More convincing evidence is needed that light behaves like a wave when it travels. Any wave motion is characterized by the phenomena of interference and diffraction. In order to be sure that light has a wave nature, it is necessary to find experimental evidence of interference and diffraction of light.

Interference is a rather complex phenomenon. To better understand its essence, we will first focus on the interference of mechanical waves.

Addition of waves. Very often, several different waves simultaneously propagate in a medium. For example, when several people are talking in a room, the sound waves overlap each other. What happens?

The easiest way to observe the superposition of mechanical waves is by observing waves on the surface of the water. If we throw two stones into the water, thereby creating two annular waves, then it is easy to notice that each wave passes through the other and subsequently behaves as if the other wave did not exist at all. In the same way, any number of sound waves can simultaneously propagate through the air without interfering with each other in the least. A bunch of musical instruments in an orchestra or voices in a choir create sound waves that are simultaneously detected by our ears. Moreover, the ear is able to distinguish one sound from another.

Now let's take a closer look at what happens in places where the waves overlap each other. Observing waves on the surface of the water from two stones thrown into the water, you can notice that some areas of the surface are not disturbed, but in other places the disturbance has intensified. If two waves meet in one place with crests, then in this place the disturbance of the water surface intensifies.

If, on the contrary, the crest of one wave meets the trough of another, then the surface of the water will not be disturbed.

In general, at each point in the medium, the oscillations caused by two waves simply add up. The resulting displacement of any particle of the medium is an algebraic (i.e., taking into account their signs) sum of displacements that would occur during the propagation of one of the waves in the absence of the other.

Interference. The addition of waves in space, in which a time-constant distribution of the amplitudes of the resulting oscillations is formed, is called interference.

Let us find out under what conditions wave interference occurs. To do this, let us consider in more detail the addition of waves formed on the surface of the water.

You can simultaneously excite two circular waves in a bath using two balls mounted on a rod that makes harmonic vibrations(Fig. 118). At any point M on the surface of the water (Fig. 119), oscillations caused by two waves (from sources O 1 and O 2) will add up. The amplitudes of oscillations caused at point M by both waves will, generally speaking, differ, since the waves travel different paths d 1 and d 2. But if the distance l between the sources is much less than these paths (l « d 1 and l « d 2), then both amplitudes
can be considered almost identical.

The result of the addition of waves arriving at point M depends on the phase difference between them. Having traveled various distances d 1 and d 2, the waves have a path difference Δd = d 2 -d 1. If the path difference is equal to the wavelength λ, then the second wave is delayed compared to the first by exactly one period (just during the period the wave travels the path equal to length waves). Consequently, in this case the crests (as well as the troughs) of both waves coincide.

Maximum condition. Figure 120 shows the time dependence of the displacements X 1 and X 2 caused by two waves at Δd= λ. The phase difference of the oscillations is zero (or, which is the same, 2n, since the period of the sine is 2n). As a result of the addition of these oscillations, a resulting oscillation with double amplitude appears. Fluctuations in the resulting displacement are shown in color (dotted line) in the figure. The same thing will happen if the segment Δd contains not one, but any integer number of wavelengths.

The amplitude of oscillations of the medium at a given point is maximum if the difference in the paths of the two waves exciting oscillations at this point is equal to an integer number of wavelengths:

where k=0,1,2,....

Minimum condition. Let now the segment Δd fit half the wavelength. It is obvious that the second wave lags behind the first by half the period. The phase difference turns out to be equal to n, i.e. the oscillations will occur in antiphase. As a result of the addition of these oscillations, the amplitude of the resulting oscillation is zero, that is, there are no oscillations at the point under consideration (Fig. 121). The same thing will happen if any odd number of half-waves fits on the segment.

The amplitude of oscillations of the medium at a given point is minimal if the difference in the paths of the two waves exciting oscillations at this point is equal to an odd number of half-waves:

If the path difference d 2 - d 1 takes an intermediate value
between λ and λ/2, then the amplitude of the resulting oscillation takes on some intermediate value between double the amplitude and zero. But the most important thing is that the amplitude of oscillations at any point he changes over time. A certain, time-invariant distribution of vibration amplitudes appears on the surface of the water, which is called an interference pattern. Figure 122 shows a drawing from a photograph of the interference pattern of two circular waves from two sources (black circles). The white areas in the middle part of the photograph correspond to the swing maxima, and the dark areas correspond to the swing minima.

Coherent waves. To form a stable interference pattern, it is necessary that the wave sources have the same frequency and the phase difference of their oscillations is constant.

Sources that satisfy these conditions are called coherent. The waves they create are also called coherent. Only when coherent waves are added together does a stable interference pattern form.

If the phase difference between the oscillations of the sources does not remain constant, then at any point in the medium the phase difference between the oscillations excited by two waves will change. Therefore, the amplitude of the resulting oscillations changes over time. As a result, the maxima and minima move in space and the interference pattern is blurred.

Energy distribution during interference. Waves carry energy. What happens to this energy when the waves cancel each other? Maybe it turns into other forms and heat is released in the minima of the interference pattern? Nothing like this. The presence of a minimum at a given point in the interference pattern means that energy does not flow here at all. Due to interference, energy is redistributed in space. It is not distributed evenly over all particles of the medium, but is concentrated in the maxima due to the fact that it does not enter the minima at all.

INTERFERENCE OF LIGHT WAVES

If light is a stream of waves, then the phenomenon of light interference should be observed. However, it is impossible to obtain an interference pattern (alternating maxima and minima of illumination) using two independent light sources, for example two light bulbs. Turning on another light bulb only increases the illumination of the surface, but does not create an alternation of minimums and maximums of illumination.

Let's find out what is the reason for this and under what conditions the interference of light can be observed.

Condition for coherence of light waves. The reason is that the light waves emitted by different sources are not consistent with each other. To obtain a stable interference pattern, consistent waves are needed. They must have the same wavelengths and a constant phase difference at any point in space. Recall that such consistent waves with identical wavelengths and a constant phase difference are called coherent.

Almost exact equality of wavelengths from two sources is not difficult to achieve. To do this, it is enough to use good light filters that transmit light in a very narrow wavelength range. But it is impossible to realize the constancy of the phase difference from two independent sources. Atoms of the sources emit light independently of each other in separate “scraps” (trains) of sine waves, about a meter long. And such wave trains from both sources overlap each other. As a result, the amplitude of oscillations at any point in space changes chaotically with time, depending on how, at a given moment in time, wave trains from different sources are shifted relative to each other in phase. Waves from different light sources are incoherent because the phase difference between the waves does not remain constant. No stable pattern with a specific distribution of maxima and minima of illumination in space is observed.

Interference in thin films. Nevertheless, the interference of light can be observed. The curious thing is that it was observed for a very long time, but they just did not realize it.

You, too, have seen an interference pattern many times when, as a child, you had fun blowing soap bubbles or watched the rainbow colors of a thin film of kerosene or oil on the surface of water. “A soap bubble floating in the air... lights up with all the shades of colors inherent in the surrounding objects. A soap bubble is perhaps the most exquisite miracle of nature" (Mark Twain). It is the interference of light that makes a soap bubble so admirable.

The English scientist Thomas Young was the first to come up with the brilliant idea of ​​​​the possibility of explaining the colors of thin films by adding waves 1 and 2 (Fig. 123), one of which (1) is reflected from the outer surface of the film, and the second (2) from the inner. In this case, interference of light waves occurs - the addition of two waves, as a result of which a time-stable pattern of amplification or weakening of the resulting light vibrations is observed at different points in space. The result of interference (amplification or weakening of the resulting vibrations) depends on the angle of incidence of light on the film, its thickness and wavelength. Light amplification will occur if the refracted wave 2 lags behind the reflected wave 1 by an integer number of wavelengths. If the second wave lags behind the first by half a wavelength or an odd number of half-waves, then the light will weaken.

The coherence of waves reflected from the outer and inner surfaces of the film is ensured by the fact that they are parts of the same light beam. The wave train from each emitting atom is divided into two by the film, and then these parts are brought together and interfere.

Jung also realized that differences in color were due to differences in wavelength (or frequency of light waves). Light beams of different colors correspond to waves of different lengths. For mutual amplification of waves that differ from each other in length (the angles of incidence are assumed to be the same), different film thicknesses are required. Therefore, if the film has unequal thickness, then when illuminated with white light, different colors should appear.

A simple interference pattern occurs in a thin layer of air between a glass plate and a plane-convex lens placed on it, the spherical surface of which has a large radius of curvature. This interference pattern takes the form of concentric rings, called Newton's rings.

Take a plano-convex lens with a slight curvature of a spherical surface and place it on a glass plate. Carefully examining the flat surface of the lens (preferably through a magnifying glass), you will find a dark spot at the point of contact between the lens and the plate and a collection of small rainbow rings around it. The distances between adjacent rings quickly decrease as their radius increases (Fig. 111). These are Newton's rings. Newton observed and studied them not only in white light, but also when the lens was illuminated with a single-color (monochromatic) beam. It turned out that the radii of rings of the same serial number increase when moving from the violet end of the spectrum to the red; red rings have the maximum radius. You can check all this through independent observations.

Newton was unable to satisfactorily explain why rings appear. Jung succeeded. Let's follow the course of his reasoning. They are based on the assumption that light is waves. Let us consider the case when a wave of a certain length falls almost perpendicularly onto a plane-convex lens (Fig. 124). Wave 1 appears as a result of reflection from the convex surface of the lens at the glass-air interface, and wave 2 as a result of reflection from the plate at the air-glass interface. These waves are coherent: they have the same length and a constant phase difference, which arises due to the fact that wave 2 travels a longer path than wave 1. If the second wave lags behind the first by an integer number of wavelengths, then, adding up, the waves reinforce each other friend. The oscillations they cause occur in one phase.

On the contrary, if the second wave lags behind the first by an odd number of half-waves, then the oscillations caused by them will occur in opposite phases and the waves cancel each other out.

If the radius of curvature R of the lens surface is known, then it is possible to calculate at what distances from the point of contact of the lens with the glass plate the path differences are such that waves of a certain length λ cancel each other out. These distances are the radii of Newton's dark rings. After all, the lines of constant thickness of the air gap are circles. By measuring the radii of the rings, the wavelengths can be calculated.

Light wavelength. For red light, measurements give λ cr = 8 10 -7 m, and for violet light - λ f = 4 10 -7 m. The wavelengths corresponding to other colors of the spectrum take intermediate values. For any color, the wavelength of light is very short. Imagine an average sea wave several meters long, which grew so large that it occupied the entire Atlantic Ocean from the shores of America to Europe. The wavelength of light at the same magnification would be only slightly larger than the width of this page.

The phenomenon of interference not only proves that light has wave properties, but also allows us to measure the wavelength. Just as the pitch of a sound is determined by its frequency, the color of light is determined by its vibrational frequency or wavelength.

Outside of us, there are no colors in nature, there are only waves of different lengths. The eye is a complex physical device capable of detecting differences in color, which correspond to a very slight (about 10 -6 cm) difference in the length of light waves. Interestingly, most animals are unable to distinguish colors. They always see a black and white picture. Colorblind people - people suffering from color blindness - also do not distinguish colors.

When light passes from one medium to another, the wavelength changes. It can be detected like this. Fill the air gap between the lens and the plate with water or another transparent liquid with a refractive index. The radii of the interference rings will decrease.

Why is this happening? We know that when light passes from a vacuum into some medium, the speed of light decreases by a factor of n. Since v = λv, then either the frequency or the wavelength must decrease n times. But the radii of the rings depend on the wavelength. Therefore, when light enters a medium, it is the wavelength that changes n times, not the frequency.

Interference of electromagnetic waves. In experiments with a microwave generator, one can observe the interference of electromagnetic (radio) waves.

The generator and receiver are placed opposite each other (Fig. 125). Then a metal plate is brought from below in a horizontal position. Gradually raising the plate, an alternating weakening and strengthening of the sound is detected.

The phenomenon is explained as follows. Part of the wave from the generator horn directly enters the receiving horn. The other part of it is reflected from the metal plate. By changing the location of the plate, we change the difference between the paths of the direct and reflected waves. As a result, the waves either strengthen or weaken each other, depending on whether the path difference is equal to an integer number of wavelengths or an odd number of half-waves.

Observation of the interference of light proves that light exhibits wave properties when propagating. Interference experiments make it possible to measure the wavelength of light: it is very small, from 4 10 -7 to 8 10 -7 m.

Interference of two waves. Fresnel biprism - 1

INTERFERENCE PATTERN

INTERFERENCE PATTERN

Regular alternation of areas of higher and down. light intensity resulting from the superposition of coherent light beams, i.e., under conditions of a constant (or regularly changing) phase difference between them (see LIGHT INTERFERENCE). For spherical Max. intensity is observed at a phase difference equal to even number half-waves, and the minimum - with a phase difference equal to an odd number of half-waves. (See STRIPES OF EQUAL THICKNESS).

Physical encyclopedic Dictionary. - M.: Soviet Encyclopedia. Chief Editor A. M. Prokhorov. 1983 .

See what “INTERFERENCE PICTURE” is in other dictionaries:

interference pattern- The distribution of light intensity resulting from interference at the location where it is observed. [Collection of recommended terms. Issue 79. Physical optics. Academy of Sciences of the USSR. Committee of Scientific and Technical Terminology. 1970] Topics… …

interference pattern- interferencinis vaizdas statusas T sritis fizika atitikmenys: engl. fringe pattern; interference figure; interference image vok. Interferenzbild, n rus. interference pattern, f pranc. image d'interferences, f; image interferentielle, f … Fizikos terminų žodynas

diffraction pattern- An interference pattern that arises from the interference of light diffracted by optical inhomogeneities. [Collection of recommended terms. Issue 79. Physical optics. Academy of Sciences of the USSR. Committee of Scientific and Technical Terminology. 1970]… … Technical Translator's Guide

- (from the Greek hólos all, complete and...graphy) a method of obtaining a three-dimensional image of an object, based on wave interference. The idea of ​​G. was first expressed by D. Gabor (Great Britain, 1948), but the technical implementation of the method turned out to be... ...

A measuring device that uses wave interference. There are signals for sound and electromagnetic waves: optical (ultraviolet, visible, and infrared regions of the spectrum) and radio waves of various lengths. I. are used... ... Great Soviet Encyclopedia

Interference of light Young's experiment Interference of light is a redistribution of light intensity as a result of the superposition (superposition) of several coherent light waves. This phenomenon is accompanied by alternating ma... Wikipedia

Encyclopedia "Aviation"

interference research method- Rice. 1. Schematic diagram installations. Interference research method is one of the main optical methods for studying flows. Characteristics I.M.I.: a) the use of two coherent ... ... in interference devices Encyclopedia "Aviation"

The branch of physics that deals with all phenomena related to light, including infrared and ultraviolet radiation(see also PHOTOMETRY; ELECTROMAGNETIC RADIATION). GEOMETRIC OPTICS Geometric optics is based on... ... Collier's Encyclopedia

This is an article about interference in physics. See also Interference and Interference of light Interference pattern large quantity circular coherent waves, depending on the wavelength and distance between the sources Interference of waves is mutual ... Wikipedia

Let us consider and describe the interference pattern for harmonic waves.

Let the sources S t and S 2 be coherent and obtained by one of the listed methods.

Let's consider two cylindrical coherent light waves emanating from sources S t and S 2, which have the form of parallel thin luminous threads or narrow slits (Fig. 5.4). The region where these waves overlap is called the interference field. Throughout this entire area, there is an alternation of places with maximum and minimum light intensity. If a screen is placed in the interference field, then an interference pattern will be visible on it, which has the form of alternating light and dark stripes. Let us calculate the width of these stripes under the assumption that the screen is parallel to the plane passing through the sources S 1 and S 2. The position of the point on the screen will be characterized by the x coordinate, measured in the direction perpendicular to the lines S 1 and S 2 .. We will choose the origin at point O, relative to which S 1 and S 2. located symmetrically. We will consider the sources to be oscillating in the same phase. From Fig. 5.4 it is clear that

Hence,

Below it will be clarified that in order to obtain a discernible interference pattern, the distance between the sources d must be significantly less than the distance to the screen l. The distance x within which interference fringes are formed is also significantly less than l. Under these conditions we can put , then

Multiplying s 2 -s 1 by the refractive index of the medium n, we obtain the optical path difference

Substituting this path difference value into the maximum condition

gives that intensity maxima will be observed at x values ​​equal to

Here is the wavelength in the medium filling the space between the sources and the screen.

Substituting the value (5.1) into the condition

we obtain the coordinates of intensity minima:

Let's call the distance between two adjacent intensity maxima the distance between interference fringes, and the distance between adjacent intensity minima the width of the interference fringe. From formulas (5.2) and (5.3) it follows that the distance between the stripes and the width of the strip have the same value, equal to

According to formula (5.4), the distance between the stripes increases as the distance between the sources d decreases. With d comparable to l, the distance between the stripes would be of the same order as l, i.e., it would be several tenths of a micron. In this case, the individual stripes would be completely indistinguishable. In order for the interference pattern to become clear, the above-mentioned condition must be met: d<

Interference is the phenomenon of strengthening or weakening of oscillations, which occurs as a result of the addition of two or more waves with the same periods, propagating in space, and depends on the relationship between the phases of the resulting oscillations. In optics, what is usually observed is not the amplitude, but intensity Sveta.
The phenomenon of light interference is that when two or more light waves are added, the total light intensity differs from the sum of the intensities.

In the ideal case of monochromatic sources, when two beams of light with intensities are superimposed, the intensity distribution in the interference pattern is described by the formula:

The nature of the observed interference pattern depends on the relative position of the sources and the observation plane P (Fig. 1.1). Interference fringes can, for example, take the form of a family of concentric rings or hyperbolas. The simplest form is the interference pattern obtained by superposing two plane monochromatic waves, when the sources and

are located at a sufficient distance from the screen. In this case, the interference pattern has the form of alternating dark and light rectilinear stripes (interference maxima and minima), located at the same distance from each other. It is this case that is realized in many optical interference schemes.

Each interference maximum (light stripe) corresponds to the path difference, where m is an integer called the interference order. In particular, at , an interference maximum of zero order appears.

Interference is one of the most striking manifestations of the wave nature of light. This interesting and beautiful phenomenon can be observed when two or more light beams are superimposed. The light intensity in the area where the beams overlap has the character of alternating light and dark stripes, with the intensity at the maxima being greater and at the minima less than the sum of the beam intensities. When using white light, the interference fringes appear in different colors of the spectrum. We encounter interference phenomena quite often. The colors of oil stains on asphalt, the color of freezing window glass, the bizarre color patterns on the wings of some butterflies - all this is a manifestation of interference.

A simple qualitative explanation of the phenomena observed during interference can be given on the basis of wave concepts. Indeed, according to the principle of superposition, the total light field resulting from the superposition of waves is equal to their sum. The resulting field depends significantly on phase relationships, which turn out to be different at different points in space. At some points in space, interfering waves arrive in phase and give a resulting oscillation with an amplitude equal to the sum of the amplitudes of the terms (meaning the interference of two beams); at other points the waves turn out to be antiphase, and the amplitude of the resulting oscillation is . The intensity of the resulting field in the first case turns out to be equal to , in the second , while the sum of intensities is Thus, in the first case, in the second, at those points in space at which the phase shift is different from 0 and , some intermediate intensity value is realized - we thus obtain a smooth alternation of light and dark stripes, characteristic of the interference of two beams. Of course, the above considerations can be applied not only to light, but also to waves of any physical nature.

Let two waves of the same frequency, superimposed on each other, excite oscillations of the same direction at some point in space:

A 1 cos(ωt + α 1), A 2 cos(ωt + α 2). The amplitude of the resulting oscillation at a given point is determined by the formula A 2 =A 1 2 +A 2 2 + 2A 1 A 2 cos(α 2 –α 1).

If the phase difference α 2 - α 1 of the oscillations excited by the waves remains constant over time, then the waves are called coherent. The sources of such waves are also called coherent. When incoherent wavesα 2 - α 1 changes continuously, taking on any values ​​with equal probability, as a result of which the time-average value of cos(α 2 - α 1) is equal to zero. In this case, A2 = A 1 2 + A 2 2.

From here, taking into account the relation I~nA 2, we conclude that the intensity observed when incoherent waves are superimposed is equal to the sum of the intensities created by each of the waves separately:

In the case of coherent waves, cos(α 2 -α 1) has a constant value in time (but different for each point in space), so

I = I 1 + I 2 + 2 cos(α 2 - α 1).

At those points in space for which cos(α 2 -α 1) > 0, I will exceed I 1 + I 2; at points for which cos(α 2 -α 1)< 0,Iбудет меньшеI 1 +I 2 .

Thus, when coherent light waves are superimposed, a redistribution of the light flux in space occurs, resulting in intensity maxima in some places and intensity minima in others. This phenomenon is called wave interference. Interference is especially clearly manifested in the case when the intensity of both interfering waves is the same: I 1 = I 2. Then at minimums I = 0, and at maximums I = 4I 1. For incoherent waves, under the same condition, the same illumination is obtained everywhere I = 2I 1.

The interference of light is usually considered not at one point, but on a flat screen. Therefore, they talk about an interference pattern, which is understood as alternating bands of relatively higher and lower light intensity. The main characteristics of the interference pattern are the width of the interference fringes and the visibility of the interference pattern.

Study of light interference and determination of the wavelength of the radiation used

Methodological instructions for laboratory work

PENZA 2007

Goal of the work- study of methods for observing the interference pattern and measuring its parameters, determining the wavelength of the radiation used.

DEVICES AND ACCESSORIES

1.Optical bench.

3.Fresnel biprism.

5. Reflective screen.

METHODS FOR OBTAINING AN INTERFERENCE PATTERN

It is known from experience that if light from two sources (for example, from two incandescent lamps) falls on a certain surface, then the illumination of this surface is the sum of the illumination created by each source separately. The illumination of a surface is determined by the amount of luminous flux per unit area; therefore, the total luminous flux incident, in the case under consideration, on any element of the surface is equal to the sum of the fluxes from each source. This kind of observation led to the discovery of the law of independence of light beams.

However, the situation changes fundamentally if the surface is illuminated by two light waves emitted by the same point source, but taking different paths to the meeting point. In this case, as experience shows, individual areas of the surface will be illuminated very poorly; light waves, overlapping, cancel each other out. The illumination of other areas in which the overlapping waves reinforce each other will significantly exceed the double illumination that one of these waves could create.

Thus, a pattern of alternating maxima and minima of illumination will be observed on the surface, which is called an interference pattern (Fig. 1).

The appearance of such a pattern when light waves are superimposed is called light interference. A necessary condition for wave interference is coherence, i.e. equality of their frequencies and constancy of the phase difference over time. Two independent light sources, such as two light bulbs, produce incoherent waves and do not produce an interference pattern. There are various methods that make it possible to artificially create coherent waves and observe the interference of light. Let's look at some of them.

1.1. Young's method

The first experiment that allowed a quantitative analysis of the phenomenon of interference was Young's experiment, carried out in 1802.

Let's imagine a very small source of monochromatic light o (Fig. 2), illuminating two equally small and close to each other holes in the screen A.

According to Huygens' principle, these holes can be considered as independent sources of secondary spherical waves. If points and are located at equal distances from the light source S, then the phases of oscillations at these points will be the same (the waves are coherent), and at any point R second screen IN, where light waves from and will arrive, the phase difference of the overlapping oscillations will depend on the difference, which is called the path difference.

With a path difference equal to an even number of half-waves, the oscillation phases will differ by a multiple of 2π, and the light waves, when superimposed at the point R will reinforce each other, period R the screen will be more illuminated than neighboring points on a straight line OR.

The condition for maximum illumination of point P can be written as:

Where TO=1,2,3,4…

If the path difference is equal to an odd number of half-waves, then at the point R oscillations propagating from and will cancel each other out, and this point will not be illuminated. Condition for minimum illumination of a point

Same screen points IN, the path difference up to which satisfies the condition

will be illuminated, but their illumination will be less than maximum. Therefore, the interference pattern observed on the screen is a system of stripes, within which the illumination, when transitioning from a light stripe to a dark one, changes smoothly according to a sinusoidal law

For a point ABOUT screen, equidistant from the sources and , the difference in the path of the rays and is equal to zero, i.e. as a result of interference, this point will be maximally illuminated (zero order maximum).

Let us determine the distance to those points at which the following interference maxima will be observed, i.e. let's determine

From right triangles we have (by the Pythagorean theorem):

Subtracting term by term we get

Let us rewrite this equality in the form

Assuming that the distance between the sources is much less than the distance from the sources to the screen, we can assume that

Then equality (5) will take the form

In turn, then, from where

And finally, we find the distance to the points at which maxima are observed from conditions (1) and (8)

From (9)

Therefore, the first maximally illuminated line will be located at a distance starting from the middle of the screen:

The second line with maximum illumination will be located at a distance

The distance to the points where minima are observed (dark lines) is obtained from the condition

where = 0,1,2,3...

The period of the interference pattern, i.e. the distance between the nearest lines of equal illumination (for example, maximum or minimum), as follows from (9) or (10), is equal to

When illuminating the holes with white (polychromatic) light, colored stripes are obtained on the screen, rather than dark and light as in the described experiment.

1.2. Lloyd's method

In Fig. 3 shows an interference device consisting of a real light source S and a plane mirror (Lloyd's mirror). One beam of light emanating from a light source is reflected from the mirror and hits the screen. This beam of light can be imagined as emanating from a virtual image

light source formed by a mirror. In addition, the screen is hit by rays coming directly from the light source S. In the area of ​​the screen where both beams of light overlap, i.e. If two coherent waves are superimposed, an interference pattern will be observed.

1.3. Fresnel biprism

Coherent waves can also be transmitted using a Fresnel biprism - two prisms (with very small refractive angles) folded at their bases.

Figure 4 shows a diagram of the path of the rays in this experiment.

A beam of diverging rays from a light source S, passing the upper prism, is refracted to its base and spreads further, as if from a point - an imaginary image of a point. Another beam incident on the lower prism is refracted and deflected upward. The point from which the rays of this beam diverge is also an imaginary image of the point. Both beams overlap each other and produce an interference pattern on the screen. The result of interference at each point of the screen, for example, at point P, depends on the difference in the path of the rays incident on this point, i.e. from the difference in distances to imaginary light sources and .

2. INSTALLATION DESCRIPTION
AND OUTPUT OF THE CALCULATION FORMULA

In this work, it is required to determine the wavelength of the monochromatic radiation used based on the results of measuring the period of the observed interference pattern. The radiation source is a laser placed together with other components of the experimental setup on an optical bench (the physics of laser operation is described in the appendix). The optical diagram of the installation is shown in Fig. 5.

Parallel beam of light generated by laser LH, focused by lens L 1, and its focal point is the source illuminating the Fresnel biprism BF. Considering that the distance from the point to the biprism is much greater than the light spot on the biprism, i.e. divergence of a beam of rays emanating from the focus of a lens L 1, is small, as a first approximation we can assume that all rays incident on the biprism are parallel. Then the rays incident on the upper wedge of the biprism are deflected downward by an angle

Where P- refractive index of the biprism;

Refracting angle of a biprism.

The rays incident on the lower wedge are also deflected upward by an angle . Thus, from biprism to lens L 2 two parallel beams of light (two plane waves) propagate, the angle between which is equal to 2. Lens L 2 focuses these beams and forms two point sources in its focal plane, spaced apart from each other

where is the focal length of the lens L 2.

Considering that the hijack as well as the angle is very small, the distance between the sources can be written in the form

Coherent waves propagating from these sources superimpose on each other and form an interference pattern on the screen, the period of which is described by expression (11). Substituting in this expression

(which follows from formulas (12), (14) and Fig. 5) for the period we write

From here we get the calculation formula

The parameters included in formula (17) are summarized in the table.

PROCEDURE FOR PERFORMANCE OF THE WORK

1. Plug the power cord of the laser power supply into a power outlet. Use the “network” toggle switch located on the front panel of the power supply to turn on the laser.

2. On the optical bench, by moving the biprism and lens (moving the carts), install them in a position in which the interference pattern similar to Fig. 1 will be clearly visible.

3. Using the scale of the optical bench, determine the distance L from the lens L 1 to the screen E.

4. Using the scale grid of the screen, determine the period of the interference pattern (to most accurately determine the period, count how many light stripes fit on a segment of 20-30 mm, and then divide the length of the segment by the number of stripes).

5. Using the table data and calculation formula (17), calculate the wavelength .

6. Operations specified in paragraphs. 2-5, repeat 3-4 times, moving the lens each time L 1 50-100mm from the original position.

7. Average the obtained wavelength values.

Experience no.	P		, m	L, m	, m	, m	Wed, m
	1,53
	1,53
	1,53
	1,53

Control questions

1. What is wave interference?

2. What are the conditions for the appearance of an interference pattern?

3. Name the methods for producing coherent light waves.

4. What are the conditions for the formation of interference maxima and minima?

5. Explain how the period of the interference pattern depends on the refracting angle of the biprism and the wavelength of the light.

6. What is the purpose of the laser in this work?

7. Draw an optical diagram of the installation and explain the purpose of the elements.

Application

Physical basis of laser operation

By studying the mechanism of studying and absorption by a quantum system (atom or molecule), we found out that when a quantum system transitions from one energy state to another, a portion of electromagnetic energy is emitted or absorbed (Fig. 6).

At the same time, only such a radiation mechanism was discussed in which the atom moves to a lower energy level spontaneously (spontaneously), i.e. without any external stimulus (thermal radiation, luminescence, etc.). However, this radiation mechanism is not the only possible one.

A. Einstein established in 1917 that a quantum system can emit a quantum of energy (transitioning into a state with a lower energy) under the influence of an external electromagnetic field. This effect is called induced (stimulated) emission. It is a process inverse to the process of absorption of photons by the medium (negative absorption coefficient). That is, when an excited atom is exposed to another, external photon, having an energy equal to the energy of a photon emitted spontaneously, the excited atom will go to a lower energy level and emit a photon, which will be added to the incident one ("Fig. 6, b).

Induced electromagnetic radiation has a remarkable property; it is identical to the primary radiation incident on the substance, i.e. coincides with it in frequency, directional propagation and polarization, and is coherent throughout the entire volume of the substance. During spontaneous emission, photons have different phases and directions, and their frequencies are contained in a certain range of values.

Media in which induced (stimulated) radiation is possible have a negative absorption coefficient, since the radiant flux passing through such media is not weakened, but enhanced. These media differ from ordinary ones in that they contain more excited atoms than unexcited ones.

Under normal conditions, absorption always prevails over stimulated emission. This is explained by the fact that usually the number of unexcited atoms is always greater than the number of excited atoms, and the probabilities of transitions in one direction or another under the influence of external photons are the same (see Fig. b,a).

The possibility of creating a quantum system capable of delivering energy to an electromagnetic wave was first substantiated in 1939 by the Soviet physicist V.A. Fabrikant. Later, in 1955, Soviet physicists N.G. Basov and A.M. Prokhorov and, independently of them, American physicists L. Townes and J. Gordon developed the first operating quantum devices based on the use of stimulated radiation.

Devices using stimulated emission can operate in both amplification and generation modes. Accordingly, they are called quantum amplifiers or quantum generators. They are also called abbreviated as lasers (if it is amplification or generation of visible light) and masers - when amplification (or generation) of longer wavelength radiation (infrared rays, radio waves).

In a laser, the main main parts are: an active medium in which stimulated emission occurs, a source of excitation of particles of this medium (“incandescence”) and a device that allows the photon avalanche to be amplified.

Various substances are used as the working element (active medium) of modern quantum amplifiers and generators, most often in solid and gaseous states.

Let's consider one type of quantum generator based on synthetic ruby ​​(Fig. 7). The working element is cylinder 2 made of pink ruby ​​(active medium), which in chemical composition is aluminum oxide - corundum, in which aluminum atoms are replaced in small quantities by chromium atoms. The higher the chromium content, the more intense the red color of the ruby. Its color owes its origin to the fact that chromium atoms have selective absorption of light in the green-yellow part of the spectrum. In this case, the chromium atoms that absorbed the radiation go into an excited state. The reverse transition is accompanied by the emission of photons.

The cylinder dimensions can range from approximately 0.1 to 2 cm in diameter and from 2 to 23 cm in length. Its flat end ends are carefully polished and parallel with a high degree of precision. They are coated with silver so that one end of the ruby ​​becomes completely reflective (mirror-like), and the other, radiating, is not so densely silvered and is partially reflective (transmittance is usually from 10 to 25%).

The ruby ​​cylinder is surrounded by coils of a spiral flash lamp 1, which produces mainly green and blue radiation. Due to the energy of this radiation, excitation occurs. Only chromium ions participate in the phenomenon of light generation.

In Fig. Figure 8 shows a simplified diagram of the occurrence of stimulated emission in ruby. When a ruby ​​crystal is irradiated with light (from a lamp) with a wavelength of 5600A (green), chromium ions, which were previously in the ground state at energy level 1, move to the upper energy level 3, more precisely, to levels lying in band 3.

Within a short (but very specific) time, some of these ions will move back to level 1 with radiation, others will go to level 2, which is called metastable ( R-level). During this transition, no radiation occurs: chromium ions transfer energy to the ruby ​​crystal lattice. The ions remain at the metastable (intermediate) level for a longer time than at the upper level, as a result of which excess population (inverse population) of metastable level 1 is achieved. This is called optical pumping.

If we now direct radiation at a ruby ​​with a frequency corresponding to the energy of transition from level 2 to level 1, i.e.

then this radiation stimulates ions located at level 2 to give up their excess energy and move to level 1. The transition is accompanied by the emission of photons of the same frequency

Thus, the original signal is amplified many times over and an avalanche-like emission of narrow red lines occurs

Photons that move non-parallel to the longitudinal axis of the crystal leave the crystal, passing through the transparent side walls.

For this reason, the output beam is formed due to the fact that photon streams, undergoing multiple reflections from the front and rear mirror faces of the ruby ​​cylinder, having reached sufficient power, go out through that end face, which has some transparency.

The sharp focus of the beam allows energy to be concentrated into extremely small areas. The laser pulse energy is about 1 J, and the pulse time is about 1 μs. Consequently, the pulse power is about 1000 W.

If such a beam is concentrated onto an area of ​​100 μm, then the specific power during the pulse will be 10 9 W/cm. At this power, any refractory materials turn into steam. A powerful and very narrow beam of coherent light has already found application in technology for micro-welding and making holes in medicine - as a surgical knife for eye operations (“welding” a detached retina), etc.

GAS LASERS

A year after the creation of a ruby ​​laser in 1960 by the American physicist T. Maiman, a gas laser was created in which the active medium was a mixture of helium and neon gases at a pressure several hundred times less than atmospheric. The gas mixture was placed in a glass or quartz tube (Fig. 9), in which an electric discharge was maintained using an external voltage applied to the soldered electrodes E, i.e. electric current in gas.

In this respect, a gas laser tube differs little from ordinary neon advertising tubes. At the ends of the gas-discharge tube (several tens of centimeters long) mirrors 3 are placed, forming the same optical resonator as in a ruby ​​laser. However, population inversion in this laser is achieved in a different way than in solid-state lasers optically pumped by a flash lamp.

Free electrons, forming an electric discharge current in a gas, collide with atoms of the auxiliary gas, in this case helium, and transfer the helium atoms to an excited state, giving them kinetic energy upon impact. This excited state is metastable, i.e. a helium atom can remain in it for a relatively long time before it goes into the ground state due to spontaneous radiation. In fact, such a radiative transition does not have time to occur at all, since the helium atom gives up its energy to the neon atom that collides with it. As a result, the helium atom returns to its original state, and an inverse population occurs at the energy levels of neon, which ensures amplification and generation of radiation with a wavelength corresponding to red light.

The radiation power of a helium-neon laser operating in continuous mode is low, amounting to several thousandths of a watt. However, due to the high optical homogeneity of the gas medium, this radiation has a very high directivity and monochromaticity, as well as coherence. Such radiation can easily be caused to interfere, which is what is used in this work.

.