Life on Earth arose and exists thanks to sunlight. Thanks to it, we perceive and understand the world around us. Rays of light tell us about the position of near and distant objects, their shape and color. Light, amplified by optical instruments, reveals to humans two worlds that are polar in scale: the cosmic world with its enormous extent and the microscopic world, inhabited by tiny organisms indistinguishable to the naked eye.

The question of the nature of light arose a long time ago. For example, the Greek thinker Pythagoras (c. 580 BC) believed that visual sensations arise from “hot vapors” that escape from the eye to objects. The Greek mathematician Euclid (c. 450 - 380 BC) developed the theory of “optic rays”, a follower of which was Ptolemy (2nd century AD). According to Euclid's views, sensitive threads come out of the eye, feel the body with their ends and create visual sensations.

The foundations of optics were laid in ancient times. Melting clear glass was known to the ancient Egyptians and the inhabitants of Mesopotamia 1600 BC, and in ancient Rome glassware and decorations were made with great perfection. In the 13th century, humanity received the first optical instruments - glasses and magnifying glasses. Much later, at the beginning of the 17th century, the telescope and microscope were invented.

In 1609, the Italian scientist Galileo invented a telescope with a negative lens as an eyepiece and used it widely for observation. In Russia, glasses and spotting scopes appeared at the beginning of the 17th century.
The creation of the theory of optical instruments began at the end of the 17th century thanks to the works of outstanding scientists: R. Descartes, P. Fermat, I. Newton, K. Gauss and others. Russian scientists M.V. Lomonosov, L. Euler, V.N. Chikolev, mechanics I.P. Kulibin, O.N. Malofeev made a great contribution to the development of world science and technology in the field of optics.

In Russia, under Peter 1, optics received its further development. In 1725, the Department of Optics and an optical workshop were organized at the Academy of Sciences. One of the heads of the optics department was L. Euler, who wrote the book “Dioptrics”, where he outlined the fundamentals of geometric optics.
M.V. Lomonosov was the first Russian scientist to use a microscope for scientific research; he created a whole range of fundamentally new optical instruments, developed methods for making colored glass and colored mosaics. The works of outstanding Russians M.V. Lomonosov and L. Euler in the 18th century laid the most important foundations for the development of optical production in Russia.

After the revolution of 1917, the State Optical Institute was organized in Petrograd in 1918, headed by Academician D.S. Rozhdestvensky. GOI was the center that determined scientific policy in the field of creating a domestic optical-mechanical industry. Outstanding scientists worked at GOI: S.I. Vavilov, A.A. Lebedev, I.V. Grebenshchikov, N. Kachalov and others.
In the post-war years, our optical industry successfully mastered the production of unique high-precision instruments, electron microscopes, interferometers, and instruments for space research.
Based on the phenomena of the photoelectric effect, discovered by the Russian scientist A.G. Stoletov, the photoelectric field of optics is successfully developing, which has found application in automation, television, and spacecraft control.

Among the major achievements of domestic optics are the works of Professor M.M. Rusinov. The wide-angle aerial photography lenses he created brought Soviet aerial photography to a leading position in the world.
The creation of equipment for photographing the far side of the Moon, invisible from the Earth, was the beginning of the development of a new direction in optical instrumentation - cosmic optical instruments.

The research of Soviet physicists N.G. Basov and A.M. Prokhorov in the mid-50s of the 20th century became the seed from which a new field of science grew - quantum electronics. In 1971, Denis Gabor received the Nobel Prize for the discovery of holography.
Back in 1930, in Germany, Lamm transmitted not only light, but also images via optical fibers. But the technology for making glass fibers was very complex, so Lamm’s ideas remained forgotten for many years.

In the 17th century, the first scientific hypotheses about the nature of light were expressed. Light has energy and transfers it in space. Energy can be transferred either by bodies or waves, so two theories have been put forward about the nature of light.
The corpuscular theory of light (from the Latin corpusculum - particle) was proposed in 1672 by the English scientist Isaac Newton (1643 - 1727). According to this theory, light is a stream of particles that are emitted in all directions by a light source. Using this theory, optical phenomena such as, for example, different colors of radiation were explained.
The Dutch scientist Christiaan Huygens (1629 – 1695), also in the 17th century, created the wave theory of light, according to which light has a wave nature. Using this theory, phenomena such as interference, diffraction of light, etc. are well explained.

Both of these theories existed in parallel for a long time, since neither of them separately could fully explain all optical phenomena. By the beginning of the 19th century, after research by the French physicist Augustin Jean Fresnel (1788 - 1827), the English physicist Robert Hooke (1635 - 1703) and other scientists, it became clear that the wave theory of light has an advantage over the corpuscular theory. In 1801, the English physicist Thomas Young (1773 – 1829) formulated the principle of interference (increasing or weakening of illumination when light waves are superimposed on each other), which allowed him to explain the colors of thin films. Fresnel explained what diffraction of light is (the bending of light around obstacles) and the straightness of light propagation.

Yet the wave theory of light had one significant drawback. It was assumed that light radiation is transverse mechanical waves that can only arise in an elastic medium. Therefore, a hypothesis was created about the invisible world ether, which is a hypothetical medium that fills the entire Universe (the entire space between bodies and molecules). The world ether had to have a number of contradictory properties: it had to have the elastic properties of solid bodies and be weightless at the same time. These difficulties were resolved in the 2nd half of the 19th century with the consistent development of the doctrine of the electromagnetic field by the English physicist James Clerk Maxwell (1831 - 1879). Maxwell came to the conclusion that light is a special case of electromagnetic waves.

However, in the early 20th century, the discontinuous, or quantum, properties of light were discovered. These properties were explained by the corpuscular theory. Thus, light has wave-particle duality (duality of properties). During the process of propagation, light exhibits wave properties (that is, it behaves like a wave), and during emission and absorption, it exhibits corpuscular properties (that is, it behaves like a stream of particles).
The laws of light propagation in transparent media based on the concept of a light beam are discussed in the section of optics called Geometric Optics. It is understood that a light beam is a line along which the energy of light electromagnetic waves propagates.

The struggle between the wave and corpuscular concepts of light in the first half of the 19th century ends with the victory of the wave concept - it was established that light is a transverse wave movement. A decisive contribution to this victory was the explanation of the phenomena of diffraction and interference of light using the wave concept.

DEVELOPMENT OF VIEWS ON THE NATURE OF LIGHT

Two ways to communicate interactions

Corpuscular and wave theories of light

PHENOMENON OF LIGHT INTERFERENCE

Addition of two monochromatic waves

Conditions for maxima and minima of the interference pattern

Interference pattern

Why are light waves from two sources not coherent?

Idea by Augustin Fresnel

Fresnel biprism

Light source sizes

Light wavelength

Light wavelength and color of light perceived by the eye

INTERFERENCE PHENOMENON IN THIN FILMS

Thomas Young's idea

Localization of interference fringes

NEWTON'S RINGS

Change in wavelength in a substance

Why films must be thin

SOME APPLICATIONS OF INTERFERENCE

Michelson's experiment

Checking the quality of surface treatment

Optics coating

Interference microscope

Stellar interferometer

Radio interferometer

Bibliography

DEVELOPMENT OF VIEWS ON THE NATURE OF LIGHT

The first ideas of ancient scientists about what light was were very naive. It was believed that special thin tentacles emerge from the eyes and visual impressions arise when they feel objects. There is, of course, no need to dwell in detail on such views, but it is worth briefly following the development of scientific ideas about what light is.

Two ways to communicate interactions

From the source, light spreads in all directions and falls on surrounding objects, causing, in particular, their heating. When light enters the eye, it causes visual sensations - we see. We can say that when light propagates, influences are transferred from one body (light source) to another body (light receiver).

In general, the action of one body on another can be carried out in two different ways: either through the transfer of matter from a source to a receiver, or through a change in the state of the environment in which the bodies are located, i.e. without transfer of substance.

You can, for example, make a bell located some distance away ring by successfully hitting it with a ball. Here we are dealing with the transfer of matter. But you can do it differently: tie a cord to the tongue of a bell and make the bell ring, sending waves along the cord that swing its tongue. In this case, no transfer of substance occurs. Waves propagate along the cord, i.e. the shape of the cord changes. Thus, action from one body to another can also be transmitted through waves.

Corpuscular and wave theories of light

In accordance with two possible methods of transmitting action from source to receiver, two completely different theories arose and began to develop about what light is and what its nature is. Moreover, they arose almost simultaneously in the 17th century. One of these theories is associated with the name of the English physicist Isaac Newton, and the other with the name of the Dutch physicist Christiaan Huygens.

Newton adhered to the so-called corpuscular (from the Latin word corpusculum - particle) theory of light, according to which light is a stream of particles spreading from a source in all directions (i.e. transfer of matter). According to Huygens' ideas, light is waves propagating in a special, hypothetical medium - ether, which fills all space and penetrates into all bodies.

Both theories existed in parallel for a long time. None of them could win a decisive victory. Only Newton's authority forced most scientists to give preference to the corpuscular theory. The experimentally discovered laws of light propagation at that time were more or less successfully explained by both theories. Based on the corpuscular theory, it was difficult to explain why light beams, intersecting in space, do not act on each other. After all, light particles must collide and scatter.

The wave theory easily explained this. Waves, for example, on the surface of water, pass freely through each other without exerting mutual influence. However, the rectilinear propagation of light, leading to the formation of sharp shadows behind objects, is difficult to explain based on the wave theory. According to the corpuscular theory, the rectilinear propagation of light is simply a consequence of the law of inertia. This uncertainty regarding the nature of light lasted until the beginning of the 19th century, when the phenomena of light diffraction (light bending around obstacles) and light interference (strengthening or weakening of light when light beams are superimposed on each other) were discovered. These phenomena are inherent exclusively to wave motion. They cannot be explained using corpuscular theory. Therefore, it seemed that the wave theory had won a final and complete victory.

This confidence was especially strengthened when the English physicist James Clerk Maxwell proved in the second half of the 19th century that light is a special case of electromagnetic waves. Maxwell's work laid the foundations of the electromagnetic theory of light.

After the experimental discovery of electromagnetic waves at the end of the 19th century by the German physicist Heinrich Hertz, there was no doubt that light behaves like a wave when propagating. However, at the beginning of the 20th century, ideas about the nature of light began to change radically. Unexpectedly, it turned out that the rejected corpuscular theory was still related to reality.

It turned out that when emitted and absorbed, light behaves like a stream of particles. The discontinuous, or as physicists call it, quantum, properties of light have been discovered. An unusual situation arose: the phenomena of interference and diffraction could still be explained by considering light to be a wave, and the phenomena of emission and absorption could be explained by accepting that light was a stream of particles. In the 30s of the 20th century, these two seemingly incompatible ideas about the nature of light were able to be united in a consistent way in a new physical theory - quantum electrodynamics. Over time, it became clear that the duality of properties is inherent not only in light, but also in any other form of matter. So, in order to be sure that light has a wave nature, it is necessary to find experimental evidence of interference and diffraction of light.

PHENOMENON OF LIGHT INTERFERENCE

It is known that to observe the interference of transverse mechanical waves on the surface of water, two wave sources were used (for example, two balls mounted on an oscillating rocker). It is impossible to obtain an interference pattern (alternating minimums and maximums of illumination) using two natural independent light sources, for example two light bulbs. Turning on another light bulb only increases the illumination of the illuminated surface. Let's find out what is the reason for this.

Addition of two monochromatic waves

Let's see what happens as a result of the addition of two traveling waves with the same oscillation frequencies. It is known that harmonic light waves are called monochromatic (Subsequently we will see that color is determined by the frequency of the wave (or its length), so a harmonic wave can be called monochromatic (i.e. one-color)). Let these waves propagate from two point sources S1 and S2 located at a distance from each other. We will consider the result of the addition of waves at a distance from the sources that is much greater (i.e.). We will place the screen onto which the light waves fall parallel to the line connecting the sources (see Figure 1).

A light wave is, according to the electromagnetic theory of light, an electromagnetic wave. In an electromagnetic wave propagating in a vacuum, the electric field strength in modulus, in the Gaussian system, is equal to the magnetic induction. We will consider the addition of electric field intensity waves. However, the traveling wave equation has the same form for waves of any physical nature.

So, sources S1 and S2 emit two spherical monochromatic waves. The amplitudes of these waves decrease with distance. However, if we consider the addition of waves at distances r1 and r2 from the sources, much greater than the distance between the sources (i.e. and), then the amplitudes from both sources can be considered equal.

The waves arriving from sources S1 and S2 to point A of the screen have approximately the same amplitudes and the same frequencies ω of oscillations. In general, the initial phases of oscillations in wave sources may differ. The equation of a traveling spherical wave in the general case can be written as follows:

where φ0 is the initial phase of oscillations in the source ().

When two waves are added at point A, a resulting harmonic voltage oscillation occurs:

Here we believe that tension fluctuations occur along one straight line. Let's denote by:

The initial phase of oscillations of the first wave at point A, and through: - the initial phase of oscillations of the second wave at the same point. Then:

for the phase difference we obtain the expression:

The amplitude of the resulting voltage fluctuations at point A is equal to:

It is known that the intensity of radiation I is directly proportional to the square of the amplitude of the voltage oscillations, which means for one wave: I~E, and for the resulting oscillations: I~E. Therefore, for the wave intensity at point A we have:

Conditions for maxima and minima of the interference pattern

The intensity of light at a given point in space is determined by the difference in oscillation phases φ 1 - φ 2. If the source oscillations are in phase, then φ 01 - φ 02 = 0 and:

The phase difference is determined by the difference in distances from the sources to the observation point. Let us recall that the difference in distances is called the difference in the path of interfering waves from their sources. At those points in space for which the following condition is satisfied:

K=0, 1, 2… (3)

the waves cancel each other (I = 0).

As a result, an interference pattern appears in space, which is an alternation of maxima and minima of light intensity, and therefore of screen illumination. The conditions for interference maxima (see formula 3) and minima (see formula 4) are exactly the same as in the case of interference of mechanical waves.

Interference pattern

If any plane is drawn through the sources, then the maximum intensity will be observed at points of the plane that satisfy the condition:

These points lie on a curve called a hyperbola. It is for the hyperbola that the condition is satisfied: the difference in distances from any point on the curve to two points, called the foci of the hyperbola, is a constant value. This results in a family of hyperbolas corresponding to different values ​​of k when the light sources are the focal points of the hyperbola.

When the hyperbola rotates around an axis passing through the sources S1 and S2, two surfaces are obtained that form a two-cavity hyperboloid of revolution (see Figure 2), when different values ​​of k correspond to different hyperboloids. The interference pattern on the screen depends on the location of the screen. The shape of the interference fringes is determined by the lines of intersection of the screen plane with these hyperboloids. If the screen A is perpendicular to the line l connecting the light sources S1 and S2 (see Figure 2), then the interference fringes have the shape of circles. If screen B is located parallel to the line connecting the light sources S1 and S2, then the interference fringes will be hyperbolas. But these hyperbolas, with a large distance D between the light sources and the screen near point O, can be approximately considered as segments of parallel straight lines.

Let's find the distribution of light intensity on the screen (see Figure 1) along the straight line MN parallel to the line S1S2. To do this, we find the dependence of the phase difference (see formula 2) on the distance: h=OA. Applying the Pythagorean theorem to triangles and, we get:

Subtracting the second equality term by term from the first, we find:

Counting l<

The light intensity (see formula 1) changes with h:

The graph of this function is shown (see Figure 3). The intensity changes periodically and reaches maximums provided:

K=0, 1, 2,… (6)

The value hk determines the position of the maximum number k.

Distance between adjacent maxima:

It is directly proportional to the light wavelength λ and the greater, the smaller the distance l between the light sources compared to the distance D to the screen.

In reality, the intensity will not be constant from one interference maximum to another interference maximum, nor will it remain constant along one interference fringe. The fact is that the amplitudes of light waves from light sources S1 and S2 are exactly equal, only at point O. At other points they are only approximately equal.

As in the case of mechanical waves, the formation of an interference pattern does not mean the transformation of light into any other forms. It is only redistributed in space. The average value of the total light intensity is equal to the sum of the intensities from two light sources. Indeed, the average value of light intensity over the entire length of the interference pattern (see formula 5) is equal to 2I0, since the average value of the cosine for all possible values ​​of the argument depending on h is zero.

Why are light waves from two sources not coherent?

The interference pattern from two sources that we have described arises only when monochromatic waves of the same frequencies are added. For monochromatic waves, the phase difference between oscillations at any point in space is constant. Waves with the same frequency and constant phase difference are called coherent. Only coherent waves, superimposed on each other, give a stable interference pattern with a constant location in space of the maxima and minima of oscillations. Light waves from two independent sources are not coherent.

The atoms of the sources emit light independently of each other in separate “scraps” (i.e., trains) of sine waves. The duration of continuous radiation of an atom is about 10 -8seconds During this time, the light travels a path about 3 m long (see Figure 4).

These wave trains from both sources are superimposed on each other. The phase difference of oscillations at any point in space changes chaotically with time, depending on how the trains from different sources are shifted relative to each other at a given moment in time. Waves from different light sources are not coherent due to the fact that the difference in the initial phases does not remain constant (the exception is quantum light generators - lasers created in 1960). Phases φ 01And φ 02change randomly, and because of this, the phase difference of the resulting oscillations changes randomly at any point in space.

With random “breaks” and “emergences” of oscillations, the phase difference changes randomly, taking on all possible values ​​from 0 to 2 during the observation period π . As a result, over time τ , much longer than the time of irregular phase changes (about 10 -8seconds), average value cos( φ 1-φ 2) in the formula for intensity (see formula 1) is equal to zero. The light intensity turns out to be equal to the sum of the intensities from the individual sources, and no interference pattern will be observed.

The incoherence of light waves is the main reason why light from two sources does not produce an interference pattern. This is the main, but not the only reason. Another reason is that the wavelength of light, as we'll see shortly, is very, very short. This makes it very difficult to observe interference, even if we have coherent wave sources. So, in order for a stable interference pattern to be observed when light waves are superimposed, it is necessary that the light waves be coherent, i.e. had the same wavelength and constant phase difference.

Idea by Augustin Fresnel

To obtain coherent light sources, the French physicist Augustin Fresnel found a simple and ingenious method in 1815. It is necessary to divide the light from one source into two beams and, forcing them to take different paths, bring them together. Then the train of waves emitted by an individual atom will split into two coherent trains. This will be the case for trains of waves emitted by each atom of the source. Light emitted by one atom gives a certain interference pattern. When these patterns are superimposed on each other, a fairly intense distribution of illumination on the screen is obtained: the interference pattern can be observed.

There are many ways to obtain coherent light sources, but their essence is the same. By dividing the beam into two parts, two imaginary light sources are obtained that produce coherent waves. For this, two mirrors (Fresnel bi-mirrors), a Fresnel biprism (two prisms folded at the bases), a bilens (a lens cut in half with the halves apart) and much more are used. Now we will take a closer look at one of the devices.

Fresnel biprism

A Fresnel biprism consists of two prisms with small refractive angles placed together (see Figure 5). Light from source S falls on the upper faces of the biprism, and after refraction, two light beams appear.

The continuations of the rays refracted by the upper and lower prisms in the opposite direction intersect at two points S 1and S 2, which are virtual images of the source S. For small values ​​of refractive angles θ prism, the source and its two imaginary images lie practically in the same plane. The waves in both beams are coherent, since they are actually emitted by the same source.

Both beams overlap and interfere. The interference pattern described earlier appears.

A very clear proof that we are dealing with interference is a simple change in the experiment. If one half of the biprism is covered with an opaque screen, then the interference pattern disappears, since there is no superposition of waves. The distance between the interference fringes (see formula 7) depends on the length of the interfering waves λ , distance b from the biprism to the screen, distance l between imaginary light sources. Let's calculate this distance.

To calculate l, the easiest way is to consider the path of a ray incident normally on a prism (i.e., perpendicular to its surface). In reality there is no such beam, but it can be constructed by mentally continuing the refracting facet of the prism (see Figure 6). The continuations of all rays incident on the face of the prism intersect at point S1 - the imaginary source. As can be seen from the figure, and, where a is the distance from the source to the biprism. According to the law of refraction for small angles: . (The angles are small when the refractive angle of the prism is small and when a is much larger than the size of the biprism.)

Distance:

The distance between the interfering bands (see formula 8) is equal to:

where b is the distance from the biprism to the screen.

Thus, the smaller the refractive angle of the prism θ, the greater the distance between the interference maxima. Accordingly, the interference pattern is easier to observe. That is why a biprism must have small refractive angles.

Light source sizes

To observe interference using a biprism and similar devices, the geometric dimensions of the light source must be small. The fact is that groups of atoms on the left, for example, part of the source, give their own interference pattern, and on the right - theirs. These patterns are offset relative to each other (see Figure 7).

With a large light source, the maxima of one interference pattern will coincide with the minima of another interference pattern and, as a result, the interference pattern will be “smeared” (i.e., the illumination of the screen will become uniform).

Light wavelength

The interference pattern allows us to determine the wavelength of light. This can be done, in particular, in experiments with a biprism. Knowing the distances a and b, as well as the refractive angle of the biprism θ and its refractive index n, measuring the distances between interference maxima Δ h, the light wavelength can be calculated (see formula 8). When a biprism is illuminated with white light, only the central maximum remains white, and all other maximums have a “rainbow” color. Closer to the center of the interference pattern, a violet color appears, and further than the center of the interference pattern, a red color appears. This means (see formula 6) that the wavelength of light perceived by the eye as red is maximum, and the wavelength of light perceived by the eye as violet is minimum. Interference maximum distance from center:

Only at k=0, hk=0 for all wavelengths, so the “zero” maximum is not “rainbow”, but white. The dependence of the color of light perceived by the eye on the wavelength of light can be easily detected by placing various light filters in the path of white light incident on the biprism. The distances between maxima for red light rays are greater than for yellow light rays, than for green light rays and all other ray colors. Measurements are given for red light in meters, and for violet light in meters. The wavelengths corresponding to other colors of the spectrum have values ​​intermediate to the above-mentioned light wavelengths.

For any color, the wavelength of light is very, very small. Some visual representation of the wavelength of light can be obtained from the following comparison. If a sea wave, several meters long, were to increase by the same number of times as the length of the light wave would need to be increased in order for it to be equal to the width of this report on my course work, then throughout the entire Atlantic Ocean (from New York in the USA to Lisbon in Portugal) would fit only one sea wave. But still, the length of light is approximately a thousand times greater than the diameter of one atom, which is approximately equal to m.

Light wavelength and color of light perceived by the eye

The phenomenon of interference not only proves that light has wave properties, but also allows us to measure the wavelength of light. At the same time, it turns out that just as the pitch of sound perceived by the ear is determined by the frequency of propagating mechanical vibrations, the color of light perceived by the eye is determined by the frequency of propagating electromagnetic vibrations belonging to the “Visible Light” range. Knowing on what physical characteristic of a light wave the color perception of light depends, we can give a deeper definition of the phenomenon of light dispersion. Dispersion should be called the dependence of the refractive index of an optically transparent medium not on the color of the propagating light, but on the frequency of the propagating electromagnetic oscillations.

Outside of us in nature there are no colors, there are only electromagnetic vibrations of various frequencies, propagating in the form of electromagnetic waves of various lengths. The eye is a complex physical device capable of distinguishing insignificant (about 10 -6cm) difference in light wavelength. It is interesting that most animals, including dogs, are unable to distinguish colors, but only distinguish the intensity of light, i.e. they see a black and white picture, as in a non-color movie or on a non-color TV screen. Colorblind people who suffer from color blindness also cannot distinguish colors.

INTERFERENCE PHENOMENON IN THIN FILMS

So, Fresnel came up with a method for producing coherent waves to observe the phenomenon of interference of light. However, he was not the first to observe the phenomenon of interference and he was not the one who discovered the phenomenon of light interference for humanity. Somewhat curious was that the phenomenon of light interference had been observed for a very long time, but they were not aware of it. Many people have had to observe an interference pattern many times, when in childhood, while having fun blowing soap bubbles, they saw their iridescent colors in all the colors of the rainbow, or they repeatedly saw a similar picture on the surface of water covered with a thin film of petroleum products.

Thomas Young's idea

The English physicist Thomas Young was the first to come up with the brilliant idea in 1802 about the possibility of explaining the colors of thin films by the superposition of light waves, one of which is reflected from the outer surface of the film, and the second from the inner. (In fairness, it should be noted that when publishing his work on the phenomenon of interference, Fresnel knew nothing about Young’s work) Light waves, since they are emitted by one atom S of an extended light source (see Figure 8). Light waves 1 and 2 strengthen or weaken each other depending on the path difference. This path difference Δr arises due to the fact that light wave 2 travels an additional path AB + BC inside the film, while light wave 1 travels only an additional distance DC. It is easy to calculate that, neglecting the refraction of light (i.e.), the path difference is:

where h is the film thickness, α is the angle of incidence of light. Light amplification occurs if the path difference Δr of light waves 1 and 2 is equal to an integer number of wavelengths, and light attenuation occurs when the path difference Δr is equal to an odd number of half-wavelengths.

Light waves corresponding to different colors have different wavelengths. To mutually cancel longer light waves, a greater film thickness is “needed” than to mutually cancel shorter light waves. Therefore, if the film has unequal thickness in different places, then different colors should appear when the film is illuminated with white light.

The phenomenon of interference in thin films is observed when their surface is illuminated by very extended light sources, even when illuminated by diffuse light from a cloudy sky. There is no need for strict restrictions on the size of the source, as in Fresnel’s experiments with a biprism and other devices. But in Fresnel's experiments the interference pattern is not localized. The screen behind the biprism (see Figure 5) can be placed in any place where light beams from imaginary sources overlap. The interference pattern in thin films is already localized in a certain way, since to observe it on the screen you need to use a lens to obtain an image of the film surface on it, because during visual observation the image of the film surface is obtained on the retina of the eye.

In this case, light rays from different parts of the source falling on the same place on the film are then collected together on the screen (or on the retina of the eye) (see Figure 9). For any pair of light rays, the path difference is approximately the same, since the film thickness is the same for them, and the angles of incidence differ very slightly. Rays with very different angles of incidence will not hit the lens, much less the pupil of the eye, which has very small dimensions.

Since for all sections of film of equal thickness the path difference of the interfering rays is the same, then, consequently, the illumination of the screen on which the image of these sections is obtained is the same. As a result, stripes are visible on the screen, each of which corresponds to the same film thickness. That's why they (strips) are called that - strips of equal film thickness.

If the surface of the light source is focused on the screen, then light rays from a given area of ​​the surface of the light source fall into the same point on the screen after reflection from different areas of the surface of the film having different thicknesses (see Figure 10). Therefore, the interference pattern on the screen turns out blurry, since for different pairs of light rays the path difference is different due to different film thicknesses.

NEWTON'S RINGS

A simple interference pattern appears in a thin layer of air between a glass plate and a plane-convex lens of large radius of curvature placed on it. This interference pattern of lines of equal thickness takes the form of concentric rings called Newton's rings.

Let's take a lens with a large focal length F (and, investigator, with a small curvature of its convex surface) and place its convex side on a flat glass plate. Carefully examining the surface of the lens (preferably through a magnifying glass), we will find a dark spot at the point of contact between the lens and the plate and small rainbow rings around it. The distance between adjacent rings decreases rapidly as their radius increases (see photo 1). These are Newton's rings. They were first discovered by the English physicist Robert Hooke, and Newton studied them not only in white light, but also when the lens was illuminated with single-color (i.e., monochromatic) light. It turned out that the radii of the rings increase in proportion to the square root of the ring's serial number, and the radii of rings of the same serial number increase when moving from the violet end of the visible light spectrum to the red (see photos 2 and 3). Newton could not explain why rings appeared, since he was an ardent supporter of the corpuscular theory of light. For the first time, Jung managed to do this based on the phenomenon of interference. Let's calculate the radii of Newton's dark rings. To do this, you need to calculate the difference in the path of two rays reflected from the convex surface of the lens at the glass-air boundary and from the surface of the plate at the air-glass boundary (see Figure 11).

Radius r k ring number k is related to the thickness of the air layer by a simple relationship. According to the Pythagorean theorem (see Figure 12):

where R is the radius of curvature of the lens. Since the radius of curvature of the lens is large compared to h, then h<

The second light wave travels a path 2hk longer than the first. However, the path difference turns out to be greater than 2hk. When a light wave is reflected, just as when a mechanical wave is reflected, the phase of oscillations can change by π, which means that the difference increases by an additional factor. It turns out that when a light wave is reflected at the boundary of a medium with a large refractive index, the phase of the oscillations changes by π. (the same thing happens with a mechanical wave traveling along a rubber cord, the other end of which is rigidly fixed.) When reflected from an optically less dense medium, the phase of oscillations does not change. In this case, the phase of the light wave changes only when reflected from the glass plate.

Taking into account the additional increase in the path difference, the condition for minima of the interference pattern will be written as follows:

K=0, 1, 2,… (10)

Substituting expression (8) for hk into this formula, we determine the radius of the dark ring k depending on λ and R:

The dark ring in the center (k=0, hk = 0) arises due to a phase change by π upon reflection from the glass plate.

The radii of the light rings are determined by the expression:

K=0, 1, 2,… (12)

Change in wavelength in a substance

It is known that when light passes from one medium to another, the wavelength changes. It can be detected like this. Let's fill the air gap between the lens and the plate with water or another transparent liquid with refractive index n. The radii of the interference rings will decrease. Why is this happening?

We know that when light passes from a vacuum into any medium, the speed of light decreases by a factor of n. Since, in this case, either the frequency or the wavelength of the light must decrease. But the radii of the rings depend on the wavelength of light. Therefore, when light enters a medium, it is the wavelength that changes n times, not the frequency.

Why films must be thin

When observing interference in thin films, there are no restrictions on the size of the light source, but there are restrictions on the thickness of the film. In window glass we will not see an interference pattern similar to that produced by thin films of kerosene and other liquids on the surface of water. Look again at photo 1 of Newton's rings in white light. As you move away from the center, the thickness of the air gap increases. In this case, the distances between the interference maxima decrease, and with a sufficiently large thickness of the interlayer, the entire interference pattern is blurred, and the rings are not visible at all.

The fact that the difference in the radii of neighboring rings decreases with increasing order of the spectrum k follows from formulas 9 and 10. But it is not clear why the interference pattern disappears altogether at large k, i.e. with large air gap thicknesses h.

The thing is that light is never strictly monochromatic. It is not an infinite monochromatic wave that falls on the film (or air gap), but a finite train of waves. The less monochromatic the light, the shorter this train. If the train length is less than twice the film thickness, then light waves 1 and 2 reflected from the film surfaces will never meet (see Figure 13).

Let us determine the thickness of the film at which interference can still be observed. Non-monochromatic light consists of different wavelengths. Let us assume that the spectral interval is equal to Δλ, i.e. all wavelengths from λ to λ+Δλ are present.

Then each value of k corresponds not to one interference line, but to a multi-colored stripe. To prevent the interference pattern from being blurred, it is necessary that the bands corresponding to adjacent values ​​of k do not overlap. In the case of Newton's rings it is necessary that. Substituting the radii of the rings from formula 13, we get:

This gives us the condition:

If, then k must be large and:

So, the width of the spectral interval must be much less than the light wavelength λ divided by the order of the spectrum k. This relationship is valid not only for Newton’s rings, but also for interference in any thin films.

SOME APPLICATIONS OF INTERFERENCE

The applications of interference are very important and vast.

There are special devices - interferometers, the operation of which is based on the phenomenon of interference. Their purpose can be different: Precise measurements of light wavelengths, measurement of the refractive index of gases, and others. There are interferometers for special purposes. About one of them, designed by Michelson to record very small changes in the speed of light.

Michelson's experiment

In 1881, the American physicist Albert Abraham Michelson conducted an experiment to test the hypothesis of the Dutch theoretical physicist Hendrik Anton Lorentz, according to which there should be a selected frame of reference associated with the world ether, which is at absolute rest. The essence of this experiment can be understood with the help of the following example.

From city A, the plane flies to cities B and C (see Figure 14, a). The distances between cities are the same and equal to l = 300 km, and the route AB is perpendicular to the route AC. The speed of the aircraft relative to the air is c = 200 km/h. Let the wind blow in the direction AB at a speed υ =10 km/h. The question is: which flight will take longer: from A to B and back or from A to C and back?

In the first case, the flight time is equal to:

In the second case, the plane should head not towards the city C itself, but towards some point D, lying against the wind (see Figure 14, b). The plane will fly a distance AD ​​relative to the air. The air flow carries the plane to a distance DC. The ratio of these distances is equal to the ratio of speeds:

Relative to the Earth, the plane will fly the distance AC.

Since (see Figure 14 b), then.

But: , therefore.

Consequently, the time t2 spent by the aircraft to travel this path there and back at speed c is determined as follows:

The time difference is obvious. Knowing it, as well as the distance AC and speed c, you can determine the speed of the wind relative to the Earth.

A simplified diagram of Michelson's experiment is shown in Figure 15. In this experiment, the role of an airplane is played by a light wave with a speed of 300,000 km/s relative to the ether. (There was no doubt about the existence of the ether at the end of the 19th century.) The role of the ordinary wind was played by the supposed “etheric wind” blowing the Earth. Relative to the stationary ether, the Earth cannot be at rest all the time, since it moves around the Sun at a speed of about 30 km/s and this speed continuously changes direction. The role of city A was played by a translucent plate P, dividing the flow of light from the source S into two mutually perpendicular beams. Cities B and C are replaced by mirrors M 1them 2, directing the light beams back.

Next, both beams were connected and entered the telescope lens. In this case, an interference pattern appeared, consisting of alternating light and dark stripes (see Figure 16). The location of the stripes depended on the difference in time on one and on the other path.

The interferometer was installed on a square stone slab with sides of 1.5 m and a thickness of more than 30 cm. The slab floated in a bowl of mercury so that it could be rotated around a vertical axis without shaking (see Figure 17).

The direction of the "ethereal wind" is unknown. But when the interferometer rotates, the orientation of the light paths OM 1and OM 2(see Figure 15) relative to the “ethereal wind” should have changed. Consequently, the difference in the travel times of the OM paths should have changed 1and OM 2, and therefore the interference fringes in the field of view of the tube should have shifted. From this displacement they hoped to determine the speed of the “ethereal wind” and its direction.

However, to the surprise of scientists, the experiment showed that no shift of the interference fringes occurs when the interferometer is rotated. The experiments were carried out at different times of the day and at different times of the year, but always ended with the same negative result: the movement of the Earth in relation to the “ether” could not be detected. The accuracy of the latest experiments was such that they could detect a change in the speed of light propagation (when the interferometer is rotated) even by 2 m/s.

All this was similar to what it would be like if you, sticking your head out of the window of a carriage, at a speed of 100 km/h, would not notice the pressure of the air flow counter to the train.

Thus, Lorentz's hypothesis about the existence of a preferential frame of reference was not confirmed in the process of experimental testing. In turn, this meant that no special medium - the “luminiferous ether” - with which such a preferential frame of reference could be associated existed.

Checking the quality of surface treatment

Another significant application of the interference phenomenon is testing the quality of surface finishes. It is with the help of interference that the quality of polishing of a product can be assessed with an error of up to 0.01 microns. To do this, you need to create a thin layer of air between the surface of the sample and a very smooth reference plate (see Figure 18).

Then irregularities on the ground surface of the product exceeding 0.01 μm will cause noticeable curvatures of interference fringes, which are formed when light is reflected from the surface being tested and the lower edge of the reference plate.

In particular, the quality of the surface grinding of the lens being manufactured can be checked by observing Newton's rings. The rings will be regular circles only if the surface of the lens is strictly spherical. Any deviation from sphericity greater than 0.1 of the length of the interfering light waves will noticeably affect the shape of the rings. In the place where there is a distortion of geometrically regular sphericity on the surface of the lens being manufactured, Newton's rings will not have the shape of a geometrically regular circle.

It is curious that back in the middle of the 17th century, the Italian physicist Evangelista Torricelli was able to grind lenses with an accuracy of up to 0.01 microns. His lenses are kept in the museum, and the quality of their surface treatment has been tested using modern methods. How did he manage to do this? No one can answer this question unequivocally, since at that time the secrets of the craft were usually not given out. Apparently, Torricelli discovered interference rings long before Newton and guessed that they could be used to check the quality of grinding. But, of course, Torricelli could not have any idea why the rings appear.

Let us also note that, using almost strictly monochromatic light, one can observe the interference pattern when reflected from planes located at a large distance from each other (on the order of several meters). This allows you to measure distances of hundreds of centimeters with an error of up to 0.01 µm.

Optics coating

Another important application of the interference phenomenon in practice is the clearing of optics. Optical lenses of modern cameras and film projectors, submarine periscopes and many, many other optical devices consist of a large number of optical glasses - lenses, prisms, etc. Passing through such devices, light is partially reflected at the interface between two optically transparent media, with each lens having at least two such surfaces. The number of such reflective optically transparent surfaces in modern photographic lenses exceeds a dozen, and in submarine periscopes this number reaches forty. When light is incident perpendicular to an optically transparent surface, 5% to 9% of the light energy is reflected from each such surface. Therefore, only 10% to 20% of the light energy that “falls” on the first of the optically transparent surfaces often passes through the optical system of the lenses. As a result, the illumination of the resulting image is extremely weak. In addition, image quality deteriorates. Part of the light beam, after repeated reflection from internal optically transparent surfaces, still passes through the optical system and, being scattered, no longer participates in creating a clear image. In photographic images, for example, a “veil” appears for this reason.

To eliminate these unpleasant consequences of multiple reflection of light from optically transparent surfaces, it is necessary to reduce the proportion of reflected light energy from each of these surfaces. The image produced by the optical system becomes brighter, i.e., as physicists say, “brightened.” This is where the term “coating of optics” comes from.

Optical clearing is based on the phenomenon of interference. A thin film with a refractive index n less than the lens index n is applied to an optically transparent surface, such as a lens. For simplicity, let's consider the case of normal incidence of light on the film (see Figure 19).

The condition that the light waves reflected from the upper and lower surfaces of the film cancel each other will be written (for a film of minimal thickness) as follows:

where is the light wavelength in the film, and 2h is the path difference of the interfering waves. In the case when the refractive index of air is less than the refractive index of the film, and the refractive index of the film is less than the refractive index of glass, a phase change occurs. As a result, these reflections do not affect the phase difference between waves 1 and 2; it is determined only by the thickness of the film.

If the amplitudes of both reflected waves are the same or very close to each other, then the light extinction will be complete. To achieve this, the refractive index of the film is selected accordingly, since the intensity of the reflected light is determined by the ratio of the refractive indices of the two optically transparent adjacent media. Under normal conditions, white light falls on the lens. The expression (see formula 13) shows that the required film thickness depends on the wavelength of the light. Therefore, it is impossible to suppress reflected light waves of all frequencies. The film thickness is selected so that complete extinction at normal light incidence occurs for light wavelengths in the middle part of the visible light spectrum (i.e. for green light, the wavelength of which is λ3 = 550 nm), it should be equal to a quarter of the light wavelength in film:

It should be noted that in practice a layer is applied whose thickness is an integer number of light wavelengths greater, since this is much more convenient. An industrial method for applying thin transparent films to transparent surfaces was developed by Russian physicists I. V. Grebenshchikov and A. N. Terenin.

The reflection of light from the extreme parts of the visible light spectrum - red and violet - is slightly attenuated. Therefore, an optical lens with coated optics has a lilac tint in reflected light. Nowadays even the simplest cameras have coated optics.

Interference microscope

The first interference microscope was created in St. Petersburg by Russian physicist Alexander Lebedev in 1931. In this microscope, two beams of light interfere, one of which passed by the object, and the other through the object (accordingly, they can be called the reference and working beams). Of course, to obtain a stable interference pattern, the waves must be coherent, i.e. have a constant phase difference over time. The distribution of this difference in space, created by the observed object, is manifested in the interference contrast of the image (from the French kontraste - opposite).

Interference contrast has the advantage (over phase contrast) that it clearly manifests itself not only with sharp, but also with smooth changes in the refractive index and thickness of individual sections of the object. As a result, the distribution of illumination in the image depends only on the phase shift introduced by these areas, but not on their shape or size, and the image does not have halos inherent in phase-contrast images. Further, an interference microscope can produce both black and white and color images when working in white light. The fact is that as a result of interference, waves of certain wavelengths can cancel each other out, and then the image is painted in complementary colors. Since the eye is very sensitive to color contrast, this provides a great advantage over a phase contrast microscope, which only observes contrast between shades of the same color.

But the main advantage of an interference microscope is that it allows not only to note phase differences from different parts of an object, but also to measure the corresponding path differences of light rays, i.e. or the difference in refractive index at the same thickness, or the difference in thickness at the same refractive index. The measured stroke differences can be converted into concentration, dry matter mass in the preparation and other valuable quantitative information can be obtained. For this reason, an interference microscope is used mainly for quantitative studies, while a phase-contrast microscope is used for visual observation of objects that do not introduce amplitude contrast, i.e. practically non-absorbing light. Implementing an interference microscope (see Figure 20) is much more difficult than a phase-contrast microscope. First of all, since a ray of light must be divided into two even before it falls on an object, generally speaking, two optical systems are needed - one for each of the rays - and to a very high degree identical to each other. Only then, after the convergence of the rays, will it be possible to guarantee that the interference pattern is entirely caused only by the object placed in the path of these rays.

Since coherent waves must interfere, any difference in the path of the rays in both branches of the interference microscope should not significantly exceed the so-called coherence length. This length for white light is only about meters and increases as the wavelength range of the light used is narrowed, i.e. with increasing degree of monochromaticity. Different elements of the subject introduce different phase shifts, and they appear in the image with unequal contrast. Usually the phase shift is very small compared to 180 (in other words, the path difference between the working and reference beams is much less than the half-wavelength), and when the lengths of both arms of the interference microscope are the same or differ by an integer number of wavelengths, the image of the object appears dark against a light background. If the lengths of the interferometer branches differ by an odd number of half-waves, then the image, on the contrary, looks light against a dark background. It is no coincidence that the word “interferometer” is used here. An interference microscope is essentially a microinterferometer - a device for measuring small path differences, allowing one to observe the details of microscopic objects.

Stellar interferometer

Naturally, the interference principle can be applied when observing not only bacteria, but also when observing stars. This is so obvious that the idea of ​​an interference telescope arose half a century before the appearance of the interference microscope. But the same phenomenon in these two applications served completely different purposes. If in an interference microscope interference is used to observe the directly invisible structure of objects that do not provide amplitude contrast, then in a telescope, with its help, it is as if they tried to go beyond the resolution limit, which is dictated by the diffraction formula:

The need to increase the resolution of the telescope was dictated by the need to get an idea of ​​the size of the stars. One of the largest stars, Alpha Orion, known as Betelgeuse, has an angular diameter of only 0.047 arcseconds. To determine such insignificant angular dimensions, the principle of parallax was first used: the results obtained from two observations at points located, say, at opposite ends of the diameter of the earth's orbit, were compared, i.e. results of winter and summer measurements of the positions of stars in the sky. Then they began to build larger telescopes. But even the largest modern telescope (installed in the North Caucasus) with a mirror diameter of 6 meters has a resolution of 0.02 arc seconds, while the vast majority of astronomical objects have tens and hundreds of times smaller angular sizes.

In the last third of the 19th century, the French physicist Armand Hippolyte Louis Fizeau and Michelson proposed to improve this situation using a seemingly simple technique. Let's close the telescope lens with a diaphragm in which two small holes are made. Let's consider what happens when observing two point sources in the sky. Each of them will create its own interference pattern in the telescope, formed by the addition of waves from two small holes in the diaphragm, and the patterns will be shifted relative to each other by an amount determined by the difference in the path of light waves from the sources to the telescope. If this path difference is equal to an even number of half-waves, then the pictures will coincide and the overall picture will become clearer. If the path difference is equal to an odd number of half-waves, then the maxima of one interference pattern will fall on the minima of the other and the overall picture will be most blurred. You can vary this path difference by changing the distance d between the holes in the diaphragm, and at the same time observe how the interference fringes (if the holes in the diaphragm look like narrow slits) will become more or less distinct. The first minimum of band clarity will occur when:

where is the angular distance between sources in the sky. From here, knowing and d can be determined. Similarly, if instead of two sources we consider one extended source with angular dimensions, then we find:

where k = 1.22 for a round source with uniform brightness and k > 1.22 for the same source, whose brightness decreases from the center of the disk to its edges.

But does this result in any gain in resolution? Let us compare, for example, formulas (14) and (15). Let's put D = 1 m, then according to formula (14) arc seconds. Let the distance between the slits in the telescope diaphragm also be the limit - 1 m. Taking the value of m in the middle of the visible range, we obtain arcseconds. Does it mean there is no gain? Certainly. It cannot exist, just like in an interference microscope. But the value itself can now be measured. This is a very important advantage.

But the matter does not end there, it is just beginning. Michelson came up with the idea to “push” the holes in the diaphragm far beyond the telescope lens. This, of course, should not be taken literally: the holes themselves remained in their original places, but the light from the stars fell on them not directly, but first on two stationary distant mirrors (see Figure 21), from which the light was reflected by two other mirrors on holes in the diaphragm. And this turned out to be equivalent to what would happen if the diameter of the telescope lens increased to the distance between the mirrors located at a distance from each other, and accordingly the resolution increased by the same amount. Using such a stellar interferometer, Michelson made the first reliable measurements of the diameters of giant stars.

However, even a distance of 6 m between the mirrors in the first stellar interferometer turned out to be clearly insufficient. From formula (14) you can see that at D=6m =0.02 arc seconds. Meanwhile, the vast majority of stars are not gigantic, but approximately “solar” in size. The Sun, if placed at the distance of the nearest star (a star in the constellation Centaurus), would be visible as a disk with angular dimensions of 0.007 arcseconds and would require a telescope with mirrors spaced a good 20 m apart to measure its dimensions. The construction of such a telescope is extremely difficult , since a very rigid mechanical structure is needed.

During the observation process, the distances between the mirrors and the eyepiece can change only by fractions of the light wavelength, while these distances themselves are almost a billion times greater than the light wavelength! However, even the first Michelson interference telescope had another noticeable advantage over a conventional, non-diaphragm telescope. Observations of stars are carried out, as a rule, from the surface of the Earth (space astronomy is just in its infancy). On the way to telescopes, starlight passes through the Earth's turbulent atmosphere, in which turbulent air currents are constantly present. Due to chaotic changes in the density and refractive index of air, stars flicker and their images in a non-diaphragm telescope are greatly distorted. In an interference telescope, the influence of atmospheric disturbances is much weaker due to the small holes in the diaphragm. Slow fluctuations of the refractive index of air lead to the fact that the interference pattern “creeps” across the field of view, but almost does not change its appearance, i.e. The relative position and contrast of the interference fringes do not change (see Figure 22).

Radio interferometer

In the 40s of the 19th century, a new range of electromagnetic waves began to be used for astronomical research - radio emission from space objects. Radio telescopes and radio interferometers appeared. The largest radio telescopes have an antenna mirror diameter of about 100 m. This is much larger than the diameter of the mirror of the largest optical telescope, but let’s not forget that radio wavelengths are tens of thousands of times longer than light wavelengths, so the resolution of a radio telescope is thousands of times worse than that of its optical counterpart . So, for a 6-meter optical telescope, as mentioned above, it is approximately 0.02 arcseconds, while for a 100-meter radio telescope operating, say, at a length of 0.1 m, it is only about 4 arcseconds seconds

To achieve better resolution, individual radio telescopes began to be “combined” into radio interferometers, considering their antennas as mirrors in a Michelson stellar interferometer. Now it was possible to take almost the diameter of the globe as the base of the interferometer. It is easy to calculate that the resolution has improved by several orders of magnitude. It currently reaches approximately 0.001 fractions of an arcsecond, i.e., at least 20 thousand times higher than that of the largest optical telescope.

But such radio interferometers with ultra-long bases create their own big problems. In an optical telescope, interfering beams are brought together using mirrors and a lens. How can you combine radio waves received by two very distant radio telescopes to make them interfere? Many complications immediately arise, most of which rest on the main physical problem: how to maintain the coherence of radio waves received by two radio telescopes. Even if we assume that a radio wave from one cosmic source, without experiencing any distortions in the atmosphere, arrived at two radio telescopes and completely retained coherence in them, then this wave can easily be eliminated. It is unrealistic to pull cables from radio telescopes into a single center in which high-frequency currents from receivers corresponding to received radio waves will be added. We're not even talking about noise in the receivers and cables themselves, which leads to chaotic phase changes in the signals and disrupts their coherence.

As a result, each person has to register signals from radio waves on his own radio telescope and, instead of radio waves, “compile” their recordings on magnetic tapes. To compare two or more records made (since more than two radio telescopes can participate in the observation, moreover, there are also multi-beam interferometers in optics), at first glance, not much is needed: to tie the beginning moments of these records to each other, i.e. e. use the same clock. However, this is by no means simple. The antennas receive waves not of one frequency, but in a whole range of frequencies, determined by the bandwidth. Let, say, a radio telescope operate at a wavelength of 1 m, i.e. at a frequency of 300 MHz, and let the selectivity of its reception be 0.003, i.e. The frequency band perceived by the antenna is 1 MHz. The required synchronization accuracy is equal to the reciprocal of the frequency bandwidth of the radio signal perceived by the antenna, i.e. in this case 1 microsecond. In other words, uniform time stamps when recording on magnetic tape must have such accuracy. It is clear that it is difficult to do this from one center. Each radio telescope must have its own clock, at some point checked with other clocks at other radio telescopes and running with an accuracy no worse than specified.

But this is not enough. Recordings of currents caused by a radio wave in the receiver cannot be directly recorded either on paper or on magnetic tape: the frequency of the wave is too high for such inertial recorders. You have to do as in normal broadcast reception: mix and heterodyne the incoming signal with the signal of a local constant frequency generator (when operating at a radio frequency of 300 MHz, the frequency of the local generator should be close to it), and a difference frequency of about 1 MHz can be recorded on magnetic tape. But this means that local frequency generators also need to be synchronized; in other words, the oscillations they produce in different radio telescopes must be mutually coherent during the time the radio waves are recorded. When recording a signal, for example, at a frequency of 300 MHz for several minutes, the frequency stability of the local generator should not be less than a billionth of a percent!

Synchronization of clocks and stabilization of the frequency of generators, which require such fantastic accuracy, are unthinkable without the use of atomic standard frequencies - quantum generators. In the radio frequency range, quantum generators are often called masers, in the visible light frequency range and close to it - lasers. It was the use of such instruments that made the most complex interferometric experiments feasible and required the development of the above-mentioned theory of radiation coherence, which, however, began to develop even before the advent of new optical technology and radio technology.

So, it was precisely this comparison of independently made records (synchronized, of course) that made modern interferometry of cosmic radio emission possible and made it possible to resolve and measure such cosmic sources that are inaccessible to optical astronomy. This research method (first proposed by the American physicists Brown and Twiss) was called intensity interferometry, because it directly calculates the correlation of photon numbers (light intensity), and does not consider the contrast of the interference pattern.

In conclusion, we emphasize once again that extinguishing light with light does not mean converting light energy into other types of energy. As with the phenomenon of interference of mechanical waves, the cancellation of waves by each other in a given area of ​​space means that light energy simply does not enter this area. Attenuation of reflected waves in an optical lens with coated optics means that almost all the light passes through such a lens.

wave light monochromatic interference

Bibliography

1.Born M., Wolf E., Fundamentals of Optics, translated from English, 2nd edition, 1973;

.Kaliteevsky N.I., Wave optics, 2nd edition, 1978;

.Wolf E., Mandel L., Coherent properties of optical fields, 1965;

.Clauder J., Sudarshan E., Fundamentals of Quantum Optics, translated from English, 1970;

.Rydnik V.I., Seeing the invisible, 1981;

1 Pickup 7

1.1 Development of views on the nature of light. Light waves 7

1.2. Reflection and refraction of a plane wave on the faces of two dielectrics 10

1.3. Total internal reflection 11

1.4. Relationship between amplitude and phase 11

2 Interference 14

2.1 The phenomenon of interference. Addition of vibrations 14

2.2 Width of interference fringes 15

2.3 Methods for observing intensity by dividing the wavefront of wave 17

2.4 Methods for obtaining coherent beams by amplitude division 17

2.5 Application of interference 20

3 Diffraction 23

3.1 Huygens-Fresnel principle 23

3.2 Straightness of light propagation. Fresnel zones 25

3.3 Diffraction from the middle hole 27

3.4. Diffraction grating 29

4 Interaction of electromagnetic waves with matter 29

4.1 Light dispersion 29

4.2 Electronic theory of light dispersion 31

4.3 Absorption (light absorption) 32

4.4 Light scattering 33

5 Quantum properties of light 35

5.1 Types of photoelectric effect 35

5.2 Laws of external photoelectric effect (Stoletov’s laws) 37

5.3 Einstein’s equation for the external photoelectric effect 38

5.4 Application of the photoelectric effect 39

Conclusion 40

List of sources used 41

1 Reply

1.1 Development of views on the nature of light. Light waves

Already in the first periods of optical research, the consequences of the four basic laws of optical phenomena were experimentally established:

Law of rectilinear light scattering.

The law of independence of light beams (valid only in linear optics).

Law of reflection.

The law of light refraction at the boundaries of two media.

First: Light propagates rectilinearly in an optically homogeneous medium.

Second: The effect produced by a single beam depends on whether the remaining beams act simultaneously or are eliminated.

The reflected ray lies in the same plane as the incident ray and the perpendicular drawn to the interface between the two media at the point of incidence; angle of incidence equal to angle reflections.

Fourth: The incident ray, the refracted ray and the perpendicular drawn to the interface at the point of incidence lie in the same plane; the ratio of the sine of the angle of refraction is a constant value for given media:

Where - the relative refractive index of the second medium relative to the first. The relative refractive index of two media is equal to the ratio of their absolute refractive indices:

The absolute refractive index of a medium is called the quantity , equal to the ratio of the speed with electromagnetic waves in vacuum to their phase speed in the environment

(1.1)

The basic laws were established long ago, but the point of view on them has changed over many centuries.

So Newton adhered to the theory of the outflow of light particles that obey the laws of mechanics. Huygens came up with another (corpuscular theory of light) theory of light. He believed that light excitations should be considered as elastic impulses propagating in a special medium - the ether (wave theory of light).

During the 18th century, the corpuscular theory occupied a dominant position, although the struggle between both theories did not stop.

Then the works of Young and Fresnel in the 19th century made great contributions and additions to wave optics. Maxwell, based on his theoretical studies, formulated the conclusion that light is an electromagnetic wave. Velocity of an electromagnetic wave in a medium

(1.2)

Where - speed of light in vacuum, - speed in a medium having a dielectric constant and magnetic permeability .

Because
, That

(1.3)

(1.3) gives a connection between the optical, electrical and magnetic constants of matter. Wavelength of the optical range. The modulus of the time-average value of the energy flux density transferred by a light wave is called light intensity.

,
.

,
.

The lines along which light energy travels are called rays.
directed tangentially to the ray. In an isotropic environment
. A consequence of Maxwell's theory is the transversality of light waves: vectors of electric and magnetic fields are mutually perpendicular and oscillate perpendicular to the velocity vector propagating beam, i.e. perpendicular to the beam.

Usually in optics all reasoning is carried out relative to the light vector - the intensity vector electric field. Since when light acts on a substance, the main significance is the electrical component of the wave field acting on the electrons in the atoms of the substance.

Light is the total electromagnetic radiation of many atoms. Atoms emit light waves independently of each other, therefore the light wave emitted by the body as a whole is characterized by all kinds of equally probable vibrations of the light vector (see Fig. ray perpendicular to the plane of the picture).

Light, with all possible equally probable vector orientations called natural. If there is order, then the light is called polarized. If oscillations occur in only one plane passing through the beam, the light is called plane (linearly) polarized.

Plane polarized light is the limiting case of elliptically polarized light - i.e. end of the vector describes an ellipse in time.

; Where - ellipticity.

Slide 2

Slide 3

We see differently during the day

Slide 4

Slide 5

Natural

Light sources Artificial

Slide 6

The human eye perceives

light from 400 nm to 800 nm

Slide 7

Views on the nature of light in ancient times

The Pythagoreans were the first to hypothesize about a special fluid that is emitted by the eyes and “feels” objects, as if with tentacles, giving them sensation.

Slide 8

Views on the nature of light in the 17th-19th centuries.

Newton adhered to the corpuscular theory, according to which light is a stream of particles coming from a source in all directions. Huygens argued that light is waves propagating in a special, hypothetical medium - ether, filling space and penetrating into the interior of all bodies.

Slide 9

Modern ideas about the nature of light

The quantum theory of light arose at the beginning of the 20th century. It was formulated in 1900 and substantiated in 1905. The founders of the quantum theory of light are Planck and Einstein. According to this theory, light radiation is emitted and absorbed by particles of matter not continuously, but discretely, that is, in separate portions - light quanta.

Slide 10

PARTICULAR-WAVE DUALISM

Thus, light has particle-wave properties. Quantum and wave properties do not exclude each other, but complement each other. Wave properties appear more clearly at low frequencies and less clearly at high frequencies. Particle-wave dualism is a manifestation of two forms of existence of matter - matter and field.

Slide 11

Light rays

A light ray is a line indicating the direction of propagation of energy in a beam of light.

Slide 12

N W Römer's Experience Earth Orbit Earth Orbit of Jupiter's satellite Orbit of Jupiter I II S1 S2

Slide 13

By dividing the diameter of the earth's orbit by the delay time, we can obtain the speed of light:

s=3 1011m: 1320s ≈2.27 108m/s

Slide 14

The Fizeau installation parameters are as follows. The light source and mirror T1 were located in the house of Father Fizeau near Paris, and mirror T2 was located in Montmartre. The distance between the mirrors was ℓ ~ 8.66 km, the wheel had 720 teeth. It rotated under the action of a clock mechanism driven by a descending weight. Using a revolution counter and a chronometer, Fizeau discovered that the first blackout occurs at a wheel speed of v = 12.6 rps. Light travel time t=2ℓ/s, therefore gives c = 3.14 10 8 m/s

TOPIC: Development of views on the nature of light. Speed ​​of light. GR. 161 Completed by: Lopukhov Evgeny Gvozditskikh Ivan Kondratyev Dmitry

AT THE END OF THE 17TH CENTURY, TWO APPEARED TO BE MUTUALLY EXCLUSIVE THEORIES OF LIGHT ARISE ALMOST SIMULTANEOUSLY. They relied on two possible ways of transmitting action from source to receiver. I. Newton proposed the corpuscular theory of light, according to which light is a stream of particles coming from a source in all directions (matter transfer). H. Huygens developed a wave theory in which light was considered as waves propagating in a special medium - ether, filling all space and penetrating into all bodies (changes in the state of the medium).

NEWTON HUYGENS 1. It is difficult to explain why light beams intersecting in space do not act on each other (particles must collide and scatter). 1. Waves pass freely through each other without exerting mutual influence. 2. The rectilinear propagation of light is a consequence of the law of inertia. 2. Doesn't explain. 3. Diffraction and interference are easy to explain. 4. When emitted and absorbed, light behaves like a stream of particles. 4. Light is a special case of electromagnetic waves

WHAT IS LIGHT? According to the concepts of modern physics, light simultaneously has the properties of continuous electromagnetic waves and the properties of discrete particles, which are called photons or light quanta. The duality of the properties of light is called corpuscular-wave dualism.

BY WHAT METHODS WAS THE SPEED OF LIGHT MEASURED? The figure shows a diagram of the experiment with which Galileo proposed to measure the speed of light. By opening the lantern shutter, it was necessary to determine how long it would take for the light to return after being reflected from the mirror.

THIS WAS THE FIRST KNOWN ATTEMPT TO EXPERIMENTALLY DETERMINE THE SPEED OF LIGHT, MADE BY GALILEO GALILEO. HOWEVER, THE SIGNAL DELAY COULD NOT BE DETECTED DUE TO THE HIGH SPEED OF LIGHT. The first experimental determination of the speed of light was made by the Danish astronomer Olaf Roemer in 1675.

The orbit of Io's satellite Io makes one revolution around Jupiter in 42.5 hours. As the Earth moves away from Jupiter, each subsequent eclipse of Io occurs later than expected. The total delay in the onset of the eclipse when the Earth moved away from Jupiter by the diameter of the Earth's orbit later than the expected time was 22 minutes. Earth 3 Earth's orbit I C S 2 II Römer's experiment Jupiter's orbit S 1

Dividing the diameter of the earth's orbit by the delay time, the value of the speed of light was obtained: c = 3 * 1011 m / 1320 s c = 2. 27 * 10 8 m/s The result obtained had a large error.

THE FIRST LABORATORY MEASUREMENT OF THE SPEED OF LIGHT WAS PERFORMED IN 1849 BY THE FRENCH PHYSICIST ARMAN FIZOT. In his experiment, light from source S passed through chopper K (the teeth of a rotating wheel) and, reflected from mirror Z, returned again to the gear wheel.

THE PHYSO INSTALLATION PARAMETERS ARE AS follows. THE LIGHT SOURCE AND THE MIRROR WAS LOCATED IN THE HOUSE OF FIZOT'S FATHER NEAR PARIS, AND THE MIRROR WAS IN MONTMARTRE. THE DISTANCE BETWEEN THE MIRRORS WAS ℓ ~ 8.66 KM, THE WHEEL HAD 720 TEETH. IT WAS ROTATING UNDER THE ACTION OF A CLOCK MECHANISM, DRIVEN BY THE DECLINING WEIGHT. USING A REVOLUTION COUNTER AND A CHRONOMETER, PHYSO FOUND THAT THE FIRST BLACKING OBSERVED AT A WHEEL ROTATION SPEED OF V = 12.6 RPS. TIME OF MOVEMENT OF LIGHT T=2ℓ/C, THEREFORE GIVES C = 3.14 10 8 M/S

c = 3.14 10 8 m/s A value greater than that obtained from astronomical observations, but close to it. DESPITE THE SIGNIFICANT MEASUREMENT ERROR, THE PHYSICAL EXPERIENCE WAS OF GREAT IMPORTANCE - THE POSSIBILITY OF DETERMINING THE SPEED OF LIGHT BY “EARTHLY” MEANS WAS PROVEN.

THE FINITY OF THE SPEED OF LIGHT IS PROVED EXPERIMENTALLY BY DIRECT AND INDIRECT METHODS. Currently, using laser technology, the speed of light is determined by measuring the wavelength and frequency of radio emission in independent ways and is calculated using the formula: c = λv Calculations give c = 299792456.2 ± 1.1 m/s

“HOW HOW MUCH SPEEDS DOES LIGHT HAVE? » c So far there is no indication of a change over time, but physics cannot unconditionally reject such a possibility. Well, all that remains is to wait for reports of new measurements of the speed of light. These measurements can provide much more new information for understanding nature, which is inexhaustible in its diversity.

CONCLUSIONS: 1. The nature of light has particle-wave dualism (duality). 2. It should be recognized as a scientific fact, established experimentally - the finiteness and absoluteness (invariance) of the speed of light in a vacuum. 3. Any physical theory is confirmed by experimental facts.