Lecture 3
Wave optics
Questions
1. Calculation of the interference pattern from two sources.
2. Interference of light in thin films.
3. Newton's rings.
1. Calculation of the interference pattern from two sources
Consider Jung's method as an example. The light source is a brightly lit slit S, from which the light wave falls on two narrow equidistant slits S 1 and S 2, parallel slits S. So the slit S 1 and S 2 play the role of coherent sources. Interference pattern (area BC) observed on the screen E , located at some distance parallel S 1 and S 2. Jung was the first to observe the phenomenon of interference.
Intensity anywhere M screen lying in the distance x from point 0 , determined by the stroke difference
Δ = L 2 L 1 (1)
;
;
;
As l >> dthen L 2 + L 1 2 l and
.
(2)
Maximum condition Δ \u003d mλ;
( m \u003d 0, ± 1, ± 2, ...) 
.
(3)
Minimum condition 
(m \u003d 0, ± 1, ± 2, ...) 
.
(4)
The width of the interference fringe is the distance between two adjacent maximums (or minimums)
,
(5)
fringe width 
independent of the order of interference m
and is constant. The main maximum of the interference at m
\u003d 0 in the center, from it the maxima of the first ( m
\u003d 1), the second ( m
\u003d 2) and so on of orders.
For visible light 10 -7 m, 
0.1 mm \u003d 10 -4 m (eye resolution) interference is observed when l/d
= x/
> 10 3 .
When using white light with a set of wavelengths from violet ( \u003d 0.39 μm) to red ( \u003d 0.75 μm) spectrum boundaries at m \u003d 0 the maxima of all waves coincide, then at m \u003d 1, 2,… spectrally colored stripes, closer to white purple, further red.
2. Interference of light in thin films
Light interference can be observed not only in laboratory conditions with the help of special installations and devices, but also in natural conditions. Thus, it is easy to observe the iridescent color of soap films, thin films of oil and mineral oil on the surface of the water, oxide films on the surface of hardened steel parts (discoloration). All these phenomena are caused by the interference of light in thin transparent films, which occurs as a result of the superposition of coherent waves arising from the reflection from the upper and lower surfaces of the film.
Optical path difference 1 and 2
(6)
where p Is the refractive index of the film; n 0 - refractive index of air, n 0 = 1; λ 0/2 is the half-wave length lost when ray 1 is reflected at the point ABOUTfrom the interface with an optically denser medium ( n >n 0 ,).
;
;
;
.
(7)
Maximum condition
:
(8)
Minimum condition
:
(9)
When the film is illuminated with white light, it is colored in a certain color, the wavelength of which satisfies the maximum interference. Therefore, the film thickness can be estimated by the color of the film.
Conditions (8), (9) depend at constant values n, 0 from the angle of incidence i and film thickness d, depending on this distinguish equal slope stripes and strips of equal thickness.
Stripes of equal slope are called interference fringes, resulting from the superposition of rays incident on a plane-parallel plate at the same angles.
Strips of equal thickness are called interference fringes resulting from the superposition of rays incident on a plate of variable thickness from places of equal thickness.
3. Newton's rings
Newton's rings a classic example of stripes of equal thickness.
In reflected light, the optical path difference (taking into account the half-wave loss λ 0/2 when reflected from a plane-parallel plate):
,
(10)
where d - gap width.
R 2
=
r 2
+ (R
–
d) 2
(d<<
R)
.
.
(11)
Maximum condition
light ring radius
:
(12)
Minimum condition
dark ring radius
:
(13)
The system of light and dark stripes is obtained only when illuminated with monochromatic light. In white light, the interference pattern changes, each light stripe turns into a spectrum.
Newton's rings can also be observed in transmitted light. In this case, the interference maxima in reflected light correspond to minima in transmitted light and vice versa.
By measuring the radii of Newton's rings, one can determine λ 0 (knowing the radius of curvature of the lens R) or R (knowing λ 0).
4. Application of light interference
4.1. Interference spectroscopy measurement of wavelengths.
4.2. Improving the quality of optical devices ("Anti-reflective optics") and obtaining highly reflective coatings.
Film thickness dand refractive indices of glass n art and films p pl is selected so that, with interference in reflected light, beams 1 and 2 extinguish each other. To do this, their optical path difference must satisfy the condition
,
(14)
;
.
(15)
Since it is impossible to achieve simultaneous cancellation of all wavelengths of the spectrum, this is usually done for green color (λ 0 = 550 nm), to which the human eye is most sensitive (in the solar radiation spectrum, these rays have the highest intensity).
In reflected light, lenses with coated optics appear to be colored red-violet. To improve the characteristics of the antireflection coating, it is made of several layers, which "antireflective" optical glasses more evenly over the entire spectrum.
4.3. Interferometer a device used for accurate (precision) measurement of lengths, angles, refractive indices and density of transparent media, etc.
The interference pattern is very sensitive to the path difference of the interfering waves: a negligible change in the path difference causes a noticeable shift of the interference fringes on the screen.
All interferometers are based on the same principle - dividing one beam into two coherent ones - and differ only structurally.
S light source;
R 1 translucent plate;
R 2 transparent plate;
M 1 , M 2 mirrors.
Beams 1 ′ and 2 ′ are coherent, therefore, interference is observed, the result of which will depend on the optical difference in the path of the beam 1 from point 0 to the mirror M 1 and ray 2 from point 0 to the mirror M 2. By the change in the interference pattern, one can judge the small displacement of one of the mirrors. Therefore, the Michelson interferometer is used for accurate (~ 10 -7 m) length measurements.
The most famous experiment, performed by Michelson (together with Morley) in 1887, aimed to discover the dependence of the speed of light on the speed of motion of an inertial coordinate system. As a result, it was found that the speed of light is the same in all inertial systems, which served as an experimental basis for the creation of Einstein's special theory of relativity.
Interference dilatometer device for changing body length when heated.
Soviet physicist Academician V.P. Linnik used the principle of operation of the Michelson interferometer to create microinterferometer (a combination of an interferometer and a microscope), used to control the cleanliness of surface treatment of metal products. Thus, the Linnik interferometer is a device designed for visual assessment, measurement and photographing of the heights of surface microroughness up to the 14th class of surface cleanliness.
Another sensitive optical device is refractometer Rayleigh interferometer. It is used to determine minor changes in the refractive index of transparent media depending on pressure, temperature, impurities, solution concentration, etc. Rayleigh interferometer measures the change in refractive index with very high accuracy Δ n ~ 10 -6 .
Interference patterns are light or dark streaks that are caused by beams that are in phase or out of phase with each other. Light and similar waves, when superimposed, add up if their phases coincide (both in the direction of increasing and decreasing), or they compensate each other if they are in antiphase. These phenomena are called constructive and destructive interference, respectively. If a beam of monochromatic radiation, all waves of which have the same length, passes through two narrow slits (the experiment was first carried out in 1801 by Thomas Young, an English scientist who thanks to him came to the conclusion about the wave nature of light), the two resulting beams can be directed on a flat screen, on which, instead of two overlapping spots, interference fringes are formed - a pattern of evenly alternating light and dark areas. This phenomenon is used, for example, in all optical interferometers.
Superposition
The defining characteristic of all waves is superposition, which describes the behavior of superimposed waves. Its principle is that when more than two waves are superimposed in space, then the resulting disturbance is equal to the algebraic sum of individual disturbances. Sometimes this rule is violated during large disturbances. This simple behavior leads to a number of effects called interference phenomena.
The phenomenon of interference is characterized by two extreme cases. In the constructive highs of the two waves coincide and they are in phase with each other. The result of their superposition is an increase in the disturbing effect. The amplitude of the resulting mixed wave is equal to the sum of the individual amplitudes. And, conversely, in destructive interference the maximum of one wave coincides with the minimum of the second - they are in antiphase. The amplitude of the combined wave is equal to the difference between the amplitudes of its constituent parts. In the case when they are equal, the destructive interference is complete, and the total disturbance of the medium is equal to zero.
Jung's experiment
An interference pattern from two sources unambiguously indicates the presence of overlapping waves. suggested that light is a wave that obeys the principle of superposition. His famous experimental achievement was his demonstration of the constructive and destructive in 1801. The modern version of Jung's experiment is essentially different only in that it uses coherent light sources. The laser evenly illuminates two parallel slits in an opaque surface. Light passing through them is observed on a distant screen. When the width between the slits significantly exceeds the wavelength, the rules of geometric optics are respected - two illuminated areas are visible on the screen. However, as the slits approach each other, the light diffracts, and the waves on the screen are superimposed on each other. Diffraction itself is a consequence of the wave nature of light and is another example of this effect.
Interference pattern
Determines the resulting intensity distribution on the illuminated screen. An interference pattern occurs when the path difference from the slit to the screen is equal to an integer number of wavelengths (0, λ, 2λ, ...). This difference ensures that the highs arrive at the same time. Destructive interference occurs when the path difference is an integer number of wavelengths shifted by half (λ / 2, 3λ / 2, ...). Jung used geometric arguments to show that superposition results in a series of equally spaced bands or areas of high intensity, corresponding to regions of constructive interference, separated by dark areas of total destructive.
Hole spacing
An important parameter of the double-slit geometry is the ratio of the light wavelength λ to the aperture spacing d. If λ / d is much less than 1, then the distance between the stripes will be small and no aliasing effects will be observed. By using closely spaced slits, Jung was able to separate dark and light areas. Thus, he determined the wavelengths of the colors of visible light. Their extremely small value explains why these effects are observed only under certain conditions. To separate the areas of constructive and destructive interference, the distances between the sources of light waves must be very small.
Wavelength
Observing interference effects is challenging for two other reasons. Most light sources emit a continuous spectrum of wavelengths, resulting in multiple interference patterns superimposed on each other, each with its own spacing between stripes. This eliminates the most pronounced effects, such as areas of complete darkness.
Coherence
For interference to be observed over an extended period of time, coherent light sources must be used. This means that the radiation sources must maintain a constant phase relationship. For example, two harmonic waves of the same frequency always have a fixed phase relationship at every point in space - either in phase, or in antiphase, or in some intermediate state. However, most light sources do not emit true harmonic waves. Instead, they emit light in which random phase changes occur millions of times per second. Such radiation is called incoherent.
The ideal source is a laser
Interference is still observed when waves of two incoherent sources are superimposed in space, but the interference patterns change randomly, along with a random phase shift. including the eyes, cannot register a rapidly changing image, but only the time-averaged intensity. The laser beam is almost monochromatic (i.e., consists of one wavelength) and highly coherent. It is an ideal light source for observing interference effects.
Frequency definition
After 1802, Jung's measured wavelengths of visible light could be related to the insufficiently accurate speed of light available at the time to roughly calculate its frequency. For example, for green light it is about 6 × 10 14 Hz. This is many orders of magnitude higher than the frequency. For comparison, a person can hear sound with frequencies up to 2 × 10 4 Hz. What exactly fluctuated at this rate remained a mystery for the next 60 years.
Interference in thin films
The effects observed are not limited to the double slit geometry used by Thomas Young. When rays are reflected and refracted from two surfaces separated by a distance comparable to the wavelength, interference occurs in thin films. The role of the film between the surfaces can be played by vacuum, air, any transparent liquids or solids. In visible light, interference effects are limited to dimensions on the order of a few micrometers. A well-known example of film is a soap bubble. The light reflected from it is a superposition of two waves - one is reflected from the front surface, and the other from the back. They overlap in space and add up to each other. Depending on the thickness of the soap film, the two waves can interact constructively or destructively. A complete calculation of the interference pattern shows that for light with one wavelength λ, constructive interference is observed for a film with a thickness of λ / 4, 3λ / 4, 5λ / 4, etc., and destructive interference is observed for λ / 2, λ, 3λ / 2, ...
Calculation formulas
The phenomenon of interference has found many applications, so it is important to understand the basic equations that apply to it. The following formulas can be used to calculate the various quantities associated with interference for the two most common cases.
The location of light stripes, that is, areas with constructive interference, can be calculated using the expression: y light. \u003d (λL / d) m, where λ is the wavelength; m \u003d 1, 2, 3, ...; d is the distance between the slots; L is the distance to the target.
The location of the dark stripes, that is, areas of destructive interaction, is determined by the formula: y dark. \u003d (λL / d) (m + 1/2).
For another type of interference - in thin films - the presence of constructive or destructive overlap determines the phase shift of the reflected waves, which depends on the thickness of the film and its refractive index. The first equation describes the case when there is no such bias, and the second describes a half wavelength shift:
Here λ is the wavelength; m \u003d 1, 2, 3, ...; t is the path traversed in the film; n is the refractive index.
Observation in nature
When the sun illuminates the bubble, bright bands of color can be seen as different wavelengths are destructively interfered with and removed from the reflection. The remaining reflected light appears to complement the distant colors. For example, if there is no red component as a result of destructive interference, then the reflection will be blue. Thin films of oil on water have a similar effect. In nature, the feathers of some birds, including peacocks and hummingbirds, and the shells of some beetles appear rainbow colored, and change color as the viewing angle changes. The physics of optics here consists in the interference of reflected light waves from thin layered structures or arrays of reflecting rods. Likewise, pearls and shells have an iris due to the superposition of reflections from several layers of mother-of-pearl. Gemstones such as opal exhibit beautiful interference patterns due to the scattering of light from regular structures formed by microscopic spherical particles.
Application
There are many technological applications of light interference in everyday life. The physics of the optics of cameras is based on them. Conventional anti-reflective lens coating is a thin film. Its thickness and refraction of the rays are chosen in such a way as to produce destructive interference of reflected visible light. More specialized coatings, consisting of several layers of thin films, are designed to transmit radiation only in a narrow wavelength range and, therefore, are used as light filters. Multilayer coatings are also used to increase the reflectivity of the mirrors of astronomical telescopes, as well as optical resonators of lasers. Interferometry, a precise measurement technique used to record small changes in relative distances, is based on observing the shifts in the dark and light bands produced by reflected light. For example, measuring how the interference pattern will change allows you to establish the curvature of the surfaces of optical components in fractions of an optical wavelength.
Study the interference of light and determine the wavelength of the radiation used
Methodical instruction for laboratory work
PENZA 2007
Objective - study of methods for observing the interference pattern and measuring its parameters, determining the wavelength of the radiation used.
INSTRUMENTS AND ACCESSORIES
1.Optical bench.
3. Fresnel biprism.
5.Reflective screen.
METHODS FOR OBTAINING INTERFERENCE PICTURE
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 the surface is determined by the value of the luminous flux per unit area, therefore, the total luminous flux incident, in this case, on any surface element, is equal to the sum of the fluxes from each of the sources. Observations of this kind 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 passing different paths to the meeting point. In this case, as experience shows, some areas of the surface will be very weakly illuminated; light waves, overlapping, extinguish each other. The illumination of other areas, on which the superimposed waves amplify each other, will significantly exceed the double illumination that one of these waves could create.
Thus, a pattern of alternating maximums and minimums 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 in time of the phase difference. Two independent light sources, such as two light bulbs, create incoherent waves and do not create an interference pattern. There are various methods for artificially creating coherent waves and observing the interference of light. Let's consider some of them.
1.1. Young's method
The first experiment that allowed for a quantitative analysis of the phenomenon of interference was the experiment of Young, staged in 1802.
Imagine a very small source of monochromatic light o (Fig. 2), illuminating two equally small and closely spaced holes in the screen AND.
According to Huygens' principle, these holes can be considered as independent sources of secondary spherical waves. If points and are located at the same distance from the light source S, then the oscillation phases at these points will be the same (waves are coherent), and at some point R second screen IN, where the light waves from and will come, 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, point R the screen will be more illuminated than adjacent 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 vibrations propagating from and will damp each other, and this point will not be illuminated. Condition of minimum illumination of a point
Same screen dots IN, the path difference to which satisfies the condition
will be illuminated, but their illumination will be less than the maximum. Therefore, the interference pattern observed on the screen is a system of stripes, within which the illumination, when passing from a light stripe to a dark one, changes smoothly according to a sinusoidal law
For 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 (maximum of the zero order).
Let us determine the distance to those points at which the following interference maxima will be observed, i.e. define.
From right-angled triangles and we have (by the Pythagorean theorem):
Subtracting term by term we get
We rewrite this equality as
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) takes the form
In turn, then where
And finally, the distance to the points at which the maxima are observed can be found from conditions (1) and (8)
From (9)
Therefore, the first maximum 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 (dark lines) are observed can be obtained from the condition
where \u003d 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 the holes are illuminated with white (polychromatic) light, colored stripes are obtained on the screen, and not 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 flat mirror (Lloyd's mirrors). One light beam emanating from the light source is reflected from the mirror and hits the screen. This beam of light can be imagined starting from a virtual image
a light source formed by a mirror. In addition, rays coming directly from the light source hit the screen. S... In the area of \u200b\u200bthe screen where both light beams overlap, i.e. two coherent waves are superimposed, an interference pattern will be observed.
1.3. Fresnel biprism
Coherent waves can also be charged using a Fresnel biprism - two prisms (with very small refractive angles) folded in bases.
Figure 4 shows a diagram of the path of the rays in this experiment.
A beam of divergent rays from a light source Spassing the upper prism, it is refracted to its base and spreads further as if from a point - an imaginary image of a point. Another beam, falling on the lower prism, is refracted and deflected upward. The point from which the rays of this beam diverge is also a virtual image of the point. Both beams are superimposed on each other and give an interference pattern on the screen. The result of the 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. DESCRIPTION OF THE UNIT
AND CONCLUSION OF THE CALCULATION FORMULA
In this work, it is required to determine the wavelength of the monochromatic radiation used from the results of measuring the period of the observed interference pattern. The radiation source is a laser placed together with other units of the experimental setup on an optical bench (the physics of laser operation is described in the appendix). The optical layout of the setup is shown in Fig. 5.
Parallel beam of light generated by a laser LHfocused 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 larger than the light spot on the biprism, i.e. divergence of a beam of rays emanating from the focus of the lens L 1, is small, in the first approximation we can assume that all rays incident on the biprism are parallel. Then the rays falling on the upper wedge of the biprism deflect downward by an angle
where p is the refractive index of the biprism;
Refractive angle of the biprism.
The beams falling on the lower wedge also deflect upward at an angle. Thus, from biprism to lens L 2 two parallel beams of light (two plane waves) propagate, the angle between which is 2. Lens L 2 focuses these beams and forms two point sources in its focal plane, spaced from each other at a distance
where is the focal length of the lens L 2.
Considering that the hijacking 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 overlap each other and form an interference pattern on the screen, the period of which is described by expression (11). Substituting into 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.
ORDER OF PERFORMANCE OF WORK
1. Connect the power plug of the laser power supply unit to a power outlet. Switch on the laser with the “mains” toggle switch located on the front panel of the power supply unit.
2. On the optical bench, by moving the biprism and the lens (moving the trolleys), set them in such a position in which the interference pattern similar to Fig.1 will be clearly visible.
3. On the scale of the optical bench, determine the distance L from the lens L 1 to the screen E.
4. On the scale grid of the screen, determine the period of the interference pattern (for the most accurate determination of the period, it is considered how many light stripes fit in a segment of 20-30 mm, and then the length of the segment is divided by the number of stripes).
5. Using the data in the table and the calculation formula (17), calculate the wavelength.
6. Operations specified in p. 2-5, repeat 3-4 times, moving the lens each time L 1 50-100mm from the original position.
7. Averaged the obtained wavelength values.
| Experience number | p | , m | L, m | , m | , m | Wed, m | |
| 1,53 | |||||||
| 1,53 | |||||||
| 1,53 | |||||||
| 1,53 |
test questions
1. What is wave interference?
2. What are the conditions for the appearance of an interference pattern?
3. Name the methods of obtaining 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 refractive angle of the biprism and the light wavelength.
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 basics of lasers
Studying the mechanism of study and absorption by a quantum system (atom or molecule), we found out that when a quantum system passes from one energy state to another, a portion of electromagnetic energy is emitted or absorbed (Fig. 6).
In this case, only such a mechanism of radiation was mentioned, in which the atom goes to a lower energy level spontaneously (spontaneously), i.e. without any external impulse (thermal radiation, luminescence, etc.). However, this radiation mechanism is not the only possible one.
A. Einstein in 1917 established that a quantum system can emit a quantum of energy (while passing into a state with a lower energy) under the influence of an external electromagnetic field. This effect is called induced (stimulated) radiation. It is the reverse 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 no lower energy level and emit a photon that will be added to the incident one ("Fig. 6, b).
The induced electromagnetic radiation has a remarkable property, it is identical with the primary radiation incident on the substance, i.e. coincides with it in frequency, direction of propagation and polarization and is coherent in the entire volume of matter. In 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 attenuated, but enhanced. These media differ from ordinary ones in that there are more excited atoms in them than unexcited ones.
Under normal conditions, absorption always dominates 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 the other under the influence of external photons are the same ("see Fig. B, a).
The possibility of creating a quantum system capable of giving 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. Towns and J. Gordon developed for the first time working quantum devices based on the use of induced radiation.
Instruments using stimulated radiation can operate in both amplification and generation modes. Accordingly, they are called quantum amplifiers or quantum generators. They are also called lasers for short (if it is amplification or generation of visible light) and masers - when amplifying (or generating) more long-wavelength radiation (infrared rays, radio waves).
In a laser, the main main parts are: an active medium in which stimulated radiation arises, a source of excitation of particles of this medium ("incandescence") and a device that allows amplification of a photon avalanche.
Various substances are used as a working element (active medium) of modern quantum amplifiers and generators, most often in a solid and pi gaseous state.
Consider one of the types of a quantum generator based on synthetic ruby \u200b\u200b(Fig. 7). The working element is cylinder 2 made of pink ruby \u200b\u200b(active medium), which, according to its chemical composition, is alumina-corundum, in which aluminum atoms in a small amount are replaced 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 have absorbed the radiation pass into an excited state. The reverse transition is accompanied by the emission of photons.
The dimensions of the cylinder can be approximately 0.1 to 2 cm in diameter and 2 to 23 cm in length. Its flat end ends are carefully polished and parallel to a high degree of precision. They are silver-plated so that one end of the ruby \u200b\u200bbecomes fully reflective (specular), and the other, emitting, is silvered less densely and is partially reflective (transmittance is usually 10 to 25%).
The ruby \u200b\u200bcylinder is surrounded by turns of a spiral flash tube 1, which gives off 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. 8 shows a simplified diagram of the appearance of stimulated emission in ruby. When a ruby \u200b\u200bcrystal 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 quite definite) time, some of these ions will go back to level 1 with radiation, others - to level 2, which is called metastable ( R -level). No radiation occurs during this transition: chromium ions give up energy to the ruby \u200b\u200bcrystal lattice. The ions remain at the metastable (intermediate) level for a longer time than at the upper level, as a result of which an excess population (inverse population) of the metastable level 1 is achieved. This is called optical pumping.
If we now direct radiation at the ruby \u200b\u200bwith a frequency corresponding to the energy of the 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 go to level 1. The transition is accompanied by the emission of photons of the same frequency
Thus, the initial signal is amplified many times and an avalanche emission of narrow red lines occurs.
The photons, which move not 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 the photon fluxes, undergoing multiple reflections from the front and rear mirror faces of the ruby \u200b\u200bcylinder, having reached sufficient power, go out through that end face that has a certain transparency.
The sharp beam directivity allows you to concentrate energy in extremely small areas. The laser pulse energy is of the order of 1 J, and the pulse time is of the order of 1 μs. Therefore, the pulse power is about 1000 W.
If such a beam is concentrated over an area of \u200b\u200b100 μm, then the specific power during the pulse will be 10 9 W / cm. With this power, any refractory materials turn into steam. A powerful and very narrow beam of coherent light has already found application in technology for microwelding and making holes in medicine - as a surgical knife in ocular operations ("welding" of the detached retina), etc.
GAS LASERS
A year after the ruby \u200b\u200blaser was created in 1960 by the American physicist T.Meyman, a gas laser was created in which a mixture of helium and neon gases served as an active medium 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 with the help of an external voltage applied to the soldered electrodes E; electric current in gas.
In this respect, a gas laser tube differs little from conventional 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 \u200b\u200blaser. However, population inversion in this laser is achieved in a different way than in solid-state lasers with optical pumping from a flash lamp.
Free electrons, which form an electric discharge current in the gas, collide with the atoms of the auxiliary gas, in this case, helium, and transfer the helium atoms into an excited state, giving them kinetic energy upon impact. This excited state is metastable, i.e. a helium atom can be in it for a relatively long time before it goes into the ground state due to spontaneous emission. In fact, such a radiative transition does not have time to occur at all, since the helium atom gives up its energy to the colliding neon atom. As a result, the helium atom returns to its original state, and an inverse population appears at the energy levels of neon, which provides amplification and generation of radiation with a wavelength corresponding to red light.
The radiation power of a helium-neon laser operating in a continuous mode is low, it amounts to several thousandths of a watt. However, due to the high optical homogeneity of the gaseous medium, this radiation has a very high directivity and monochromaticity, as well as coherence. Such radiation can be easily made to interfere, which is used in this work.
.The wave properties of light are manifested in the phenomena of interference. The essence of the latter lies in the fact that under certain conditions in an area illuminated by two light sources, a periodic change in illumination in the observation space is created; if one of the sources is extinguished, then the illumination in the same area changes monotonically.
Let two traveling electromagnetic waves propagate in space, the electric vectors of which are parallel:
Here r 1 and r 2 - distance from wave sources to the considered point in space, ω 1 - angular vibration frequencies, - wave numbers.
Assuming that the observation area is far from the sources and small in size, we can neglect the change in amplitude with distance. Then the total oscillation at some point will be described by the expression:
where the sign Δ denotes the difference of the corresponding values.
Since almost all light receivers react to energy and have significant inertia, the perception of these waves will be determined by the time average value of the square of the amplitude:
(here we took into account that the mean square of the cosine is 1/2). But the radiation intensity is proportional to the square of the amplitude, therefore, in this case, the intensities simply add up:
This is observed when the field of view is illuminated by independent sources. Oscillations (and sources) of this kind are called incoherent (inconsistent). A completely different result is obtained if the sources satisfy strict (but feasible in practice) conditions:
a) their vibration frequencies are strictly equal;
b) the difference between the initial phases is constant during the entire observation time (for simplicity, we will take it equal to zero).
Sources that meet the specified conditions are called coherent (agreed); In this case, instead of (3.1), we obtain:
(3.2)
Thus, now the light intensity significantly depends on the position of the observation point: at
it is maximum (and is twice the intensity of two similar incoherent sources); at
it vanishes.
From the classical point of view, the emission of light by atoms of a substance in the simplest case can be represented as follows: each atom, being excited in one way or another, emits a “fragment of a cosine wave” (a wave train) during the time τ rad (10 -10 - 10 -8 s); then it remains in an unexcited state for some time τ, after which it is again excited and creates a new train. Subsequent "scraps of cosine" are in no way related to each other; the acts of radiation of individual atoms are also completely independent. Therefore, coherence exists only within the limits of each train, and the "coherence time" τ kog cannot exceed the radiation time τ rad. The path traversed by the wave during the coherence time equal to l COG-st KOG, called "coherence length"; it is always less than the length of the train l q \u003d cτ rad.
For conventional gas light sources (not lasers), the coherence length is usually less than a centimeter. At an average frequency of light waves v \u003d 5x10 14 Hz, a large number of waves - about hundreds of thousands - fit in the train; the light is rather monochromatic. Sources of coherent radiation (lasers), in which the acts of radiation of individual atoms are connected with each other, have an enormous coherence time, reaching 10 -5 -10 -3 s, and a coherence length of the order of hundreds of meters. In this case, of course, the monochromaticity is dramatically improved. In radio-technical generators, the relative monochromaticity of the radiation is close to the laser one and even exceeds it by several orders of magnitude. Due to the long period of oscillations, the coherence time increases to tens of hours, and the coherence length (due to the large wavelength) reaches 10 10 km, ie, the size of the solar system. Therefore, at radio frequencies, one can observe the interference of waves from two independent sources - simple generators of electrical oscillations for several minutes.
So, in ordinary optics, the sources are incoherent, and to obtain coherent radiation one has to use secondary - dependent - radiation sources; they are created by splitting the wave of the primary source into two waves, traversing different paths and converging again. Naturally, the time delay of one wave relative to the other at the observation point should not exceed the source coherence time. Therefore, the size of the area where interference can be observed is determined by the difference in the distances from the observation point to the sources and the coherence length of the latter.
Augustin Fresnel's idea
The French physicist Augustin Fresnel (1788-1827) found in 1815 a simple and ingenious method to obtain coherent light sources. 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 a single atom will split into two coherent trains. This will be the case for the wave trains emitted by each source atom. The light emitted by one atom gives 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 the essence is the same. By splitting the beam into two parts, two imaginary light sources are obtained, giving coherent waves. To do this, use two mirrors (Fresnel's bizercal), a biprism (two prisms folded by bases), a bilens (a lens cut in half with the halves apart), etc.
The first experiment to observe the interference of light in laboratory conditions belongs to I. Newton. He observed an interference pattern that occurs when light is reflected in a thin air gap between a flat glass plate and a plano-convex lens with a large radius of curvature. The interference pattern was in the form of concentric rings, called Newton's rings (Fig. 3 a, b).
Fig.3a Fig.3b
Newton could not explain from the point of view of the corpuscular theory why rings appear, but he understood that this is due to some periodicity of light processes.
Young's experience with two slits
The metal skeleton is formed by a crystal lattice, in the nodes of which there are ions.
In the presence of an electric field, the disordered motion of electrons is superimposed on their ordered motion under the action of the field forces.
As they move, electrons collide with lattice ions. This explains the electrical resistance.
The electronic theory made it possible to quantitatively describe many phenomena, but in a number of cases, for example, when explaining the dependence of the resistance of metals on temperature, etc., it was practically powerless. This was due to the fact that in the general case it is impossible to apply the laws of Newtonian mechanics and the laws of ideal gases to electrons, which was clarified in the 30s of the 20th century.
In 1902, in Kaufman's experiments, it was discovered that the ratio of the charge e to its mass m is not a constant value, but depends on the speed (it decreases with increasing speed). The theory implied that q \u003d const. This means that the mass is growing.
Basic physical processes in semiconductors and their properties. Intrinsic semiconductor and intrinsic electrical conductivity
A semiconductor is a material that, in terms of its conductivity, occupies an intermediate place between conductors and dielectrics and differs from conductors in a strong dependence of conductivity on the concentration of impurities, temperature and exposure to various types of radiation. The main property of a semiconductor is an increase in electrical conductivity with increasing temperature.
Semiconductors are substances with a band gap of the order of several electron volts (eV). For example, diamond can be classified as a wide-gap semiconductor, while indium arsenide is classified as a narrow-gap semiconductor. Semiconductors include many chemical elements (germanium, silicon, selenium, tellurium, arsenic and others), a huge number of alloys and chemical compounds (gallium arsenide, etc.). Almost all inorganic substances of the world around us are semiconductors. The most widespread semiconductor in nature is silicon, which makes up almost 30% of the earth's crust.
Depending on whether the impurity atom donates an electron or captures it, the impurity atoms are called donor or acceptor. The nature of the impurity can vary depending on which atom of the crystal lattice it replaces, in which crystallographic plane it is embedded.
The conductivity of semiconductors is highly temperature dependent. Near absolute zero temperature, semiconductors have the properties of dielectrics. Semiconductors are characterized by both the properties of conductors and dielectrics. In semiconductor crystals, atoms establish covalent bonds (that is, one electron in a silicon crystal, like diamond, is bonded by two atoms), electrons need a level of internal energy to release from the atom (1.76 10 -19 J versus 11.2 10 −19 J, which characterizes the difference between semiconductors and dielectrics).
This energy appears in them with an increase in temperature (for example, at room temperature, the energy level of thermal motion of atoms is equal to 0.4 · 10 −19 J), and individual electrons receive energy to detach from the nucleus. As the temperature rises, the number of free electrons and holes increases; therefore, in a semiconductor that does not contain impurities, the electrical resistivity decreases. It is conventionally accepted to consider as semiconductors elements with an electron binding energy less than 1.5-2 eV. The electron-hole conduction mechanism is manifested in intrinsic (that is, without impurities) semiconductors. It is called intrinsic electrical conductivity of semiconductors.
During the breaking of the bond between the electron and the nucleus, a free space appears in the electron shell of the atom. This causes the transition of an electron from another atom to an atom with free space. On the atom from which the electron passed, another electron enters from another atom, and so on. This process is caused by the covalent bonds of atoms. Thus, a positive charge moves without moving the atom itself. This conditional positive charge is called a hole.
Usually the hole mobility in a semiconductor is lower than the electron mobility.
Semiconductors, in which free electrons and "holes" appear in the process of ionization of the atoms, of which the entire crystal is built, are called semiconductors with intrinsic conductivity... In semiconductors with intrinsic conductivity, the concentration of free electrons is equal to the concentration of "holes".
Own semiconductoris a pure semiconductor, the content of impurities in which does not exceed 10 −8 ... 10 −9%. The concentration of holes in it is always equal to the concentration of free electrons, since it is determined not by doping, but by the intrinsic properties of the material, namely, thermally excited carriers, radiation, and intrinsic defects. The technology makes it possible to obtain materials with a high degree of purification, among which indirect-gap semiconductors can be distinguished: Si (at room temperature, the number of carriers n i \u003d p i \u003d 1.4 10 10 cm -3), Ge (at room temperature the number of carriers n i \u003d p i \u003d 2.5 · 10 13 cm -3) and direct-gap GaAs.
A semiconductor without impurities has own electrical conductivity, which has two contributions: electron and hole. If no voltage is applied to the semiconductor, then electrons and holes undergo thermal motion and the total current is zero. When a voltage is applied in a semiconductor, an electric field arises, which leads to the appearance of a current called drift current i dr. The total drift current is the sum of two contributions from the electron and hole currents:
i dr \u003d i n + i p,
where index n corresponds to an electronic deposit, and p - hole. The resistivity of a semiconductor depends on the concentration of carriers and on their mobility, as follows from the simplest Drude model. In semiconductors, with an increase in temperature due to the generation of electron-hole pairs, the concentration of electrons in the conduction band and holes in the valence band increases much faster than their mobility decreases, therefore, with increasing temperature, the conductivity increases.
The process of death of electron-hole pairs is called recombination. In fact, the conductivity of an intrinsic semiconductor is accompanied by the processes of recombination and generation, and if their rates are equal, then they say that the semiconductor is in an equilibrium state. The number of thermally excited carriers depends on the band gap; therefore, the number of current carriers in intrinsic semiconductors is small compared to doped semiconductors and their resistance is much higher.
Evaporation: the essence of the process, ways of organizing it
Evaporation - the process of concentration of solutions, which consists in the partial removal of the solvent by evaporation during boiling.
Evaporation at temperatures below the boiling point of a given solution occurs from its surface, while during boiling, the solvent evaporates in the entire volume of the boiling solution, which significantly intensifies the process of removing the solvent from the solution.
The evaporation process is widely used:
1) to increase the concentration of dilute solutions,
2) the separation of solutes from them by crystallization,
3) sometimes for the isolation of the solvent (for example, when receiving drinking or industrial water in evaporation desalination plants).
To carry out the evaporation process, it is necessary to transfer the heat from the coolant to the boiling solution, which is possible only if there is a temperature difference between them. When analyzing and calculating the evaporation process, this temperature difference between the coolant and the boiling solution is usually called the useful temperature difference. Saturated water vapor, which is called heating or primary steam, is most often used as a heat carrier in evaporators, although, of course, other types of heating and other heat carriers can be used for this purpose. The steam formed during the evaporation of solutions is called secondary, or juice.
Thus, evaporation is a typical process of transferring heat from a more heated heat carrier - heating steam - to a boiling solution.
Evaporation is carried out: at atmospheric pressure; under vacuum; under pressure greater than atmospheric.
The main differences in the evaporation process, as a result of which evaporation in a number of thermal processes is singled out as an independent section, lies in the peculiarities of its hardware design and the method of calculating evaporation plants.
Unlike conventional heat exchangers, evaporators consist of two main units: a heating chamber, or a boiler, (usually in the form of a bundle of pipes) and a separator designed to capture drops of solution from the vapor formed during the boiling of the solution. For a more complete collection in the separator, spray traps of various designs are installed.
To reduce the rate of deposition of impurities (scale) on the walls of the pipes in the evaporators, conditions are created for intensive circulation of the solution (while the speed of the solution in the pipes is 1-3 m / s). Naturally, the circulation of the solution should also be taken into account when calculating the evaporators. The evaporator of this type operates on the principle of directed natural circulation, which is caused by the difference in the density of the boiling solution in the circulation pipe and in the boiling pipes of the heating chamber.
The difference in density is due to the difference in the specific heat flux per unit volume of the solution: in boiling pipes it is higher than in a circulation pipe.
Therefore, the intensity of boiling, and consequently, vaporization in them is also higher; the vapor-liquid mixture formed here has a lower density than in the circulation pipe. This leads to a directed circulation of the boiling solution, which goes down through the circulation pipe, and goes up through the boiling pipes. The vapor-liquid mixture then enters the separator, in which the vapor is separated from the solution, and it is removed from the apparatus. The one stripped off solution comes out of the fitting in the bottom of the apparatus. Thus, in devices with natural circulation of the solution, an organized circulation loop is created according to the scheme: boiling (lifting) pipes → steam space → circulation (downcomer) pipe → lifting pipes, etc.
If the evaporator has one evaporator, this is called a single-shell. If the installation has two or more series-connected bodies, then such an installation is called multi-body. In this case, the secondary steam from one casing is used for heating in other evaporators of the same installation, which leads to significant savings in fresh heating steam. Secondary steam taken from an evaporator for other purposes is called extra steam. In a multi-shell evaporator, fresh steam is supplied only to the first shell. The formed secondary steam from the first body enters the second body of the same installation as heating, while the secondary steam of the second body enters the third body as heating, etc.
Light diffraction. Huygens-Fresnel principle. Fresnel zone method. Fresnel diffraction on the simplest obstacles. Fraunhofer diffraction at one slit
1. The phenomenon of diffraction
Diffraction of waves consists in the bending of waves around obstacles or in the deflection of waves into the region of a geometric shadow when passing through holes, provided that the linear dimensions of these obstacles are of the order of or less than the wavelength. The type of waves does not matter: diffraction is observed for sound, and for light, and for any other wave processes.
The observation of the diffraction of light waves is possible only when the dimensions of the obstacles are of the order of 10 -6 -10 -7 m (for visible light). When the dimensions of the slit are compared in order with the wavelength, the slit becomes a source of secondary spherical waves, the interference of which determines the pattern of the intensity distribution behind the slit. In particular, light enters a geometrically inaccessible area. Thus, diffraction is not easy to observe in the visible region of the spectrum. For electromagnetic waves in other ranges, diffraction is observed on a daily basis, everywhere and everywhere, since if it were not for this phenomenon, we would not be able, for example, to listen to the radio in closed rooms.
According to the generally accepted definition, Diffraction of light, the phenomena observed when light propagates past the sharp edges of opaque or transparent bodies, through narrow holes. In this case, there is a violation of the straightness of the propagation of light, that is, a deviation from the laws of geometric optics. As a result of diffraction of light when illuminating opaque screens with a point light source at the border of the shadow, where, according to the laws of geometric optics, an abrupt transition from shadow to light should have occurred, a number of light and dark diffraction bands are observed.
Since diffraction is inherent in all wave motion, the discovery of diffraction of light in the 17th century. the Italian physicist and astronomer F. Grimaldi and its explanation in the early 19th century. French physicist O. Fresnel were one of the main proofs of the wave nature of light. The approximate theory of light diffraction is based on the application of the Huygens - Fresnel principle. For a qualitative consideration of the simplest cases of light diffraction, the construction of Fresnel zones can be applied. When light from a point source passes through a small circular hole in an opaque screen or around a circular opaque screen, diffraction fringes are observed in the form of concentric circles.
If the hole leaves an even number of zones open, then a dark spot is obtained in the center of the diffraction pattern, and with an odd number of zones - a light one. In the center of the shadow from a round screen that covers not too many Fresnel zones, a light speck is obtained. The Huygens - Fresnel principle makes it possible to explain the phenomenon of diffraction and to give methods for its quantitative calculation.
There are two cases of diffraction. If the obstacle on which the diffraction occurs is close to the light source or from the screen on which the observation is made, then the front of the incident or diffracted waves has a curved surface; this case is called Fresnel diffraction or diffraction in divergent rays, i.e., where b is the size of the hole, z is the distance of the observation point from the screen, l is the wavelength (Fresnel diffraction), and diffraction of light in parallel rays, in which the hole is much smaller one Fresnel zone, i.e. (Fraunhofer diffraction).
In the latter case, when a parallel light beam is incident on the hole, the beam becomes divergent with a divergence angle j ~ l / b (diffraction divergence). Plane waves are obtained either by moving the light source and the observation point away from the obstacle causing diffraction, or by using the appropriate lens positioning.
From the point of view of the concepts of geometrical optics about the rectilinear propagation of light, the border of the shadow behind an opaque obstacle is sharply outlined by rays that pass by the obstacle, touching its surface. Consequently, the phenomenon of diffraction is inexplicable from the point of view of geometric optics. According to Huygens' wave theory, which considers each point of the wave field as a source of secondary waves propagating in all directions, including in the region of the geometric shadow of the obstacle, it is generally unclear how any distinct shadow can arise. Nevertheless, experience convinces us of the existence of a shadow, but not sharply outlined, as the theory of rectilinear light propagation claims, but with blurred edges. Moreover, in the blur area, a system of interference maxima and minima of illumination is observed
2. Diffraction by a slit
The case of light diffraction by a slit is of great practical importance. When the slit is illuminated with a parallel beam of monochromatic light, a series of dark and light stripes are obtained on the screen, rapidly decreasing in intensity. If the light is incident perpendicular to the plane of the slit, then the stripes are located symmetrically relative to the central stripe, and the illumination changes along the screen periodically with a change in j, turning to zero at angles j for which sin j \u003d m / lb (m \u003d 1, 2, 3. ...).
At intermediate values, the illumination reaches its maximum values. The main maximum takes place at m \u003d 0, while sin j \u003d 0, that is, j \u003d 0. The following maxima, which are significantly inferior in magnitude to the main one, correspond to the values \u200b\u200bof j determined from the conditions: sin j \u003d 1.43 l / b , 2.46 l / b, 3.47 l / b, etc. As the slit width decreases, the central light stripe expands, and for a given slit width, the position of the minima and maxima depends on l, i.e., the greater the l, the greater the distance between the stripes.
Therefore, in the case of white light, there is a collection of corresponding patterns for different colors. In this case, the main maximum will be common for all l and will be represented as a white stripe passing into colored stripes with alternating colors from violet to red. If there are 2 identical parallel slits, then they give identical diffraction patterns superimposed on each other, as a result of which the maxima are correspondingly amplified, and, in addition, mutual interference of waves from the first and second slits occurs, which significantly complicates the picture. As a result, the minimums will be in the same places, since these are the directions in which none of the slits sends light. In addition, directions are possible in which the light sent by the two slits is mutually canceled.
Thus, the previous minima are determined by the conditions: b sin j \u003d l, 2l, 3l, ..., additional minima d sin j \u003d l / 2, 3l / 2, 5l / 2, ... (d is the size of the gap b together with an opaque gap a), the main maxima are d sin j \u003d 0, l, 2l, 3l, ..., i.e., one additional minimum is located between the two main maxima, and the maxima become narrower than with one slit. The increase in the number of slits makes this phenomenon even more pronounced. Light diffraction plays an essential role in the scattering of light in turbid media, such as dust particles, fog droplets, etc. The action of spectral instruments with a diffraction grating (diffraction spectrometers) is based on the diffraction of light.
Light diffraction determines the limit of the resolution of optical instruments (telescopes, microscopes, etc.). Due to the diffraction of light, the image of a point source (for example, a star in a telescope) looks like a circle with a diameter of lflD, where D is the lens diameter and f is its focal length. The divergence of laser radiation is also determined by the diffraction of light. To decrease the divergence of the laser beam, it is converted into a wider beam using a telescope, and then the divergence of the radiation is determined by the diameter D of the objective by the formula j ~ l / D.
The diffraction pattern observed on a screen placed behind a single-slit partition can be calculated based on the principle of superposition and wave interference. Let a monochromatic light beam of length λ fall on the slit. The dimensions of the slit d are comparable to λ: d ~ λ. Distance from the slot to the screen L \u003e\u003e d. Each point of the slit is, according to Huygens' principle, a source of a secondary spherical wave. These waves interfere with each other, so that the true position of the front of the resulting wave is the envelope of the secondary waves, taking into account their interference. Consider the superposition of two such waves coming from the middle of the slit and from one of the edges, and calculate the path difference of such waves at an arbitrary point on the screen. From simple geometric considerations, taking into account the smallness of the angle Θ, it can be obtained that the difference in the path of these two waves is equal to:
where y is the coordinate of the observation point on the screen. The interference of two waves will be destructive if the path difference is equal to an integer number of half-waves m (λ / 2). From here, the coordinates of those points on the screen where the dark stripes appear:
The distribution of light intensity in the diffraction pattern has a sharp maximum. It should be noted that measurements of the position of the minima make it possible (with known parameters d and L) to determine the wavelength of light.
3. Diffraction grating
A more advanced device that allows spectral analysis of light is a diffraction grating. The diffraction grating is a system of a large number of slits of the same width and parallel to each other, lying in the same plane and separated by opaque intervals of equal width. The diffraction grating is produced by drawing parallel lines on the glass surface using dividing machines. The places drawn by the indexing machine scatter the light in all directions and are thus practically opaque spaces between the undamaged parts of the plate, which act as slits.
The number of lines per 1 mm is determined by the region of the spectrum of the investigated radiation - from 300 1 / mm (in the infrared region) to 1200 1 / mm (in the ultraviolet). This device is of two types: transmissive (transparent slits alternating with opaque gaps) and reflective (light reflecting areas alternating with light scattering areas). In both cases, a large number of slits or light-scattering stripes are applied to the surface, and the number of strokes reaches 10 3 per 1 mm, and the total number of strokes is ~ 10 5. The distance between two adjacent slots is called the lattice period. Two waves coming from the edges of two adjacent slots interfere constructively if:
It is clear that in this case the waves from all the slits will amplify each other (the path difference determined by the points spaced from each other by an integer number of grating periods does not violate the conditions of constructive interference), and after focusing all beams with a lens, maxima will appear on the screen intensity. Thus, the previous formula determines the position of the maxima of the diffraction pattern created by the diffraction grating. The position of all the maxima, except for the main maximum corresponding to m \u003d 0, depends on the wavelength. Therefore, if white light falls on the grating, then it decomposes into a spectrum. With the help of a diffraction grating, it is possible to very accurately measure the wavelength, since with a large number of slits, the regions of the intensity maxima narrow, turning into thin bright stripes, and the distances between the maxima (the width of the dark stripes) increase.
Reflective diffraction gratings have the best quality. They are alternating areas so small that, reflecting light, they scatter it due to diffraction. Thus, the beam of light is split into many coherent rays.
If the width of the transparent sections is a and the width of the opaque gaps is b, then the value d \u003d a + b is called the grating period. If light with a wavelength l is incident on the grating normally (perpendicularly) to its surface, then, as follows from Fig. 1, the rays scattered at an angle j to the initial direction from the corresponding places of each of the slots have path differences dsinj (I and II rays) , 2dsinj (rays I and III), etc.
Waves amplify each other in interference if this path difference is an integer number of waves. The angles at which the maxima are observed are found from the relation
K \u003d 0, ± 1, ± 2, ± 3 ... (1)
The maxima are observed on both sides of the incident ray, and the central maximum (k \u003d 0) is observed in the direction of the incident ray.
The mirror surface of a laser compact disc is a spiral path, the pitch of which is commensurate with the wavelength of visible light. On such an ordered and finely structured surface, diffraction and interference phenomena are noticeably manifested in reflected light, which is the reason for the iridescent color of the glare it creates. The laser beam occupies such a small area on a CD that this area can be considered a one-dimensional diffraction grating.
The diagram of the device (device No. 1) for observing the diffraction of light on a piece of a compact disk playing the role of a reflective diffraction grating is shown in Figure 2. Here: 1 - a light source - a laser keychain mounted on a rotating bar, 2 - a reflective diffraction grating - a piece of a CD, 3 - a clip for attaching the preparation, 4 - a protractor for measuring diffraction angles, 5 - a protractor for measuring the angle of incidence of a light beam, 6 - a clip for attaching a polaroid.
4. Huygens - Fresnel principle
The peculiarity of diffraction effects is that the diffraction pattern at each point in space is the result of interference of rays from a large number of secondary Huygens sources. The explanation of these effects was carried out by Fresnel and received the name of the Huygens - Fresnel principle.
The essence of the Huygens - Fresnel principle can be represented in the form of several provisions:
1) the entire wave surface, excited by any source S 0 with area S, can be divided into small sections with equal areas dS, which will be a system of secondary sources emitting secondary waves;
2) these secondary sources, equivalent to the same primary source S 0, are coherent with each other. Therefore, waves propagating from a source S 0 at any point in space should be the result of the interference of all secondary waves;
3) the radiation power of all secondary sources - sections of the wave surface with the same areas - are the same;
4) each secondary source (with area dS) radiates mainly in the direction of the outer normal n to the wave surface at this point; the amplitude of the secondary waves in the direction making an angle with n, the smaller, the greater the angle a, and is equal to zero;
5) the amplitude of the secondary waves that have reached a given point in space depends on the distance of the secondary source to this point: the greater the distance, the smaller the amplitude;
6) when part of the wave surface S is covered by an opaque screen, secondary waves are emitted only by open areas of this surface. In this case, the part of the light wave, covered by the opaque screen, does not act at all, and the open areas of the wave act as if there were no screen at all.
5. Fresnel zone method
Fresnel diffraction plays a major role in wave theory, because contrary to the Huygens principle and on the basis of the Huygens - Fresnel principle, explains the straightforwardness of the propagation of light in a homogeneous environment free of obstacles. To show this, consider the action of a spherical light wave from a point source s0 at an arbitrary point in space P. The wave surface of such a wave is symmetric with respect to the straight line S0P. The amplitude of the desired wave at point P depends on the result of the interference of secondary waves emitted by all sections dS of the surface S. The amplitudes and initial phases of the secondary waves depend on the location of the corresponding sources dS with respect to point P.
Taking advantage of the symmetry of the problem, Fresnel proposed an original method for dividing the wave surface into zones (the method of Fresnel zones). According to this method, the wave surface is divided into annular zones, constructed so that the distances from the edges of each zone to the point P differ by (the length of the light wave in the medium in which the wave propagates). If we denote by r0 the distance from the top of the wave surface O to the point P, then the distances r 0 + k form the boundaries of all zones, where k is the zone number. Oscillations arriving at point P from similar points, two adjacent zones, are opposite in phase, since the difference in travel from these zones to point P is equal. Therefore, when superimposed, these oscillations mutually weaken each other, and the resulting amplitude will be expressed as the sum:
A \u003d A 1 -A 2 + A 3 -A 4 +….
The magnitude of the amplitude a k depends on the area of \u200b\u200bthe ith zone and the angle between the outer normal to the surface of the zone at any of its point and a straight line directed from this point to point P. It can be shown that the area of \u200b\u200bthe ith zone does not depend on the number of the zone under conditions. Thus, in the considered approximation, the areas of all Fresnel zones are the same and the radiation power of all Fresnel zones - secondary sources - is the same. At the same time, as k increases, the angle between the normal to the surface and the direction to the point P increases, which leads to a decrease in the radiation intensity of the kth zone in this direction, i.e. to a decrease in the amplitude A k in comparison with the amplitudes of the previous zones. Amplitude A k also decreases due to the increase in the distance from the zone to the point P with increasing k. Eventually
A 1\u003e A 2\u003e A 3\u003e A 4\u003e ...\u003e A k\u003e….
Due to the large number of zones, the decrease in A k is monotonic, and we can approximately assume that, taking into account the small amplitude of the remote zones, all expressions in parentheses are equal to zero. The result obtained means that the oscillations caused at point P by a spherical wave surface have the same amplitude as if only half of the central Fresnel zone were acting. Consequently, the light from the source S 0 to the point P propagates, as it were, within a very narrow direct channel, i.e. straightforward. We come to the conclusion that as a result of the phenomenon of interference, the action of all zones except the first one is destroyed.
6. Fraunhofer diffraction of one slit
In practice, the slit appears to be a rectangular hole, the length of which is much greater than the width. In this case, the light diffracts to the right and left of the slit. If we observe the image of the source in the direction perpendicular to the direction of the generatrix of the slit, then we can restrict ourselves to considering the diffraction pattern in one dimension (along x). If the wave falls normally to the plane of the slot, in accordance with the Huygens - Fresnel principle, the points of the slot are secondary sources of waves oscillating in one phase, since the plane of the slot coincides with the front of the incident wave. We divide the area of \u200b\u200bthe slit into a series of narrow strips of equal width, parallel to the generatrix of the slit. The phases of waves from different stripes at the same distances, by virtue of the above, are equal, the amplitudes are also equal, since the selected elements have equal areas and are equally inclined to the viewing direction.
If, when light passes through the slit, the law of rectilinear propagation of light was observed (there would be no diffraction), then an image of the slit would be obtained on the screen E installed in the focal plane of the lens L2. Therefore, direction \u003d 0 defines an undiffracted wave with an amplitude a 0 equal to the amplitude of the wave sent by the entire slit.
Due to diffraction, light rays deviate from rectilinear propagation at angles. The deviation to the right and left is symmetrical about the center line OC0 (Fig. 8.5, C and C,). To find the action of the entire slot in the direction determined by the angle, it is necessary to take into account the phase difference characterizing the waves reaching the observation point C from different stripes (Fresnel zones), since As mentioned above, all parallel rays incident on the lens at an angle to its optical axis OC0, perpendicular to the front of the incident wave, are collected in the side focus of lens C. Let us draw plane FD, perpendicular to the direction of the diffracted rays and representing the front of the new wave.
Since the lens does not introduce an additional difference in the path of the rays, the path of all rays from the plane FD to point C is the same. Consequently, the total path difference of the rays from the slit FE is given by the segment ED. Let us draw planes parallel to the wave surface FD, so that they divide the segment ED into several sections, each of which has a length / 2. These planes divide the slit into the aforementioned strips - Fresnel zones, and the difference in path from adjacent zones is equal in accordance with the Fresnel method. Then the result of diffraction at point C is determined by the number of Fresnel zones that fit into the slit: if the number of zones is even (z \u003d 2k), a minimum of diffraction is observed at point C, if z is odd (z \u003d 2k + 1), at point C there is a maximum of diffraction ...
The number of Fresnel zones lying on the FE slit is determined by how many times the ED segment contains, i.e. z \u003d 0. The segment ED, expressed in terms of the slit width and the diffraction angle, is written as ED \u003d 0. As a result, for the position of the diffraction maxima we obtain the condition, where k - 1,2,3 .. are integers. The quantity k, which takes the values \u200b\u200bof the natural numbers, is called the order of the diffraction maximum. The + and - signs in the formulas correspond to light beams diffracting from the slit at angles + and - and collecting at the side foci of the lens L2: C and C, symmetric about the main focus C 0. In the direction \u003d 0, the most intense central maximum of the zero order is observed, since oscillations from all Fresnel zones come to the point C0 in one phase.
The position of the central maximum (\u003d 0) does not depend on the wavelength and, therefore, is common for all wavelengths. Therefore, in the case of white light, the center of the diffraction pattern appears as a white stripe. It is clear that the position of the highs and lows depends on the wavelength. Therefore, a simple alternation of dark and light stripes occurs only in monochromatic light. In the case of white light, the diffraction patterns for different waves are shifted according to the wavelength. The central maximum of white color has a rainbow color only at the edges (one Fresnel zone fits in the width of the slit).
The side maxima for different wavelengths no longer coincide with each other; closer to the center are the highs corresponding to shorter waves. Long-wavelength maxima are further apart from each other than short-wavelength ones. Therefore, the diffraction maximum is the spectrum facing the center with the violet part. Complete extinction of light does not occur at any point on the screen, since the maximums and minimums of light overlap with different ones.
Theory of relativity (Albert Einstein)
Space and time are one, there is a connection between mass and energy - the special theory of relativity, which turned generally accepted ideas about the world at the beginning of the last century, still continues to excite the minds and hearts of people.
In 1905, Albert Einstein published Special Theory of Relativity (SRT), which explained how to interpret motion between different inertial frames of reference - simply put, objects that move at a constant speed in relation to each other.
Einstein explained that when two objects move at a constant speed, one should consider their motion relative to each other, instead of accepting one of them as an absolute frame of reference.
So if two astronauts, you and, say, Herman, are flying on two spaceships and want to compare your observations, the only thing you need to know is your speed relative to each other.
Special relativity considers only one special case (hence the name), when the motion is rectilinear and uniform.
If a material body accelerates or turns to the side, the SRT laws no longer apply. Then the general theory of relativity (GR) comes into force, which explains the movements of material bodies in the general case.
Einstein's theory is based on two basic principles:
1. The principle of relativity: physical laws are preserved even for bodies that are inertial frames of reference, that is, moving at a constant speed relative to each other.
2. The principle of the speed of light: the speed of light remains unchanged for all observers, regardless of their speed in relation to the light source. (Physicists refer to the speed of light as c).
One of the reasons for Albert Einstein's success is that he put experimental data above theoretical ones. When a series of experiments revealed results that contradicted the generally accepted theory, many physicists decided that these experiments were wrong.
Albert Einstein was one of the first who decided to build a new theory based on new experimental data.
At the end of the 19th century, physicists were in search of a mysterious ether - a medium in which, according to generally accepted assumptions, light waves should propagate, like acoustic waves, for which air is needed to propagate, or another medium - solid, liquid or gaseous.
The belief in the existence of the ether has led to the belief that the speed of light must change depending on the speed of the observer in relation to the ether.
Albert Einstein abandoned the concept of ether and suggested that all physical laws, including the speed of light, remain unchanged regardless of the speed of the observer - as experiments have shown.