Light is like an electromagnetic wave. speed of light

Light - electromagnetic wave. At the end of the 17th century, two scientific hypotheses arose about the nature of light - corpuscular and wave. According to the corpuscular theory, light is a stream of tiny light particles (corpuscles) that fly at great speed. Newton believed that the movement of light corpuscles obeys the laws of mechanics. Thus, the reflection of light was understood similarly to the reflection of an elastic ball from a plane. The refraction of light was explained by the change in the speed of particles during the transition from one medium to another. The wave theory considered light as wave process, similar mechanical waves. According to modern ideas, light has a dual nature, i.e. it is simultaneously characterized by both corpuscular and wave properties. In phenomena such as interference and diffraction, the wave properties of light come to the fore, and in the phenomenon of the photoelectric effect, corpuscular ones. In optics, light is understood as electromagnetic waves of a rather narrow range. Often, light is understood not only as visible light, but also as wide areas of the spectrum adjacent to it. Historically, the term "invisible light" appeared - ultraviolet light, infrared light, radio waves. The wavelengths of visible light range from 380 to 760 nanometers. One of the characteristics of light is its Colour, which is determined by the frequency of the light wave. White light is a mixture of waves of different frequencies. It can be decomposed into colored waves, each of which is characterized by a certain frequency. Such waves are called monochromatic. According to the latest measurements, the speed of light in vacuum The ratio of the speed of light in vacuum to the speed of light in matter is called absolute refractive index substances.

When a light wave passes from vacuum to matter, the frequency remains constant (the color does not change). Wavelength in a medium with a refractive index n changes:

Light interference- Jung's experience. Light from a light bulb with a light filter, which creates an almost monochromatic light, passes through two narrow, adjacent slots, behind which a screen is installed. A system of light and dark bands - interference bands - will be observed on the screen. In this case, a single light wave is split into two coming from different slits. These two waves are coherent with each other and, when superimposed on each other, give a system of maxima and minima of the light intensity in the form of dark and light bands of the corresponding color.

Light interference- max and min conditions. Maximum condition: If an even number of half-waves or an integer number of waves fit into the optical difference of the wave path, then at a given point on the screen, an increase in light intensity (max) is observed. , where is the phase difference of the added waves. Minimum condition: If the optical path difference of the waves fits odd number half-waves, then at the minimum point.

According to the wave theory, light is an electromagnetic wave.

Visible radiation (visible light) - electromagnetic radiation, directly perceived by the human eye, characterized by wavelengths in the range of 400 - 750 nm, which corresponds to a frequency range of 0.75 10 15 - 0.4 10 15 Hz. Light radiation of different frequencies is perceived by a person as different colors.

Infrared radiation - electromagnetic radiation occupying the spectral region between the red end of visible light (with a wavelength of about 0.76 microns) and short-wave radio emission (with a wavelength of 1-2 mm). Infrared radiation creates a feeling of warmth, which is why it is often referred to as thermal radiation.

Ultraviolet radiation - electromagnetic radiation invisible to the eye, occupying the spectral region between the visible and X-rays within wavelengths from 400 to 10 nm.

Electromagnetic waves – electromagnetic oscillations(electromagnetic field) propagating in space with a finite speed depending on the properties of the medium (in vacuum - 3∙10 8 m/s). Features of electromagnetic waves, the laws of their excitation and propagation are described by Maxwell's equations. The nature of the propagation of electromagnetic waves is affected by the medium in which they propagate. Electromagnetic waves can experience refraction, dispersion, diffraction, interference, total internal reflection and other phenomena inherent in waves of any nature. In a homogeneous and isotropic medium far from charges and currents that create an electromagnetic field, the wave equations for electromagnetic (including light) waves have the form:

where and are the electrical and magnetic permeabilities of the medium, respectively, and are the electrical and magnetic constants, respectively, and are the strengths of the electric and magnetic field, is the Laplace operator. In an isotropic medium, the phase velocity of propagation of electromagnetic waves is equal to The propagation of plane monochromatic electromagnetic (light) waves is described by the equations:

kr ; kr (6.35.2)

where and are the amplitudes of oscillations of the electric and magnetic fields, respectively, k is the wave vector, r is the radius vector of the point, – circular oscillation frequency, is the initial phase of oscillations at the point with coordinate r= 0. Vectors E and H oscillate in the same phase. An electromagnetic (light) wave is transverse. Vectors E , H , k are orthogonal to each other and form a right triplet of vectors. Instantaneous values and at any point are related by the relation Considering that the physiological effect on the eye has electric field, the equation of a plane light wave propagating in the direction of the axis can be written as follows:

The speed of light in vacuum is

. (6.35.4)

The ratio of the speed of light in vacuum to the speed of light in a medium is called the absolute refractive index of the medium:

(6.35.5)

When moving from one medium to another, the wave propagation speed and wavelength change, the frequency remains unchanged. The relative refractive index of the second medium relative to the first is the ratio

where and are the absolute refractive indices of the first and second media, and are the speed of light in the first and second media, respectively.

From theory electromagnetic field, developed by J. Maxwell, followed: electromagnetic waves propagate at the speed of light - 300,000 km / s, that these waves are transverse, just like light waves. Maxwell suggested that light is an electromagnetic wave. Later, this prediction was experimentally confirmed.

Like electromagnetic waves, the propagation of light obeys the same laws:

Law rectilinear propagation Sveta. In a transparent homogeneous medium, light travels in straight lines. This law explains how solar and lunar eclipses occur.

When light falls on the interface between two media, part of the light is reflected into the first medium, and part passes into the second medium, if it is transparent, while changing the direction of its propagation, i.e., it is refracted.

LIGHT INTERFERENCE

Suppose that two monochromatic light waves, superimposed on each other, excite oscillations of the same direction at a certain point in space: x 1 \u003d A 1 cos (t +  1) and x 2 \u003d A 2 cos (t +  2). Under X understand the intensity of electric E or magnetic H wave fields; the vectors E and H oscillate in mutually perpendicular planes (see § 162). The strengths of the electric and magnetic fields obey the principle of superposition (see § 80 and 110). The amplitude of the resulting oscillation at a given point A 2 \u003d A 2 l + A 2 2 + 2A 1 A 2 cos ( 2 - 1) (see 144.2)). Since the waves are coherent, then cos( 2 -  1) has a constant value in time (but its own for each point in space), therefore the intensity of the resulting wave (1 ~ A 2)

At points in space where cos( 2 -  1) > 0, intensity I > I 1 + I 2 , where cos( 2 -  1) < Oh intensity I< I 1 +I 2 . Следовательно, при наложении двух (или нескольких) когерентных световых волн происходит пространственное перераспределение luminous flux, resulting in intensity maxima in some places and intensity minima in others. This phenomenon is called light interference.

For incoherent waves, the difference ( 2 -  1) changes continuously, so the time average value cos( 2 - 1) is zero, and the intensity of the resulting wave is the same everywhere and for I 1 = I 2 is equal to 2I 1 (for coherent waves under the given condition at the maxima I = 4I 1 at the minima I = 0).

How can you create the conditions necessary for the occurrence of interference of light waves? To obtain coherent light waves, the method of dividing a wave emitted by one source into two parts is used, which, after passing through different optical paths superimposed on each other, and an interference pattern is observed.

Let the separation into two coherent waves occur at a certain point O . To the point M, in which an interference pattern is observed, one wave in a medium with a refractive index n 2 passed path s 1 , the second - in a medium with a refractive index n 2 - path s 2 . If at the point O the oscillation phase is equal to t , then at the point M the first wave will excite the oscillation А 1 cos(t - s 1 / v 1) , the second wave - fluctuation A 2 cos (t - s 2 / v 2) , where v 1 = c/n 1 , v 2 = c/n 2 - respectively, the phase velocity of the first and second waves. Phase difference of oscillations excited by waves at a point M, is equal to

(taken into account that /s = 2v/s = 2 0 where  0 is the wavelength in vacuum). Product of geometric length s path of a light wave in a given medium by the refractive index n of this medium is called the optical path length L , a  \u003d L 2 - L 1 - the difference in the optical lengths of the paths traversed by the waves - is called the optical path difference. If the optical path difference is equal to an integer number of wavelengths in vacuum

then  = ± 2m , M both waves will occur in the same phase. Therefore, (172.2) is the condition for the interference maximum.

If the optical path difference

then  = ±(2m + 1) , and oscillations excited at the point M both waves will occur in antiphase. Therefore, (172.3) is the condition for the interference minimum.

APPLICATIONS OF LIGHT INTERFERENCE

The phenomenon of interference is due to the wave nature of light; its quantitative regularities depend on the wavelength Do. Therefore, this phenomenon is used to confirm the wave nature of light and to measure wavelengths (interference spectroscopy).

The phenomenon of interference is also used to improve the quality of optical devices (optical coating) and to obtain highly reflective coatings. The passage of light through each refractive surface of the lens, for example, through the glass-air interface, is accompanied by a reflection of 4% of the incident flux (when showing the body of glass refraction 1.5). Since modern lenses contain a large number of lenses, then the number of reflections in them is large, and therefore the losses of the light flux are also large. Thus, the intensity of the transmitted light is attenuated and the luminosity of the optical device decreases. In addition, reflections from lens surfaces lead to glare, which often (for example, in military technology) unmasks the position of the device.

To eliminate these shortcomings, the so-called illumination of the optics. To do this, thin films with a refractive index lower than that of the lens material are applied to the free surfaces of the lenses. When light is reflected from the air-film and film-glass interfaces, interference of coherent rays 1 and 2 "(Fig. 253) occurs.

AR layer

Film thickness d and the refractive indices of glass n c and film n can be chosen so that the waves reflected from both surfaces of the film cancel each other out. To do this, their amplitudes must be equal, and the optical path difference is equal to - (see (172.3)). The calculation shows that the amplitudes of the reflected rays are equal if

(175.1)

Since n with, n and the refractive index of air n 0 satisfy the conditions n c > n > n 0 , then the loss of the half-wave occurs on both surfaces; hence the minimum condition (assume the light is incident normally, i.e. I = 0)

where nd- optical film thickness. Usually take m = 0, then

Thus, if condition (175.1) is satisfied and the optical thickness of the film is equal to  0 /4, then as a result of interference, the reflected rays are quenched. Since it is impossible to achieve simultaneous quenching for all wavelengths, this is usually done for the wavelength most susceptible to the eye  0  0.55 μm. Therefore, lenses with coated optics have a bluish-red tint.

The creation of highly reflective coatings became possible only on the basis of multipath interference. Unlike two-beam interference, which we have considered so far, multipath interference occurs when a large number of coherent light beams are superimposed. The intensity distribution in the interference pattern differs significantly; the interference maxima are much narrower and brighter than when two coherent light beams are superimposed. Thus, the resulting amplitude of light oscillations of the same amplitude at the intensity maxima, where the addition occurs in the same phase, in N times more, and the intensity in N 2 times more than from one beam (N is the number of interfering beams). Note that to find the resulting amplitude it is convenient to use the graphical method, using the rotating amplitude vector method (see § 140). Multipath interference is carried out in a diffraction grating (see § 180).

Multipath interference can be implemented in a multilayer system of alternating films with different refractive indices (but the same optical thickness equal to  0 /4) deposited on a reflective surface (Fig. 254). It can be shown that at the film interface (between two ZnS layers with a high refractive index n 1 there is a cryolite film with a lower refractive index n 2) big number reflected interfering rays, which, with the optical thickness of the films  0 /4, will be mutually enhanced, i.e., the reflection coefficient increases. characteristic feature Such a highly reflective system is that it operates in a very narrow spectral region, and the greater the reflection coefficient, the narrower this region. For example, a system of seven films for a region of 0.5 μm gives a reflectance of   96% (with a transmittance of  3.5% and an absorption coefficient of<0,5%). Подобные отражатели применяются в лазерной технике, а также используются для создания интерференционных светофильтров (узкополосных оптических фильтров).

The phenomenon of interference is also used in very precise measuring instruments called interferometers. All interferometers are based on the same principle and differ only in design. On fig. 255 shows a simplified diagram of the Michelson interferometer.

Monochromatic light from source S falls at an angle of 45° onto a plane-parallel plate Р 1 . The side of the record away from S , silvered and translucent, splits the beam into two parts: beam 1 (reflected from the silver layer) and beam 2 (passes through the veto). Beam 1 is reflected from mirror M 1 and, returning back, again passes through the plate P 1 (beam l "). Ray 2 goes to the mirror M 2, is reflected from it, returns back and is reflected from the plate R 1 (beam 2). Since the first of the rays passes through the plate P 1 twice, then to compensate for the resulting path difference, a plate P 2 is placed in the path of the second beam (exactly the same as P 1 , only not covered with a layer of silver).

Beams 1 and 2" are coherent; therefore, interference will be observed, the result of which depends on the optical path difference of beam 1 from the point O to mirror M 1 and beam 2 from point O to the mirror M 2 . When one of the mirrors is moved to a distance of  0/4, the difference between the paths of both beams will increase by  0/2 and the illumination of the visual field will change. Therefore, by a slight shift of the interference pattern, one can judge the small displacement of one of the mirrors and use the Michelson interferometer for accurate (about 10 -7 m) measurement of lengths (measuring the length of bodies, the wavelength of light, changes in the length of a body with temperature changes (interference dilatometer)) .

The Russian physicist V.P. Linnik (1889-1984) used the principle of the Michelson interferometer to create a microinterferometer (a combination of an interferometer and a microscope) used to control the surface finish.

Interferometers are very sensitive optical devices that allow you to determine minor changes in the refractive index of transparent bodies (gases, liquids and solids) depending on pressure, temperature, impurities, etc. Such interferometers are called interference refractometers. On the path of the interfering beams there are two identical cuvettes with a length l, one of which is filled, for example, with a gas with a known (n 0), and the other with an unknown (n z) refractive indices. The additional optical path difference that has arisen between the interfering beams  \u003d (n z - n 0) l. A change in the path difference will lead to a shift in the interference fringes. This shift can be characterized by the value

where m 0 shows by which part of the width of the interference fringe the interference pattern has shifted. Measuring the value of m 0 with known l, m 0 and , you can calculate n z , or change n z - n 0 . For example, when the interference pattern is shifted by 1/5 of the fringe at l\u003d 10 cm and  \u003d 0.5 microns (n ​​z - n 0) \u003d 10 -6, i.e. interference refractometers allow you to measure the change in the refractive index with very high accuracy (up to 1/1,000,000).

The use of interferometers is very diverse. In addition to the above, they are used to study the quality of manufacture of optical parts, measure angles, study fast processes occurring in the air flowing around aircraft, etc. Using an interferometer, Michelson for the first time compared the international standard of a meter with the length of a standard light wave. With the help of interferometers, the propagation of light in moving bodies was also studied, which led to fundamental changes in the ideas about space and time.

Gymnasium 144

abstract

The speed of light.

Light interference.

standing waves.

11th grade student

Korchagin Sergey

St. Petersburg 1997.

Light is an electromagnetic wave.

In the 17th century, two theories of light arose: wave and corpuscular. The corpuscular 1 theory was proposed by Newton, and the wave theory by Huygens. According to Huygens, light is waves propagating in a special medium - ether, which fills all space. The two theories have existed side by side for a long time. When one of the theories did not explain a phenomenon, it was explained by another theory. For example, the rectilinear propagation of light, leading to the formation of sharp shadows, could not be explained on the basis of wave theory. However, at the beginning of the 19th century, such phenomena as diffraction 2 and interference 3 were discovered, which gave rise to thoughts that the wave theory finally defeated the corpuscular one. In the second half of the 19th century, Maxwell showed that light is a special case of electromagnetic waves. These works served as the foundation for the electromagnetic theory of light. However, at the beginning of the 20th century, it was discovered that when emitted and absorbed, light behaves like a stream of particles.

The speed of light.

There are several ways to determine the speed of light: astronomical and laboratory methods.

The speed of light was first measured by the Danish scientist Roemer in 1676 using the astronomical method. He recorded the time that the largest of Jupiter's moons, Io, was in the shadow of this huge planet. Roemer took measurements at the moment when our planet was closest to Jupiter, and at the moment when we were a little (according to astronomical terms) farther from Jupiter. In the first case, the interval between outbreaks was 48 hours 28 minutes. In the second case, the satellite was late by 22 minutes. From this it was concluded that the light needs 22 minutes to travel the distance from the place of the previous observation to the place of the present observation. Knowing the distance and time delay of Io, he calculated the speed of light, which turned out to be huge, about 300,000 km/s 4 .

For the first time, the speed of light was measured by the laboratory method by the French physicist Fizeau in 1849. He obtained the value of the speed of light equal to 313,000 km/s.

According to modern data, the speed of light is 299,792,458 m/s ±1.2 m/s.

Light interference.

It is rather difficult to obtain a picture of the interference of light waves. The reason for this is that the light waves emitted by different sources are not consistent with each other. They must have the same wavelengths and a constant phase difference at any point in space 5 . Equality of wavelengths is not difficult to achieve using light filters. But it is impossible to achieve a constant phase difference, due to the fact that atoms of different sources emit light independently of each other 6 .

Nevertheless, the interference of light can be observed. For example, iridescent overflow of colors on a soap bubble or on a thin film of kerosene or oil on water. The English scientist T. Jung was the first to come to the brilliant idea that color is explained by the addition of waves, one of which is reflected from the outer surface, and the other from the inner one. In this case, interference of 7 light waves occurs. The result of interference depends on the angle of incidence of light on the film, its thickness and wavelength.

standing waves.

It was noticed that if one end of the rope is swung with a correctly selected frequency (its other end is fixed), then a continuous wave will run to the fixed end, which will then be reflected with the loss of a half-wave. The interference of the incident and reflected wave will result in a standing wave that appears to be stationary. The stability of this wave satisfies the condition:

L=nl/2, l=u/n, L=nu/n,

Where L * is the length of the rope; n * 1,2,3, etc.; u * is the speed of wave propagation, which depends on the tension of the rope.

Standing waves are excited in all bodies capable of oscillating.

The formation of standing waves is a resonant phenomenon that occurs at the resonant or natural frequencies of the body. Points where interference is canceled are called nodes, and points where interference is enhanced are antinodes.

Light ѕ electromagnetic wave………………………………………..2

The speed of light…………………………………………………………2

Light interference………………………………………………….3

Standing waves……………………………………………………………3

Physics 11 (G.Ya. Myakishev B.B. Lukhovtsev)

Physics 10 (N.M. Shakhmaev S.N. Shakhmaev)

Supporting notes and test tasks (G.D. Luppov)

1 The Latin word “corpuscle” translated into Russian means “particle”.

2 Rounding obstacles with light.

3 The phenomenon of amplification or attenuation of light when superimposing light beams.

4 Roemer himself received a value of 215,000 km/s.

5 Waves having the same length and constant phase difference are called coherent.

6 The only exceptions are quantum light sources - lasers.

7 The addition of two waves, as a result of which there is a time-stable amplification or weakening of the resulting light vibrations at various points in space.

The nature of light

The first ideas about the nature of light arose among the ancient Greeks and Egyptians. With the invention and improvement of various optical instruments (parabolic mirrors, microscope, spotting scope), these ideas developed and transformed. At the end of the 17th century, two theories of light arose: corpuscular(I. Newton) and wave(R. Hooke and H. Huygens).

wave theory considered light as a wave process, similar to mechanical waves. The wave theory was based on Huygens principle. Great merit in the development of wave theories belongs to the English physicist T. Jung and the French physicist O. Fresnel, who studied the phenomena of interference and diffraction. An exhaustive explanation of these phenomena could only be given on the basis of the wave theory. An important experimental confirmation of the validity of the wave theory was obtained in 1851, when J. Foucault (and independently A. Fizeau) measured the speed of light propagation in water and obtained the value υ < c.

Although the wave theory was generally accepted by the middle of the 19th century, the question of the nature of light waves remained unresolved.

In the 60s of the XIX century, Maxwell established the general laws of the electromagnetic field, which led him to the conclusion that light is electromagnetic waves. An important confirmation of this point of view was the coincidence of the speed of light in vacuum with the electrodynamic constant:

\(~c = \dfrac(1)(\sqrt(\varepsilon_0 \mu_0))\) .

The electromagnetic nature of light was recognized after the experiments of G. Hertz (1887–1888) on the study of electromagnetic waves. At the beginning of the 20th century, after P. N. Lebedev’s experiments on measuring light pressure (1901), the electromagnetic theory of light turned into a firmly established fact.

The most important role in elucidating the nature of light was played by the experimental determination of its speed. Since the end of the 17th century, repeated attempts have been made to measure the speed of light by various methods (the astronomical method of A. Fizeau, the method of A. Michelson). Modern laser technology makes it possible to measure the speed of light with very high accuracy based on independent wavelength measurements λ and frequencies of light ν (c = λ · ν ). In this way, the value was found c= 299792458 ± 1.2 m/s, exceeding in accuracy all previously obtained values ​​by more than two orders of magnitude.

Light plays an extremely important role in our lives. The overwhelming amount of information about the world around a person receives with the help of light. However, in optics as a branch of physics, light is understood not only visible light, but also wide ranges of the electromagnetic radiation spectrum adjacent to it - infrared(IR) and UV(UV). According to its physical property, light is fundamentally indistinguishable from electromagnetic radiation of other ranges - different parts of the spectrum differ from each other only in wavelength λ and frequency ν .

To measure wavelengths in the optical range, units of length are used 1 nanometer(nm) and 1 micrometer(µm):

1 nm = 10 -9 m = 10 -7 cm = 10 -3 µm.

Visible light occupies a range of approximately 400 nm to 780 nm, or 0.40 µm to 0.78 µm.

A periodically changing electromagnetic field propagating in space is electromagnetic wave.

The most essential properties of light as an electromagnetic wave

1. When light propagates at each point in space, periodically repeating changes in the electric and magnetic fields occur. It is convenient to represent these changes in the form of oscillations of the vectors of the electric field strength \(~\vec E\) and the magnetic field induction \(~\vec B\) at each point in space. Light is a transverse wave, since \(~\vec E \perp \vec \upsilon\) and \(~\vec B \perp \vec \upsilon\) .
2. The oscillations of the vectors \(~\vec E\) and \(~\vec B\) at each point of the electromagnetic wave occur in the same phases and in two mutually perpendicular directions \(~\vec E \perp \vec B\) at each point space.
3. The period of light as an electromagnetic wave (frequency) is equal to the period (frequency) of oscillations of the source of electromagnetic waves. For electromagnetic waves, the relation \(~\lambda = \upsilon \cdot T = \dfrac(\upsilon)(\nu)\) is true. In vacuum, \(~\lambda_0 = c \cdot T = \dfrac(c)(\nu)\) is the largest wavelength compared to λ in a different environment because ν = const and only changes υ and λ when moving from one environment to another.
4. Light is a carrier of energy, and the energy transfer occurs in the direction of wave propagation. The volumetric energy density of an electromagnetic field is given by \(~\omega_(em) = \dfrac(\varepsilon \cdot \varepsilon_0 \cdot E^2)(2) + \dfrac(B^2)(2 \cdot \mu \cdot \mu_0)\)
5. Light, like other waves, propagates in a straight line in a homogeneous medium, undergoes refraction when passing from one medium to another, and is reflected from metal barriers. They are characterized by the phenomena of diffraction and interference.

Light interference

To observe wave interference on the water surface, two wave sources (two balls fixed on an oscillating rod) were used. It is impossible to obtain an interference pattern (alternating minima and maxima of illumination) using two conventional independent light sources, for example, two electric light bulbs. Turning on another light bulb only increases the illumination of the surface, but does not create an alternation of minima and maxima of illumination.

In order for a stable interference pattern to be observed when light waves are superimposed, it is necessary that the waves be coherent, that is, they have the same wavelength and a constant phase difference.

Why are light waves from two sources not coherent?

The interference pattern from two sources, which we have described, arises only when monochromatic waves of the same frequency are added. For monochromatic waves, the phase difference of 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 an invariable arrangement in space of the maxima and minima of the oscillations. Light waves from two independent sources are not coherent. Atoms of sources radiate light independently from each other as separate "snatches" (trains) of sinusoidal waves. The duration of continuous emission of an atom is about 10 s. During this time, the light travels a path about 3 m long (Fig. 1).

These trains of waves 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 time. Waves from different light sources are incoherent due to the fact that the difference in the initial phases does not remain constant. Phases φ 01 and φ 02 change randomly, and because of this, the phase difference of the resulting oscillations at any point in space changes randomly.

With random breaks and the occurrence of oscillations, the phase difference changes randomly, taking for the observation time τ all possible values ​​from 0 to 2 π . As a result, over time τ much longer than the time of irregular phase changes (of the order of 10 -8 s), the average value of cos ( φ 1 – φ 2) in the formula

\(~I = 4 I_0 \cos^2 \dfrac(\varphi_1 - \varphi_2)(2) = 2 I_0 \) .

equals zero. The intensity of the light 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 give an interference pattern. This is the main, but not the only reason. Another reason is that the wavelength of light, as we shall soon see, is very short. This greatly complicates the observation of interference, even if one has coherent wave sources.

Conditions for maxima and minima of the interference pattern

As a result of the superposition of two or more coherent waves in space, interference pattern, which is an alternation of maxima and minima of the light intensity, and hence the illumination of the screen.

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

\(~\Delta \varphi = \varphi_1 - \varphi_2 = 2 \pi \dfrac(r_2 - r_1)(\lambda)\) . (one)

The phase difference is determined by the difference in distances from the sources to the observation point Δ r = r 1 – r 2 (distance difference is called stroke difference ). At those points in space for which the condition

\(~\Delta r = r_1 - r_2 = k \lambda ; k = 0, 1, 2, \ldots\) . (2)

the waves, adding up, reinforce each other, and the resulting intensity is 4 times greater than the intensity of each of the waves, i.e. observed maximum . On the contrary, at

\(~\Delta r = r_1 - r_2 = \dfrac(\lambda)(2) (2k + 1)\) . (3)

waves cancel each other out I= 0), i.e. observed minimum .

Huygens–Fresnel principle

The wave theory is based on the Huygens principle: each point that a wave reaches serves as the center of secondary waves, and the envelope of these waves gives the position of the wave front at the next moment in time.

Let a plane wave normally fall on a hole in an opaque screen (Fig. 2). According to Huygens, each point of the section of the wave front distinguished by the hole serves as a source of secondary waves (in a homogeneous isotropic medium they are spherical). Having constructed the envelope of the secondary waves for a certain moment of time, we see that the wave front enters the region of the geometric shadow, i.e., the wave goes around the edges of the hole.

The Huygens principle solves only the problem of the direction of propagation of the wave front, explains the phenomenon of diffraction, but does not address the issue of the amplitude, and, consequently, the intensity of waves propagating in different directions. Fresnel put physical meaning into Huygens' principle, supplementing it with the idea of ​​interference of secondary waves.

According to Huygens-Fresnel principle, a light wave excited by some source S can be represented as the result of a superposition of coherent secondary waves "radiated" by fictitious sources.

Infinitely small elements of any closed surface enclosing the source S can serve as such sources. Usually, one of the wave surfaces is chosen as this surface, so all fictitious sources act in phase. Thus, the waves propagating from the source are the result of the interference of all coherent secondary waves. Fresnel ruled out the possibility of the occurrence of backward secondary waves and assumed that if an opaque screen with a hole is located between the source and the observation point, then the amplitude of the secondary waves on the surface of the screen is zero, and in the hole it is the same as in the absence of a screen. Taking into account the amplitudes and phases of the secondary waves makes it possible in each specific case to find the amplitude (intensity) of the resulting wave at any point in space, i.e., to determine the laws of light propagation.

Methods for obtaining an interference pattern

Idea of ​​Augustin Fresnel

To obtain coherent light sources, the French physicist Augustin Fresnel (1788-1827) found in 1815 a simple and ingenious way. It is necessary to divide the light from one source into two beams and, forcing them to go through different paths, bring them together. Then the train of waves emitted by an individual atom will be divided into two coherent trains. This will be the case for trains of waves emitted by each atom of the source. The light emitted by a single atom produces a definite interference pattern. When these pictures 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, giving coherent waves. For this, two mirrors (Fresnel bimirrors), a biprism (two prisms folded at the bases), a bilens (a lens cut in half with the halves apart), etc. are used.

Newton's rings

The first experiment on the observation of light interference in the laboratory belongs to I. Newton. He observed an interference pattern arising from the reflection of light in a thin air gap between a flat glass plate and a plano-convex lens with a large radius of curvature. The interference pattern looked like concentric rings, called Newton's rings(Fig. 3 a, b).

Newton could not explain from the point of view of the corpuscular theory why rings appear, but he understood that this was due to some kind of periodicity of light processes.

Young's experiment with two slits

The experiment proposed by T. Jung convincingly demonstrates the wave nature of light. To better understand the results of Young's experiment, it is useful to first consider the situation where light passes through a single slit in a partition. In the single-slit experiment, monochromatic light from a source passes through a narrow slit and is recorded on a screen. It is unexpected that with a sufficiently narrow slit, not a narrow luminous strip (the image of the slit) is visible on the screen, but a smooth distribution of light intensity, which has a maximum in the center and gradually decreases towards the edges. This phenomenon is due to the diffraction of light by a slit and is also a consequence of the wave nature of light.

Now let two slots be made in the partition (Fig. 4). Successively closing one or the other slit, one can be convinced that the intensity distribution pattern on the screen will be the same as in the case of one slit, but only the position of the intensity maximum will each time correspond to the position of the open slit. If both slits are opened, then an alternating sequence of light and dark stripes appears on the screen, and the brightness of the light stripes decreases with distance from the center.

Some applications of interference

The applications of interference are very important and extensive.

There are special devices interferometers- the action of which is based on the phenomenon of interference. Their purpose can be different: accurate measurement of the lengths of light waves, measurement of the refractive index of gases, etc. There are interferometers for special purposes. One of them, designed by Michelson to capture very small changes in the speed of light, will be discussed in the chapter "Fundamentals of Relativity".

We will focus on only two applications of interference.

Surface quality check

With the help of interference, it is possible to evaluate the quality of grinding the surface of the product with an error of up to 10 -6 cm. To do this, you need to create a thin layer of air between the surface of the sample and a very smooth reference plate (Fig. 5).

Then surface irregularities up to 10 -6 cm will cause noticeable curvature of the interference fringes formed when light is reflected from the surface under test and the lower face of the reference plate.

In particular, the quality of lens grinding can be checked by observing Newton's rings. The rings will be regular circles only if the lens surface is strictly spherical. Any deviation from sphericity greater than 0.1 λ will have a noticeable effect on the shape of the rings. Where there is a bulge on the lens, the rings will bulge towards the center.

It is curious that the Italian physicist E. Torricelli (1608-1647) was able to grind lenses with an error of up to 10 -6 cm. His lenses are stored in the museum, and their quality is checked by modern methods. How did he manage to do it? It is difficult to answer this question. At that time, the secrets of craftsmanship were not usually 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.

We also note that, using almost strictly monochromatic light, one can observe an 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 10 -6 cm.

Enlightenment of optics

The lenses of modern cameras or movie projectors, submarine periscopes and various other optical devices consist of a large number of optical glasses - lenses, prisms, etc. Passing through such devices, light is reflected from many surfaces. The number of reflective surfaces in modern photographic lenses exceeds 10, and in submarine periscopes it reaches 40. When light falls perpendicular to the surface, 5-9% of the total energy is reflected from each surface. Therefore, only 10-20% of the light entering it often passes through the device. As a result, the illumination of the image is low. In addition, the image quality deteriorates. Part of the light beam, after multiple reflections from internal surfaces, still passes through the optical device, but is scattered and no longer participates in creating a clear image. In photographic images, for example, a "veil" is formed for this reason.

To eliminate these unpleasant consequences of light reflection from the surfaces of optical glasses, it is necessary to reduce the fraction of the reflected light energy. The image given by the device becomes at the same time brighter, "is enlightened". This is where the term comes from. enlightenment of optics.

Enlightenment of optics is based on interference. A thin film with a refractive index is applied to the surface of an optical glass, such as a lens. n n, less than the refractive index of glass n with. For simplicity, let us consider the case of normal light incidence on the film (Fig. 6).

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

\(~2h = \dfrac(\lambda)(2 n_n)\) . (4)

where \(~\dfrac(\lambda)(n_n)\) is the wavelength in the film, and 2 h- stroke difference.

If the amplitudes of both reflected waves are the same or very close to each other, then the extinction of the light will be complete. To achieve this, the refractive index of the film is selected appropriately, since the intensity of the reflected light is determined by the ratio of the refractive indices of the two adjacent media.

White light falls on the lens under normal conditions. Expression (4) shows that the required film thickness depends on the wavelength. Therefore, it is impossible to suppress the reflected waves of all frequencies. The film thickness is selected so that complete extinction at normal incidence occurs for the wavelengths of the middle part of the spectrum (green color, λ z = 5.5·10 -7 m); it should be equal to a quarter of the wavelength in the film:

\(~h = \dfrac(\lambda)(4 n_n)\) . (4)

The reflection of the light of the extreme parts of the spectrum - red and violet - is attenuated slightly. Therefore, a lens with coated optics in reflected light has a lilac tint. Now even simple cheap cameras have coated optics. In conclusion, we emphasize once again that the extinction of light by light does not mean the transformation of light energy into other forms. As with the interference of mechanical waves, the damping of waves by each other in a given region of space means that light energy simply does not enter here. Attenuation of reflected waves in a lens with coated optics means that all light passes through the lens.

Appendix

Addition of two monochromatic waves

Let us consider in more detail the addition of two harmonic waves of the same frequency ν at some point BUT homogeneous medium, assuming that the sources of these waves S 1 and S 2 are from the point BUT at distances, respectively. l 1 and l 2 (Fig. 7).

Let us assume for simplicity that the considered waves are either longitudinal or transverse plane polarized, and their amplitudes are equal to a 1 and a 2. Then, according to \(~x(s,t) = a \cdot \sin (\omega t - k s + \varphi_0)\) , the equations of these waves at the point BUT look like

\(~x_1(l_1,t) = a_1 \cdot \sin (\omega t - k l_1 + \varphi_(01))\) . (5) \(~x_2(l_2,t) = a_2 \cdot \sin (\omega t - k l_2 + \varphi_(02))\) . (6)

The equation of the resulting wave, which is a superposition of waves (5), (6), is their sum:

\(~x(t) = x_1(l_1,t) + x_2(l_2,t) = a \cdot \sin (\omega t + \varphi)\) , (7)

moreover, as can be proved using the cosine theorem known from geometry, the square of the amplitude of the resulting oscillation is determined by the formula

\(~a^2 = a^2_1 + a^2_2 + 2 a_1 a_2 \cos \Delta \varphi\)> , (8)

where ∆ φ - oscillation phase difference:

\(~\Delta \varphi = k(l_1 - l_2) - (\varphi_(01) - \varphi_(02))\) . (nine)

(Expression for the initial phase φ 01 of the resulting oscillation, we will not give because of its cumbersomeness).

From (8) it can be seen that the amplitude of the resulting oscillation is a periodic function of the path difference Δ l. If the wave path difference is such that the phase difference Δ φ is equal to

\(~\Delta \varphi = \pm 2 \pi n ; n = 0, 1, 2, \ldots\) , (10)

then at the point BUT the amplitude of the resulting wave will be maximum ( maximum condition), if

\(~\Delta \varphi = \pm (2n +1) \pi\) , (11)

then the amplitude at the point BUT minimum ( minimum condition).

Assuming for simplicity that φ 01 = φ 02 and a 1 = a 2 , and taking into account the equality \(~k = \dfrac(\omega)(\upsilon) = \dfrac(2 \pi)(\lambda)\) , conditions (10) and (11) and the corresponding expressions for the amplitude a, we can write in the form:

\(~\Delta l = \pm n \lambda\) ( maximum condition), (12)

and then a = a 1 + a 2 , and

\(~\Delta l = \pm (2n +1) \dfrac(\lambda)(2)\) ( minimum condition), (13)

and then a = 0.

Literature

1. Myakishev G.Ya. Physics: Optics. The quantum physics. Grade 11: Proc. for in-depth study of physics / G.Ya. Myakishev, A.Z. Sinyakov. – M.: Bustard, 2002. – 464 p.
2. Burov L.I., Strelchenya V.M. Physics from A to Z: for students, applicants, tutors. - Minsk: Paradox, 2000. - 560 p.