through a crystalline plate of thickness cut parallel to the optical axis d(Fig. 12l, a), two beams polarized in mutually perpendicular planes will come out of the plate 1 and 2 1 , between which there will be a phase difference (31.2). Let's put some kind of polarizer in the path of these rays, for example, a polaroid or a nicol. The oscillations of both beams after passing through the polarizer will lie in the same plane. Their amplitudes will be equal to the components of the beam amplitudes 1 and 2 in the direction of the plane of the polarizer (Fig. 121, b).
Since both beams were obtained by dividing the light received from one source, they would seem to interfere, and for a crystal thickness d such that the path difference (31.1) arising between the rays is, for example, λ 0 /2, the intensity of the rays emerging from the polarizer (for a certain orientation of the polarizer plane) must be equal to zero.
Experience, however, shows that if the rays 1 and 2 arise due to the passage of natural light through the crystal, they do not interfere, i.e., they are not coherent. This is explained quite simply. Although the ordinary and extraordinary rays are generated by the same light source, they mainly contain vibrations belonging to different trains of waves emitted by individual atoms. Oscillations corresponding to one such train of waves occur in a randomly oriented plane. In an ordinary ray, oscillations are mainly due to trains, the planes of oscillations of which are close to one direction in space, in an extraordinary ray, trains, the planes of oscillations of which are close to another, perpendicular to the first direction. Since individual trains are incoherent, the ordinary and extraordinary rays arising from natural light, and, consequently, the rays 1 and 2 , are also incoherent.
The situation is different if the crystal plate shown in Fig. 121, plane polarized light is incident. In this case, the oscillations of each train are divided between the ordinary and extraordinary rays in the same proportion (depending on the orientation of the optical axis of the plate relative to the plane of oscillations in the incident beam), so that the rays about and e, and hence the rays 1 and 2 , turn out to be coherent.
Two coherent plane-polarized light waves, the planes of oscillation of which are mutually perpendicular, when superimposed on each other, generally speaking, give elliptically polarized light. In a particular case, circularly polarized light or plane polarized light can be obtained. Which of these three possibilities takes place depends on the thickness of the crystal plate and the refractive indices. n e and n o, and also on the ratio of the amplitudes of the rays 1 and 2 .
A plate cut parallel to the optical axis, for which ( n about - n e) d = λ 0 /4 is called quarter wave plate ; plate for which, ( n about - n e) d = λ 0 /2 is called half wave plate etc. 1 .
rays will be different. Therefore, when superimposed, these rays form light polarized along an ellipse, one of the axes of which coincides in direction with the axis of the plate O. With φ equal to 0 or /2, the plate will have
14th lecture. dispersion of light.
Elementary theory of dispersion. Complex permittivity of matter. Curves of dispersion and absorption of light in matter.
wave package. group speed.