The phenomena of interference and diffraction of light serve as evidence of its wave nature.

Interference waves is the phenomenon of superposition of waves, in which their mutual strengthening occurs at some points in space and weakening at others. A time-constant (stationary) interference pattern appears only when waves are added equal frequency with constant phase difference. Such waves and the sources that excite them are called coherent.

Interference of light is one of the manifestations of its wave nature; it occurs, for example, when light is reflected in a thin air layer between a flat glass plate and a plano-convex lens. IN in this case interference occurs when coherent waves are added 1 And 2 , reflected from both sides of the air gap. This interference pattern, which has the form of concentric rings, is called Newton’s rings in honor of I. Newton, who first described it and established that the radii of these rings for red light are larger than for blue light.

Believing that light is waves, the English physicist T. Young explained the interference of light as follows. Ray incident on a lens 0 after reflection from its convex surface and refraction, it gives rise to two reflected rays ( 1 And 2 ). Wherein light waves in the beam 2 lag behind the beam 1 on Dj, and the phase difference Dj depends on the “extra” path that the beam has traversed 2 , compared to the beam 1 .

Obviously, if Dj = n l, where n- an integer, then waves 1 And 2 , adding up, will reinforce each other and, looking at the lens at this angle, we will see a bright ring of light of a given wavelength. On the contrary, if

Where n- an integer, then waves 1 And 2 , when folded, they will cancel each other out, and therefore, looking at the lens from above at this angle, we will see a dark ring. Thus, wave interference leads to a redistribution of vibration energy between various closely spaced particles of the medium.

Interference depends on the wavelength, and therefore, by measuring angular distances between adjacent minima and maxima of the interference pattern, the wavelength of the light can be determined. If interference occurs in thin films of gasoline on the surface of water or in films soap bubbles, then this leads to the coloring of these films in all the colors of the rainbow. Interference is used to reduce the reflection of light from optical glasses and lenses, which is called coating of optics. To do this, a film is applied to the surface of the glass. transparent substance such a thickness that the phase difference between the light waves reflected from the glass and the film is .

Diffraction of light– the bending of light waves around the edges of obstacles, which is another proof of the wave nature of light, was first demonstrated by T. Young in an experiment when a plane light wave fell on a screen with two closely spaced slits. According to Huygens' principle, slits can be considered as sources of secondary coherent waves. Therefore, passing through each of the slits, the light beam broadened, and an interference pattern in the form of alternating light and dark stripes was observed on the screen in the area where the light beams from the slits overlapped. The appearance of the interference pattern is explained by the fact that the waves from the slits to each point P different distances r 1 and r 2 pass on the screen, and the corresponding phase difference between them determines the brightness of the point R.

Polarization of light

The polarization of light waves, which is a consequence of their transverse nature, changes when light is reflected, refracted, and scattered in transparent media.

The transverse nature of light waves is one of the consequences electromagnetic theory J.C. Maxwell and is expressed in the fact that the electric field strength vectors oscillating in the waves E and induction magnetic field IN perpendicular to each other and to the direction of propagation of these waves. To describe an electromagnetic wave, it is enough to know how one of these two vectors changes, for example, E which is called light vector. Polarization of light call the orientation and nature of changes in the light vector in a plane perpendicular to the light beam. Light in which the directions of vibration of the light vector are somehow ordered is called polarized.

If, during the propagation of an electromagnetic wave, the light vector retains its orientation, then such a wave is called linearly polarized or plane-polarized, and the plane in which the light vector oscillates is plane of oscillation. An electromagnetic wave emitted by any atom (or molecule) in a single act of radiation is always linearly polarized. Linearly polarized light sources are also lasers.

If the plane of oscillation of an electromagnetic wave constantly and randomly changes, then light is called unpolarized. Natural light(sun, lamps, candles, etc.) is the sum of radiation huge number individual atoms, each of which emits linearly polarized light waves at a certain moment. However, since the planes of vibration of these light waves change chaotically and are not consistent with each other, the total light turns out to be unpolarized. Therefore, unpolarized light is often called natural.

If the amplitude of the light vector in one direction is greater than in others, then such light is called partially polarized. Natural light, when reflected from non-metallic surfaces (water, glass, etc.), becomes partially polarized so that the amplitude of the light vector in the direction parallel to the reflecting plane becomes larger. The refraction of natural light at the boundary of two media also turns it into partially polarized light, but in these cases, as a rule, the amplitude of the light vector in the direction parallel to the reflecting plane becomes smaller.

Natural light can be converted to linearly polarized light using polarizers- devices that transmit waves with a light vector only in a certain direction. Tourmaline crystals are often used as polarizers, which strongly absorbs rays with a light vector perpendicular to the optical axis of the crystal. Therefore, natural light passing through a tourmaline plate becomes linearly polarized with an electric vector oriented parallel to the tourmaline's optical axis.

Interference- this is the superposition of two or more waves, leading to a time-stable increase in oscillations at some points in space and a weakening at others.

They can only interfere coherent waves are waves that have the same frequency and a constant phase difference over time. The amplitude of the resulting oscillation is zero at those points in space at which waves with identical amplitudes and frequencies arrive with a phase shift of oscillations by p or half the oscillation period. With the same law of oscillation of two sources of waves, the difference will be half the period of oscillation, provided that the difference Dl(path difference of interfering waves) distances l 1 And l 2 from the wave sources to this point is equal to half the wavelength:

or an odd number of half-waves (Fig. 84, A):

.

This is the condition of the interference minimum.

Interference maxima are observed at points in space where waves arrive with the same oscillation phase (Fig. 84, b). With the same law of oscillation of two sources, to fulfill this condition, the path difference Dl must be equal to an integer number of waves:

Where does the energy of two waves disappear in places of interference minima? If we consider only one place where two waves meet, then such a question cannot be answered correctly. Wave propagation is not a collection independent processes vibrations at individual points in space. The essence of the wave process is the transfer of vibrational energy from one point in space to another, etc. When waves interfere in places of interference minima, the energy of the resulting oscillations is actually less than the sum of the energies of the two interfering waves. But in the places of interference maxima, the energy of the resulting oscillations exceeds the sum of the energies of the interfering waves by exactly the same amount as the energy in the places of interference minima has decreased. When waves interfere, the oscillation energy is redistributed in space, but at the same time the law of conservation of energy is satisfied.

The deviation of the direction of wave propagation from straight line at the boundary of an obstacle is called wave diffraction. Diffraction of waves occurs when they encounter an obstacle of any shape and size. Usually, when the size of the obstacle or hole in the obstacle is large compared to the wavelength, wave diffraction is little noticeable. Diffraction manifests itself most clearly when waves pass through an opening with dimensions on the order of the wavelength or when encountering obstacles of the same dimensions. At sufficiently large distances between the wave source, the obstacle and the place where the waves are observed, diffraction phenomena can also occur when large sizes holes or obstructions.

The cause of diffraction is interference. This is explained Huygens-Fresnel principle: each point in the medium to which the wave has reached becomes a source of secondary waves that interfere at subsequent points in space.

Standing waves

Let the wave run along the abscissa axis, reach an obstacle located at the origin of coordinates, and without loss of energy begin to move along the abscissa axis from right to left, meeting and adding to the wave running from left to right. There are two possible cases here.

1) The wave is reflected at a point ABOUT in the same phase in which she came to her (Fig. 85, A). In this case, the equation of a wave traveling from left to right has the form

,

and for the reflected wave the equation will be written as follows:

.

Adding both equations, we get:

.

Transforming the sum of cosines into a product, we get

.

Here the value does not depend on time, therefore, this is the amplitude of the new oscillation of all points of the wave. The expression under the cosine sign in the second factor does not depend on the coordinate.

So, as a result of the addition of the traveling and reflected waves, we obtained a new wave, the phase of which does not depend on the coordinate, but the amplitude of the oscillations depends on the coordinate. This wave is called standing wave.

U standing wave there are points where the amplitude of oscillations is zero. These points are called nodes standing wave (Fig. 85, b). Let us find their coordinates, assuming .

But cosine equal to zero, if its argument is an odd number p/2, hence

,

from which we obtain that the coordinates of the nodes are determined from the condition

.

A standing wave has points where the amplitude of the standing wave is twice the amplitude of the traveling wave. These points are called antinodes standing wave. Obviously, we get the coordinates of the antinodes by putting , for which it is necessary that the condition be satisfied

whence it follows that the coordinates of the antinodes satisfy the relation:

2) The wave is reflected at a point ABOUT in the opposite phase compared to the traveling wave (Fig. 86). In this case, the equation of the wave traveling from left to right will be written in the same form, and the equation of the reflected wave will take the form:

.

Adding both wave equations, we again obtain the standing wave equation, which the reader can easily see for himself. But the amplitude of the standing wave in this case will have the form:

.

It is not difficult to deduce from this that in this case, instead of nodes, antinodes will appear, and instead of antinodes, standing wave nodes will appear.

Sound waves

The branch of physics that deals with the study of sound phenomena is called acoustics, and phenomena associated with the emergence and propagation of sound waves – acoustic phenomena.

The process of propagation of compression or rarefaction in a gas occurs as a result of collisions of gas molecules, therefore the speed of sound in a gas is approximately equal to the speed of movement of the molecules. average speed The thermal motion of molecules decreases with decreasing gas temperature; therefore, the speed of sound propagation decreases with decreasing gas temperature. For example, in hydrogen, when the temperature decreases from 300 to 17 K, the speed of sound decreases from 1300 to 320 m/s. By modern measurements speed of sound in air at normal conditions equal to 331 m/s.

Communication between atoms and molecules in liquids and solids much more rigid than in gases. Therefore, the speed of propagation of sound waves in liquids and solids is much greater than the speed of sound in gases. So the speed of sound in water is 1500 m/s, and in steel – 6000 m/s.

A person characterizes any sounds in accordance with his perception by volume level.

The force of a sound wave on the eardrum of the human ear depends on the sound pressure. Sound pressure- This extra pressure, which occurs in a gas or liquid during the passage of a sound wave. The lower limit of the perception of sound by the human ear corresponds to a sound pressure of approximately 10 -5 Pa. Upper limit The sound pressure at which a sensation of pain in the ears occurs is approximately 100 Pa. Sound waves with a large amplitude of sound pressure changes are perceived by the human ear as loud sounds, and with a small amplitude of sound pressure changes - as quiet sounds.

Sound vibrations occurring along harmonic law, are perceived by a person as a certain musical tone. Oscillations high frequency perceived as sounds high tone, low frequency sounds are like sounds low tone. Range sound vibrations, corresponding to a double change in the frequency of sound vibrations, is called an octave.

Sound vibrations that do not obey the harmonic law are perceived by humans as a complex sound with timbre. At the same pitch, the sounds produced, for example, by a violin and a piano, differ in timbre.

The frequency range of sound vibrations perceived by the human ear ranges from approximately 20 to 20,000 Hz. Longitudinal waves in an environment with a pressure change frequency of less than 20 Hz are called infrasound, with a frequency of more than 20,000 Hz – ultrasound.

Ultrasound affects biological objects. At low intensities, it activates metabolic processes and increases permeability cell membranes, produces tissue micromassage. At high intensities, it destroys red blood cells, causing dysfunction and death of microorganisms and small animals. By destroying the membranes of plant and animal cells with ultrasound, they are extracted from them biologically. active substances(enzymes, toxins). In surgery, ultrasound is used to destroy malignant tumors, sawing bones, etc.

Ultrasound is produced and perceived by many animals. For example, dogs, cats, mice hear ultrasound with a frequency of up to 100 kHz. Many insects are also sensitive to them. Some animals use ultrasound for orientation in space (ultrasonic location). Bat periodically emits short ultrasonic signals (30-120 kHz) in the direction of flight. By catching signals reflected from objects, the animal determines the position of the object and estimates the distance to it. This location method is also used by dolphins, who freely navigate muddy water, In the dark. Using ultrasound for echolocation is quite natural. The shorter the wavelength of the radiation, the smaller the objects that need to be identified may be. In this case, the linear dimensions of the object must be greater than or at least on the order of the sound wavelength. So a frequency of 80 kHz corresponds to a wavelength of 4 mm. In addition, as the wavelength decreases, the directionality of the radiation is more easily realized, and this is very important for echolocation.

A person uses ultrasonic location to study the topography of the seabed, detect schools of fish and icebergs. In medicine, ultrasound diagnostics is used, for example, to identify tumors on internal organs.

Infrasounds – low frequency elastic waves- accompany a person to Everyday life. Powerful sources of infrasound are lightning discharges (thunder), gun shots, explosions, landslides, storms, machine operation, and urban transport. Constantly operating powerful infrasounds of certain frequencies (3-10 Hz) are harmful to human health, they can cause blurred vision, nervous disorders, resonant vibrations internal organs, memory loss.

The peculiarity of infrasounds is their weak absorption by matter. Therefore, they easily pass through obstacles and can spread over very long distances. This allows, for example, to predict the approach natural disaster- storms, tsunamis. Many fish, marine mammals and birds appear to perceive infrasound as they react to approaching storms.

Sound waves encountering any body cause forced vibrations. If natural frequency free vibrations body coincides with the frequency of the sound wave, then the conditions for transferring energy from the sound wave to the body are the best - the body is an acoustic resonator. Amplitude forced oscillations at the same time reaches the maximum value - it is observed acoustic resonance.

Acoustic resonators are, for example, pipes of wind instruments. In this case, the air in the pipe acts as a body experiencing resonant oscillation. The ability of the ear to distinguish sounds by pitch and timbre is associated with resonant phenomena, occurring in the main membrane. Acting on the main membrane, sound wave causes resonant vibrations of certain fibers in it, the natural frequency of which corresponds to the frequencies of the harmonic spectrum of a given vibration. Nerve cells, connected to these fibers, are excited and send nerve impulses V central department auditory analyzer, where they, when summed up, cause a feeling of pitch and timbre of sound.

Light waves

In a light wave they make fast ( n=10 14 Hz) continuous oscillations of the vectors of electric field strength and magnetic field induction. Their oscillations are interconnected and occur in directions perpendicular to the beam (the light wave is transverse), and so that the vectors of tension and induction are mutually perpendicular (Fig. 87).

As experiments show, the effect of light on the eye and other receivers is due to vibrations electric vector, called, therefore, light. For a plane sinusoidal wave propagating at speed u in the direction r, oscillations of the light vector are described by the equation

.

Light that has a specific frequency (or wavelength) is called monochromatic. If oscillations of the light vector occur only in one plane passing through the beam, then the light is called plane polarized. Natural light contains vibrations in all directions.

When light passes from one medium to another, its frequency remains unchanged, but the corresponding wavelength changes, because speed of light in different environments different. Speed ​​of light in vacuum s=3 10 8 m/s.

Coherent light waves (like waves of any other nature) interfere. Moreover, independent light sources (with the exception of lasers) cannot be coherent, because in each of them light is emitted by many atoms that emit inconsistently. Coherence can be achieved by splitting a wave from one source into two parts and then bringing them together. Radiated by one group of atoms, the two waves thus obtained will be coherent and, when superimposed, can interfere. In practice, dividing one wave into two can be done different ways. In the installation proposed by T. Jung, White light passes through a narrow hole S(Fig. 88, A), then using two holes S 1 And S 2 the beam is divided into two. These two beams, overlapping each other, form a white stripe in the center of the screen, and iridescent ones at the edges. The color of soap bubbles and thin oil films on water is explained by the interference of light. Light waves are partially reflected from the surface of a thin film and partially transmitted into it. At the second boundary of the film, waves are reflected again (Fig. 88, b). Light waves reflected by two surfaces of a thin film travel in the same direction but take different paths. For a path difference that is a multiple of an integer number of wavelengths:

an interference maximum is observed.

For a difference that is a multiple of an odd number of half-waves:

,

an interference minimum is observed. When the maximum condition is satisfied for one wavelength of light, it is not satisfied for other wavelengths. Therefore, when illuminated by white light, a thin, colorless, transparent film appears colored. When the film thickness or the angle of incidence of light waves changes, the path difference changes, and the maximum condition is satisfied for light with a different wavelength.

The bright coloring of some shells (mother of pearl), iridescent with all the colors of the rainbow, and bird feathers, on the surface of which there are thinnest transparent scales invisible to the eye, can also be explained by interference.

Interference methods have found wide application in a number of fields of science and technology. The interference pattern is very sensitive to factors that change the path difference of the rays. This is the basis for high-precision measurement of lengths, densities, refractive indices, surface polishing quality, etc. One of the applications is the brightening of optics. To reduce light reflected from glass surfaces optical instruments(for example, lenses), a special transparent thin film is applied to these surfaces. Its thickness is selected so that rays of a certain wavelength reflected from both surfaces are mainly extinguished due to interference. Without film on each lens, up to 10% of light energy is lost.

The phenomenon of light deflecting from the rectilinear direction of propagation when passing at the edge of an obstacle is called diffraction of light. Due to the short wavelength of light, the diffraction pattern is clear if the obstacles or holes are small in size (comparable to the wavelength). Diffraction of light is always accompanied by interference (Huygens-Fresnel principle). Based on this, when illuminating an opaque disk on a screen, a light spot can be obtained in the center of its shadow, and from a round hole a dark spot in the center. The diffraction pattern in white light is colored.

The phenomenon of light diffraction is used in spectral instruments. One of the main elements of such devices is diffraction grating. A diffraction grating is a set of parallel narrow slits, transparent to light, separated by opaque spaces (Fig. 89). The best gratings have up to 2000 lines per 1 mm of surface. Wherein total length gratings 100-150 mm. Such gratings are usually obtained by applying a series of parallel strokes - scratches - to a glass plate using special machines. Undamaged areas play the role of cracks, and scratches that scatter light act as opaque spaces. If opaque marks (scratches) are applied to a polished metal surface, you will get a so-called reflective diffraction grating. Sum With width A cracks and gaps b between the slits is called the period or lattice constant:

Let's look at the main points elementary theory diffraction grating. Let a plane monochromatic wave of length l(Fig. 90). Secondary sources in the slits create light waves that travel in all directions. Let us find the condition under which the waves coming from the slits reinforce each other. To do this, let us consider waves propagating in the direction determined by the angle j. The path difference between the waves from the edges of adjacent slits is equal to the length of the segment AC. If this segment contains an integer number of wavelengths, then the waves from all the slits, adding up, will reinforce each other. From a triangle ABC you can find the length of the leg AC:

Maximums will be observed at an angle j, determined by the condition

,

Where k=0, 1, 2,... These maxima are called main.

It must be borne in mind that when the maximum condition is met, not only the waves coming from the left (according to the figure) edges of the slits are amplified, but also the waves coming from all other points of the slits. Each point in the first slit corresponds to a point in the second slit at a distance With. Therefore, the difference in the path of the secondary waves emitted by these points is equal, and these waves are mutually amplified.

A collecting lens is placed behind the grating, in the focal plane of which the screen is located. The lens focuses rays traveling parallel to one point, at which the waves combine and their mutual amplification occurs.

Since the position of the maxima (except for the central one, corresponding k=0) depends on the wavelength, then the grating splits white light into a spectrum(Fig. 91). The more l, the farther this or that maximum corresponding to a given wavelength is located from the central maximum. Each value k corresponds to its spectrum.

Using a diffraction grating, very precise wavelength measurements can be made. If the grating period is known, then determining the wavelength is reduced to measuring the angle j, corresponding to the direction to the maximum.

If you examine the wings of butterflies under a microscope, you will notice that they consist of large number elements whose size is on the order of the wavelength visible light. Thus, the wing of a butterfly is a kind of diffraction grating. The rainbow stripe is also visible in the eyes of dragonflies and other insects. It is formed due to the fact that their compound eyes consist of a large number of individual “eyes” - facets, i.e. are also “alive” diffraction gratings.

Diffraction and interference of waves. Typical ripple effects are the phenomena of interference and diffraction. Initially, diffraction was the deviation of the propagation of light from the rectilinear direction. This discovery was made in 1665 by Abbot Francesco Grimaldi and served as the basis for the development of the wave theory of light.

Diffraction of light was the bending of light around the contours of opaque objects and, as a consequence, the penetration of light into the region of geometric shadow. After the creation of the wave theory, it turned out that the diffraction of light is a consequence of the phenomenon of interference of waves emitted by coherent sources located at different points in space. Waves are said to be coherent if their phase difference remains constant over time. The sources of coherent waves are coherent oscillations of wave sources. Sine waves, whose frequencies do not change over time, are always coherent. Coherent waves emitted by sources located at different points propagate in space without interaction and form a total wave field. Strictly speaking, the waves themselves do not add up. But if a recording device is located at any point in space, then its sensitive element will be set into oscillatory motion under the influence of waves. Each wave acts independently of the others, and the movement sensitive element represents the sum of fluctuations.

In other words, in this process it is not waves that are formed, but oscillations caused by coherent waves.

Rice. 3.1. Dual source and detector system. L is the distance from the first source to the detector, L is the distance from the second source to the detector, d is the distance between the sources. As basic example Let's consider the interference of waves emitted by two point coherent sources, see Fig. 3.1. The frequencies and initial phases of source oscillations coincide.

The sources are located at a certain distance d from each other. The detector that records the intensity of the generated wave field is located at a distance L from the first source. The type of interference pattern depends on geometric parameters sources of coherent waves, on the dimension of the space in which the waves propagate, etc. Let us consider the functions of waves that are a consequence of oscillations emitted by two point coherent sources.

To do this, let's set the z axis as shown in Fig. 3.1. Then wave functions will look like this 3.1 Let's introduce the concept of wave path difference. To do this, consider the distances from the sources to the recording detector L and L. The distance between the first source and the detector L differs from the distance between the second source and the detector L by the value t. In order to find t, consider a right triangle containing the values ​​t and d. Then you can easily find t using the sine function 3.2 This value will be called the wave path difference. Now let's multiply this value by the wave number k and get a value called the phase difference. Let's denote it as 3.3 When two waves reach the detector, functions 3.1 will take the form 3.4 In order to simplify the law according to which the detector will oscillate, let's set the value -kL 1 to zero in the function x1 t. Let us write the value of L in the function x2 t using function 3.4. Through simple transformations we obtain that 3.5 where 3.6 You can notice that the ratios 3.3 and 3.6 are the same. Previously, this quantity was defined as the phase difference. Based on what was said earlier, Relationship 3.6 can be rewritten as follows: 3.7 Now let’s add the functions 3.5. 3.8 Using the method of complex amplitudes, we obtain the relation for the amplitude of the total oscillation 3.9 where?0 is determined by the relation 3.3. After the amplitude of the total oscillation has been found, the intensity of the total oscillation can be found as the square of the amplitude 3.10 Consider a graph of the intensity of the total oscillation for different parameters.

Corner? varies in the interval 0, this can be seen from Figure 3.1, the wavelength varies from 1 to 5. Consider special case, when L d. This is usually the case in scattering experiments. x-rays.

In these experiments, the scattered radiation detector is usually located at a distance much greater than the size of the sample being studied.

In these cases, secondary waves enter the detector, which can be approximately assumed to be plane with sufficient accuracy.

In this case, the wave vectors of individual waves of secondary waves emitted different centers scattered radiation, parallel. It is believed that in this case the Fraunhofer diffraction conditions are satisfied. 2.3.2. X-ray diffractionX-ray diffraction is a process that occurs during elastic scattering x-ray radiation and consisting in the appearance of deflected diffracted beams propagating under certain angles to the primary bundle.

X-ray diffraction is caused by the spatial coherence of secondary waves that arise when primary radiation is scattered by electrons that make up the atoms. In some directions, determined by the relationship between the wavelength of the radiation and the interatomic distances in the substance, the secondary waves add up, being in the same phase, resulting in the creation of an intense diffraction beam. In other words, under the influence electromagnetic field of the incident wave, the charged particles present in each atom become sources of secondary scattered spherical waves. Individual secondary waves interfere with each other, forming both amplified and weakened beams of radiation propagating in different directions.

If scattering is elastic, then the modulus of the wave vector also does not change. Let us consider the result of the interference of secondary waves at a point distant from all scattering centers at a distance much greater than the interatomic distances in the irradiated sample under study. Let there be a detector at this point and the oscillations caused by the scattered waves arriving at this point are added up. Since the distance from the scatterer to the detector significantly exceeds the wavelength of the scattered radiation, the sections of secondary waves arriving at the detector can be considered with a sufficient degree of accuracy as flat, and their wave vectors as parallel.

Thus, the physical pattern of X-ray scattering, by analogy with optics, can be called Fraunhofer diffraction. Depending on the scattering angle of the angle between the wave vector of the primary wave and the vector connecting the crystal and the detector, the amplitude of the total oscillation will reach a minimum or maximum. The radiation intensity recorded by the detector is proportional to the square of the total amplitude.

Consequently, the intensity depends on the direction of propagation of scattered waves reaching the detector, on the amplitude and wavelength of the primary radiation, and on the number and coordinates of scattering centers. In addition, the amplitude of the secondary wave formed separate atom, and therefore the total intensity is determined atomic factor- a decreasing function of the scattering angle, depending on the electron density of atoms. 2.3.3.

End of work -

This topic belongs to the section:

Scattering of X-rays on fullerene molecules

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Wave nature of light. In the 17th century, the Dutch scientist Christiaan Huygens expressed the idea that light has a wave nature. If the size of the object is comparable to the wavelength, then the light seems to run into the shadow area and the shadow boundary appears blurred. These phenomena cannot be explained by the rectilinear propagation of light. The idea contradicted the statements of I. Newton that light is a stream of particles, but the wave nature of light was experimentally confirmed in such phenomena as interference and diffraction.

Explain these wave phenomena is possible by using two concepts: Huygens' principle and the coherence of light.

Huygens' principle.Huygens' principle is as follows: any point wave front can be considered as a secondary source of elementary waves propagating in the original direction at the speed of the primary wave. Thus, the primary wave can be considered as the sum of secondary elementary waves. According to Huygens' principle, the new position of the wave front of the primary wave coincides with the envelope curve of elementary secondary waves (Fig. 11.20).

Rice. 11.20. Huygens' principle.

Coherence. For diffraction and interference to occur, the condition of constancy of the phase difference of light waves from different sources Sveta:

Waves whose phase difference remains constant are called coherent.

Wave phase is a function of distance and time:

The main condition for coherence is the constancy of the frequency of light. However, in reality the light is not strictly monochromatic. Therefore, the frequency, and, consequently, the phase difference of light may not depend on one of the parameters (either time or distance). If the frequency does not depend on time, coherence is called temporal, and when it does not depend on distance – spatial. In practice, it looks like the interference or diffraction pattern on the screen either does not change over time (with temporal coherence), or it is preserved when the screen moves in space (with spatial coherence).

Interference of light. In 1801, the English physicist, physician and astronomer T. Young (1773 – 1829) received convincing confirmation of the wave nature of light and measured the wavelength of light. The diagram of Young's experiment is presented in Fig. 11.21. Instead of the expected two lines if light were particles, he saw a series of alternating stripes. This could be explained by assuming that light is a wave.

Interference of light called the phenomenon of wave superposition. Light interference is characterized by the formation of a stationary (time-constant) interference pattern - a regular alternation in space of areas of increased and decreased light intensity, resulting from the superposition of coherent light waves, i.e. waves of the same frequency having a constant phase difference.

It is almost impossible to achieve a constant phase difference between waves from independent sources. Therefore, the following method is usually used to obtain coherent light waves. Light from one source is somehow divided into two or more beams and, having sent them along different paths, they are then brought together. The interference pattern observed on the screen depends on the difference in the paths of these waves.

Conditions of interference maxima and minima. The superposition of two waves with the same frequency and a constant phase difference leads to the appearance on the screen, for example, when light hits two slits, an interference pattern - alternating light and dark stripes on the screen. The reason for the appearance of light stripes is the superposition of two waves in such a way that two maxima are added at a given point. When the maximum and minimum of the wave overlap at a given point, they compensate each other and a dark stripe appears. Figure 11.22a and Figure 11.22b illustrate the conditions for the formation of minimums and maximums of light intensity on the screen. To explain these facts at a quantitative level, we introduce the following notation: Δ – path difference, d – distance between two slits, – light wavelength. In this case, the maximum condition, which is illustrated in Fig. 11.22b, represents the multiple of the difference between the path and wavelength of light:

This will happen if the oscillations excited at point M by both waves occur in the same phase and the phase difference is:

where m=1, 2, 3, ….

The condition for the appearance of minima on the screen is the multiplicity of light half-waves:

(11.4.5)

In this case, oscillations of light waves excited by both coherent waves at point M in Fig. 11.22a will occur in antiphase with a phase difference:

(11.4.6)

Rice. 11.21. Conditions for the formation of minima and maxima of the interference pattern

An example of interference is interference in thin films. It is well known that if gasoline or oil is dropped onto water, colored stains will be visible. This is due to the fact that gasoline or oil forms a thin film on water. Some of the light is reflected from top surface, and the other part from the bottom surface is the interface between the two media. These waves are coherent. The rays reflected from the upper and lower surfaces of the film (Fig. 11.22) interfere, forming maxima and minima. Thus, an interference pattern appears on the thin film. A change in the thickness of the film of gasoline or oil on the surface of the water leads to a change in the path difference for waves of different lengths and, consequently, a change in the color of the stripes.

Rice. 11.22 Interference in thin films

One of most important achievements in the use of interference is the creation of an ultra-precise device for measuring distances - Michelson interferometer(Fig. 11.24). Monochromatic light falls on a translucent mirror located in the center of the pattern, which splits the beam. One beam of light is reflected from a fixed mirror located at the top of Fig. 11.23, the second from a movable mirror located on the right in Fig. 11.23. Both beams return to the observation point, interfering with each other on the light wave interference recorder. Shifting the movable mirror by a quarter wavelength results in the replacement of light stripes with dark ones. The distance measurement accuracy achieved in this case is 10 -4 mm. This is one of the most highly accurate methods for measuring the size of microscopic quantities, which allows you to measure distances with an accuracy comparable to the wavelength of light.

The tuning of modern high-tech installations, for example, elements of the Large Hadron Collider at CERN, occurs with an accuracy of the wavelengths of light.

Rice. 11.23. Michelson interferometer

Diffraction. Experimental discovery The phenomenon of diffraction was another confirmation of the validity of the wave theory of light.

At the Paris Academy of Sciences in 1819, A. Fresnel presented the wave theory of light, which explained the phenomenon of diffraction and interference. According to the wave theory, the diffraction of light on an opaque disk should lead to the appearance of a bright spot in the center of the disk, since the difference in the path of the rays in the center of the disk is zero. The experiment confirmed this assumption (Fig. 11.24). According to Huygens' theory, points on the rim of the disk are sources of secondary light waves, and they are coherent with each other. Therefore, the light enters the region behind the disk.

Diffraction called the phenomenon of waves bending around obstacles. If the wavelength is long, then the wave does not seem to notice the obstacle. If the wavelength is comparable to the size of the obstacle, then the boundary of the obstacle’s shadow on the screen will be blurred.

Rice. 11.24. Diffraction from an opaque disk

Diffraction of light by a single slit results in the appearance of alternating light and dark stripes. Moreover, the condition for the first minimum has the form (Fig. 11.25):

where is the wavelength, d is the slit size.

The same figure shows the dependence of light intensity on the angle of deviation θ from the rectilinear direction.

Rice. 11.25. Condition for the formation of the 1st maximum.

A simple example of diffraction can be observed for ourselves: if we look at a room light bulb through a small slit in the palm or through the eye of a needle, we will notice concentric multi-colored circles around the light source.

Based on the use of diffraction phenomenon works spectroscope- a device for very precise measurement of wavelengths using a diffraction grating (Fig. 11.26).

Rice. 11.26. Spectroscope.

The spectroscope was invented by Joseph Fraunhofer in early XIX century. In it, the light passing through slits and collimating lenses turned into a thin beam of parallel rays. Light from the source enters the collimator through a narrow slit. The slit is in the focal plane. The telescope examines the diffraction grating. If the angle of inclination of the pipe coincides with the angle directed to the maximum (usually the first), then the observer will see a bright stripe. The wavelength is determined by the angle θ of the location of the first maximum on the screen. In essence, this device is based on the principle that is illustrated in Fig. 11.25.

To obtain the dependence of light intensity on wavelength (this dependence is called the spectrum), light was passed through a prism. At the exit from it, as a result of dispersion, the light was split into components. Using a telescope, you can measure radiation spectra. After the invention of photographic film, a more precise instrument was created: the spectrograph. Working on the same principle as a spectroscope, it had a camera instead of an observation tube. In the mid-twentieth century, the camera was replaced by an electron photomultiplier tube, allowing for greatly increased accuracy and real-time analysis.

Interference and diffraction of light

These phenomena reveal the wave nature of light. Interestingly, the wave theory of light was developed much earlier than it became known electromagnetic nature Sveta.

Interference. Interference is the redistribution of light intensity in space when light waves superimpose on each other. A necessary condition interference of will is yus coherence. Coherence is understood as the course of wave processes consistent in space and time. Only monochromatic waves of the same frequency are strictly coherent. Consider two coherent light waves:

Here α 1 and α 2 - initial phases of war.

Let us assume for simplicity that the wave amplitudes are equal:

The result of superposition of waves (2.25) is the wave

Let's write the expression in square brackets as the sum of cosines and we get

The resulting wave (2.26) is also monochromatic, has a frequency co and an amplitude depending on initial phases stackable waves

Resultant wave intensity

For general case with different amplitudes of the added waves we obtain

The cross term on the right side of (2.28) is called interference. Depending on the phase difference of the added waves ( α 1 - α 2) the intensity of the resulting wave may be either greater or less than the sum of the intensities of the original waves. In general, the intensity of the resulting oscillation is maximum and equal to

(n = 0, 1, 2, ...) and is minimal and equal to

So, at the resulting intensity is zero if α 1 – α 2 = π and is equal to 4 I, if α 1 – α 2 = 0.

All real electromagnetic waves are not strictly monochromatic and strictly plane-polarized, and therefore, strictly coherent.

The ability of real waves to interfere characterizes the degree of their coherence. Coherence of radio waves is relatively easy to ensure. In the microwave range, the sources of coherent waves are masers, and in the optical range, lasers. For higher frequency electromagnetic waves artificial coherent sources have not yet been created. Natural sources, as mentioned above, always emit incoherent light waves. It follows that to observe the interference of waves of different natural sources impossible.

However, if light from one source is divided into two (or more) wave systems, it turns out that these systems are coherent and capable of interfering. This is explained by the fact that each system represents radiation from the same atoms of the source.

In Fig. Figure 2.13 presents a basic system for observing the interference of light using Young’s method. The light source is a brightly illuminated target s in screen E1. Light from it hits the screen E2, in which there are two identical narrow slits s 1 and s 2. Slots s 1 and s 2 can be considered as two coherent sources.

The result of interference is observed on the EZ screen in the form of alternating dark (minimums) and light (maxima) stripes parallel to each other.

The exact result of interference depends on the phase relationship of the waves at a given point on the screen. If the waves arrive in phase (Fig. 2.14), they reinforce each other, a maximum is observed; if in antiphase - minimum (Fig. 2.15). The phase relationship depends on the wavelength of light λ in vacuum, the distance between targets - d, as well as the angle θ , under which surveillance is carried out.

Let's consider the result of superposition of waves at some point R, spaced from the center line by a distance X(see Fig. 2.13).

Ray path difference will be determined from the relation

To obtain a discernible interference pattern, you must have therefore, it can be accepted

On the other side, . From Fig. 2.14 it follows that if the path difference fits an integer number of wavelengths λ, then at the point of observation R 1 waves arrive in phase and reinforce each other, which corresponds to a maximum. Interference maxima condition

If the path difference contains a half-integer number of wavelengths, they arrive at the observation point P 2 in antiphase and cancel each other, which corresponds to a minimum (see Fig. 2.15).

Condition for interference minima

In the center of screen 33 (t.O) a central - maximum - maximum of zero order will be observed. The “±” signs correspond to the location of maxima and minima on both sides symmetrically from the central maximum. Number m determines the order of interference maxima and minima. The distance between two adjacent maxima (or minima) is called the interference fringe width ∆ X. It is equal and constant for a given experience.

Diffraction of light. If light propagates in a homogeneous region of space, and the light wavelength is negligible compared to the characteristic dimensions of the region, then the propagation of light obeys the laws geometric optics. In this case, we use the concept light beam, i.e. a very narrow beam of light propagating in a straight line. In the same case, if there are sharp optical inhomogeneities in the propagation area (holes, obstacles, boundaries opaque bodies etc.), the size of which is comparable to the wavelength of light, diffraction occurs - light waves bend around obstacles, penetrate into the region of geometric shadow, i.e. deviation from the laws of geometric optics.

In its physical meaning, diffraction is no different from interference. Both of these phenomena are associated with a redistribution of intensity luminous flux as a result of the superposition of coherent waves. The principle allows us to calculate the distribution of light as a result of diffraction - the diffraction pattern Huygens-Fresnel(1815). It is formulated in two provisions;

Each element of space that the front of a propagating light wave reaches becomes a source of secondary light waves; these waves are spherical; the envelope of these waves gives the position of the wave front at the next moment in time;

Secondary waves are coherent with each other, so they interfere when superimposed.

Let us consider as an example the diffraction of plane light waves (Fraunhofer diffraction) by a slit. The width of the slit is comparable to the wavelength of light. Let a plane monochromatic wave with wavelength λ be incident normally to the slit plane MN(Fig. 2.16).

Each point of the slit, reached by the front of the incident wave, becomes a source of secondary spherical waves, and the light, having passed through the narrow slit, spreads in all directions.

Let us take an arbitrary direction of rays from the slit at an angle φ (Fig. 2.17). It is clear that a ray from a point N lags behind the ray from a point M to a distance NF. This distance is called the ray path difference. If the slot width MN- a, then the path difference is equal to NF = ∆ = a sinφ. For analysis, it is convenient to divide the slit into several zones so that the difference in the path of the rays from the boundaries of each zone is equal to λ/2. In this case, the waves corresponding to the rays will be in antiphase (have a shift by π). Indeed, the phase of the wave

Total number zones will be equal

Secondary rays are focused by a collecting lens and projected onto the screen (Fig. 2.18). According to the Huygens-Fresnel principle, secondary waves interfere. Due to the antiphase of the corresponding waves, neighboring rays cancel each other out by interfering. Therefore, if it fits on the cracks even number zones, then at the point IN there will be a minimum:

and if it’s not even, then the maximum.

Here m- order of minimum (maximum). In the forward direction, light gives a central maximum (point B 0). The intensity distribution on the screen is called the diffraction spectrum.

If the light incident on the slit is monochromatic (for example, yellow), then the diffraction spectrum will consist of alternating dark and yellow stripes. If we direct white light, which is a superposition of seven monochromatic waves, onto the slit, then for each wavelength λ i maxima and minima will be observed at their own angles (φ i) max and (φ i) m in. Diffraction pattern will look like an alternation of “rainbows” and dark spaces, in the center of the picture there will be an uncolored central maximum (zero-order maximum).

A system of a large number of identical slits parallel to each other is called a diffraction grating. The diffraction spectrum from a grating is much more complex than the spectrum from a single slit, since here light waves from different slits additionally interfere. At the same time, the stripes are much brighter, since more light passes through the grating.

For electromagnetic radiation In the X-ray range, natural diffraction gratings are spatial crystal lattices. This is explained by the fact that the distances between grating nodes are comparable to the wavelengths of X-ray radiation.

Explanation of the rectilinear propagation of light. Using the Huygens-Fresnel principle, the rectilinear propagation of light can be explained. Let the light radiate from a point monochromatic source S (Fig. 2.19).

According to the Huygens-Fresnel principle, we replace the action of the source S with the action of secondary imaginary sources located on the auxiliary sphere Ф, which is wave surface spherical light wave. This surface is divided into ring zones so that the distances from the edges of the zones to the point M differed by λ/2. This means that waves arriving at a point M from each zone differ in phase by π, i.e. any two “neighboring” waves are antiphase.

The amplitudes of these waves are subtracted when superimposed, so the amplitude of the resulting wave at point M is:

where A 1,2,…, i, …, n- amplitude of light waves excited by the corresponding zones. Due to the very large number of zones, we can assume that the amplitude A i, is equal to the average value of the amplitudes of waves excited by adjacent zones:

Action of the entire wave on a point M comes down to the action of a small area, smaller than central zone. The radius of the first zone is on the order of tenths of a millimeter, so the propagation of light from S To M occurs as if inside a narrow channel along S.M., i.e. rectilinearly.