What are examples of optical phenomena. Optical phenomena in nature
At school, he studies the topic " optical phenomena in the atmosphere, 6th grade. However, it is of interest not only to the inquisitive mind of a child. Optical phenomena in the atmosphere, on the one hand, combine the rainbow, the change in the color of the sky during sunrises and sunsets, seen more than once by everyone. On the other hand, they include mysterious mirages, false Moons and Suns, impressive halos that in the past terrified people. The mechanism of formation of some of them remains unclear to the end today, however general principle, according to which optical phenomena in nature "live", modern physics has well studied.
air shell
The Earth's atmosphere is a shell consisting of a mixture of gases and extending for about 100 km above sea level. The density of the air layer changes with distance from the earth: its highest value is at the surface of the planet, with height it decreases. The atmosphere cannot be called a static formation. The layers of the gaseous envelope are constantly moving and mixing. Their characteristics change: temperature, density, speed of movement, transparency. All these nuances affect the sun's rays rushing to the surface of the planet.
Optical system
The processes occurring in the atmosphere, as well as its composition, contribute to the absorption, refraction and reflection of light rays. Some of them reach the target - the earth's surface, the other is scattered or redirected back into outer space. As a result of the curvature and reflection of light, the decay of part of the rays into a spectrum, and so on, various optical phenomena are formed in the atmosphere.
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atmospheric optics
At a time when science was just in its infancy, people explained optical phenomena based on the prevailing ideas about the structure of the Universe. The rainbow connected the human world with the divine, the appearance of two false Suns in the sky testified to the approaching catastrophes. Today, most of the phenomena that frightened our distant ancestors have received a scientific explanation. Atmospheric optics is engaged in the study of such phenomena. This science describes optical phenomena in the atmosphere based on the laws of physics. She is able to explain why the sky is blue during the day, but changes color during sunset and dawn, how a rainbow is formed and where mirages come from. Numerous studies and experiments today make it possible to understand such optical phenomena in nature as the appearance of luminous crosses, Fata Morgana, iridescent halos.
Blue sky
The color of the sky is so familiar that we rarely wonder why it is so. Nevertheless, physicists know the answer well. Newton proved that under certain conditions a beam of light can be decomposed into a spectrum. When passing through the atmosphere, the part corresponding to the blue color is scattered better. The red section of visible radiation is characterized by a longer wavelength and is inferior to the violet in terms of the degree of scattering by 16 times.
At the same time, we see the sky not purple, but blue. The reason for this lies in the peculiarities of the structure of the retina and the ratio of parts of the spectrum in sunlight. Our eyes are more sensitive to blue, and the violet part of the star's spectrum is less intense than blue.
scarlet sunset
When people figured out what the atmosphere is, optical phenomena ceased to be for them evidence or an omen of terrible events. However scientific approach does not interfere with getting aesthetic pleasure from colorful sunsets and gentle sunrises. bright red and orange colors together with pink and blue, they gradually give way to night darkness or morning light. It is impossible to observe two identical sunrises or sunsets. And the reason for this lies in all the same mobility atmospheric layers and changing weather conditions.
During sunsets and sunrises, the sun's rays travel a longer path to the surface than during the day. As a result, diffused violet, blue and green go to the sides, and direct light turns red and orange. Clouds, dust or ice particles suspended in the air contribute to the picture of sunset and dawn. The light is refracted as it passes through them, and colors the sky in a variety of shades. On the part of the horizon opposite from the Sun, one can often observe the so-called Belt of Venus - a pink band separating the dark night sky and the blue day sky. The beautiful optical phenomenon, named after the Roman goddess of love, is visible before dawn and after sunset. 
rainbow bridge
Perhaps no other light phenomena in the atmosphere evoke so many mythological plots and fairy-tale images as those associated with the rainbow. The arc or circle, consisting of seven colors, is known to everyone since childhood. A beautiful atmospheric phenomenon that occurs during rain, when the sun's rays pass through the drops, fascinates even those who have thoroughly studied its nature.
And the physics of the rainbow today is no secret to anyone. Sunlight, refracted by drops of rain or fog, splits. As a result, the observer sees seven colors of the spectrum, from red to violet. It is impossible to define the boundaries between them. Colors blend smoothly into each other through several shades.
When observing a rainbow, the sun is always located behind the person's back. The center of Irida's smile (as the ancient Greeks called the rainbow) is located on a line passing through the observer and the daylight. A rainbow usually appears as a semicircle. Its size and shape depend on the position of the Sun and the point at which the observer is located. The higher the luminary above the horizon, the lower the circle of the possible appearance of a rainbow falls. When the Sun passes 42º above the horizon, an observer on the Earth's surface cannot see the rainbow. The higher above sea level a person who wants to admire the smile of Irida is located, the more likely that he will see not an arc, but a circle.
Double, narrow and wide rainbow
Often, along with the main one, you can see the so-called secondary rainbow. If the first is formed as a result of a single reflection of light, then the second is the result of a double reflection. In addition, the main rainbow is distinguished by a certain order of colors: red is located on the outside, and purple is on the inside, which is closer to the surface of the Earth. The side "bridge" is the spectrum reversed in sequence: violet is at the top. This happens because the rays come out at different angles during double reflection from a raindrop.
Rainbows vary in color intensity and width. The brightest and rather narrow ones appear after a summer thunderstorm. Large drops, characteristic of such rain, give rise to a highly visible rainbow with distinct colors. Small drops give a more blurry and less noticeable rainbow.
Optical phenomena in the atmosphere: aurora
One of the most beautiful atmospheric optical phenomena is the aurora. It is characteristic of all planets with a magnetosphere. On Earth, auroras are observed at high latitudes in both hemispheres, in zones surrounding the planet's magnetic poles. Most often you can see a greenish or blue-green glow, sometimes supplemented by flashes of red and pink along the edges. The intense aurora borealis is shaped like ribbons or folds of fabric, turning into spots as it fades. Stripes several hundred kilometers high stand out well along the lower edge against the dark sky. The upper limit of the aurora is lost in the sky.
These beautiful optical phenomena in the atmosphere still keep their secrets from people: the mechanism of the occurrence of certain types of luminescence, the cause of the crackling that occurs during sharp flashes, has not been fully studied. However, the general picture of the formation of auroras is known today. The sky above the north and south poles is adorned with a greenish-pink glow as charged particles from the solar wind collide with atoms in the Earth's upper atmosphere. The latter, as a result of the interaction, receive additional energy and emit it in the form of light.
Halo
The sun and moon often appear before us surrounded by a glow resembling a halo. This halo is a highly visible ring around the light source. In the atmosphere, most often it is formed due to the smallest particles of ice that make up cirrus clouds high above the Earth. Depending on the shape and size of the crystals, the characteristics of the phenomenon change. Often the halo takes the form of a rainbow circle as a result of the decomposition of the light beam into a spectrum. 
An interesting variation of the phenomenon is called parhelion. As a result of the refraction of light in ice crystals at the level of the Sun, two bright spots are formed, resembling a daylight star. AT historical chronicles You can find descriptions of this phenomenon. In the past, it was often considered a harbinger of formidable events.
Mirage
Mirages are also optical phenomena in the atmosphere. They arise as a result of the refraction of light at the boundary between layers of air that differ significantly in density. The literature describes many cases when a traveler in the desert saw oases or even cities and castles that could not be nearby. Most often these are "lower" mirages. They arise over a flat surface (desert, asphalt) and represent a reflected image of the sky, which seems to the observer to be a reservoir.
The so-called superior mirages are less common. They form over cold surfaces. Superior mirages are straight and inverted, sometimes they combine both positions. The most famous representative of these optical phenomena is Fata Morgana. This is a complex mirage that combines several types of reflections at once. Real-life objects appear before the observer, repeatedly reflected and mixed. 
atmospheric electricity
Electrical and optical phenomena in the atmosphere are often mentioned together, although their causes are different. The polarization of clouds and the formation of lightning are associated with processes occurring in the troposphere and ionosphere. Giant spark discharges are usually formed during a thunderstorm. Lightning occurs inside clouds and can strike the ground. They are a threat to human life, and this is one of the reasons scientific interest to such events. Some properties of lightning are still a mystery to researchers. Today, the cause of ball lightning is unknown. As with some aspects of aurora and mirage theory, electrical phenomena continue to intrigue scientists.
Optical phenomena in the atmosphere, briefly described in the article, are becoming more and more understandable for physicists every day. At the same time, they, like lightning, never cease to amaze people with their beauty, mystery and sometimes grandiosity.
Farajova Leyla
Often we observe inexplicable phenomena in the sky. This work reveals the essence of the phenomenon occurring in the earth's atmosphere.
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MOU "Peschanovskaya secondary school"
VI regional scientific and practical conference
Optical phenomena in the atmosphere
6 MOU class"Peschanovskaya secondary school"
Supervisor:
Makovchuk Tatyana Gennadievna
Physics teacher
S. Sandy
2010
Introduction 3
Earth's atmosphere as an optical system 4
Types of optical phenomena 5
Conclusion 12
Literature 13
Annex 14
Introduction
The purpose of this work is to consider optical atmospheric phenomena and their physical nature. The most accessible and at the same time, the most colorful optical phenomena are atmospheric. Huge in scale, they are the product of the interaction of light and the earth's atmosphere.
On December 31, on New Year's Eve, an unusual phenomenon could be observed in the southern part of the sky, not high above the horizon. In the center is a disk of the sun and on the sides are two more, and above them is a rainbow radiance. It was a very beautiful and mesmerizing sight. It immediately became interesting what it is, how it is formed, why and what other phenomena can occur in the atmosphere? This unusual atmospheric phenomenon formed the basis of my work.
Earth's atmosphere as an optical system
Our planet is surrounded by a gaseous shell, which we call the atmosphere. Possessing the greatest density at the earth's surface and gradually rarefied as it rises, it reaches a thickness of more than a hundred kilometers. And this is not a frozen gas medium with homogeneous physical data. On the contrary, the Earth's atmosphere is in constant motion. Under influence various factors, its layers mix, change density, temperature, transparency, move long distances at different speeds.
For rays of light coming from the Sun or other celestial bodies, the earth's atmosphere is a kind of optical system with constantly changing settings. Being in their way, it reflects part of the light, scatters it, passes it through the entire thickness of the atmosphere, providing illumination of the earth's surface, under certain conditions, decomposes it into components and bends the path of the rays, thereby causing various atmospheric phenomena. The most unusual colorful of them are sunsets, rainbows, northern lights, mirages, solar and lunar halos, and much more.
Types of optical phenomena
There are many types of optical phenomena. Let's dwell on some of them.
Halo
(from Greekχαλοσ - "circle", "disk"; also aura, halo, halo) is the phenomenon of refraction and reflection of light in the ice crystals of the clouds of the upper tier. They are light or rainbow circles around the Sun or Moon, separated from the luminary by a dark gap. Halos are often observed in front of cyclones and therefore can be a sign of their approach. Sometimes lunar halos can also be observed.
Appearing in the air when water droplets freeze, ice crystals usually take one of three six-sided forms. regular prisms(Fig. 1 A): prisms in which the length is very large compared to their cross section; these are the well-known ice needles, on frosty winter days, hovering in masses in the lowest layers of the atmosphere.
A B C.
(fig.1)
Falling freely in the air, such needles are located vertically with their long axis. The planes of these crystals, which circling, gradually descend to the ground, are oriented parallel to the surface most of the time. At sunrise or sunset, the observer's line of sight can pass through this very plane, and each crystal can lead like a miniature lens that refracts sunlight.
In another kind of prisms, the height is very small compared to the cross section; then six-sided flat plates are obtained (Fig. 1B.). Sometimes, finally, ice crystals take the form of a prism, the cross section of which is a six-beam star (Fig. 1 C.). Falling on ice crystals, a ray of light, depending on the type of crystal and its position relative to the ray, can either pass directly through it without refraction, or the rays must undergo not only refraction in them, but also whole line total internal reflections. In reality, of course, it is very rare to observe a phenomenon, all parts of which would be equally bright and clearly visible: usually one or another part of it is developed brighter and more characteristically, the rest are either very weakly observed, or even absent.
An ordinary circle or small halo is a brilliant circle surrounding the luminary, its radius is about 22 °. It is colored reddish on the inside, then yellow is faintly visible, then the color turns into white and gradually merges with the general bluish tone of the sky.Spaceinside the circle it seems comparatively dark; the inner border of the circle is sharply delineated. This circle is formed by the refraction of light in ice needles, which are carried in various positions in the air. The angle of least deflection of rays in an ice prism is approximately 22°, so that all rays passing through the crystals must appear to the observer at least 22° deviated from the light source; hence the darkness of the inner space. The red color, as the least refracted, will also appear the least deviated from the luminary; it is followed by yellow; the rest of the rays, mixing with each other, will give the impression white color. Less common is a halo with an angular radius of 46°, located concentrically around a 22-degree halo. Its inner side also has a reddish tint. The reason for this is also the refraction of light, which occurs in this case in ice needles facing the luminary at angles of 90 °; this circle is usually paler than the small one, but the colors in it are more sharply separated. The ring width of such a halo exceeds 2.5 degrees. Both 46-degree and 22-degree halos tend to be brightest at the top and lower parts rings. The rare 90-degree halo is a faintly luminous, almost colorless ring that has a common center with the other two halos. If it is colored, it has a red color on the outside of the ring. The mechanism of the origin of this type of halo has not been fully elucidated.
You can often observe the lunar halo.This is a fairly common sight and occurs if the sky is covered with high thin clouds with millions of tiny ice crystals. Each ice crystal acts as a miniature prism. Most crystals are in the form of elongated hexagons. Light enters through one front surface of such a crystal and exits through the opposite one with a refraction angle of 22º .
Watching street lamps in winter, you can see the halo generated by their light, under certain conditions, of course, namely, in frosty air saturated with ice crystals or snowflakes. By the way, a halo from the Sun in the form of a large bright column can also appear during a snowfall. There are days in winter when snowflakes seem to float in the air, and sunlight stubbornly breaks through loose clouds. Against the background of the evening dawn, this pillar sometimes looks reddish - like a reflection of a distant fire. In the past, such a completely harmless phenomenon, as we see, horrified superstitious people.
Can to see such a halo: a bright, iridescent-colored ring around the Sun. This vertical circle occurs when there are many hexagonal ice crystals in the atmosphere, which do not reflect, but refract the sun's rays like a glass prism. In this case, most of the rays, of course, are scattered and do not reach our eyes. But some part of them, having passed through these prisms in the air and refracted, reaches us, so we see a rainbow circle around the Sun. Its radius is about twenty-two degrees. Sometimes more - at forty-six degrees.
It is noticed that the halo circle is always brighter on the sides. This is because two halos intersect here - vertical and horizontal. And false suns are formed most often at the intersection. The most favorable conditions for the appearance of false suns are formed when the Sun is not high above the horizon and part of the vertical circle is no longer visible to us.
What kind of crystals are involved in this "performance"?
The answer to the question was given by special experiments. It turned out that false Suns appear due to hexagonal ice crystals, in their shape resembling ... nails. They float vertically in the air, refracting the light with their side faces.
The third "sun" appears when only one upper part of the halo circle is visible above the real sun. Sometimes it is a segment of an arc, sometimes a bright spot of an indefinite shape. Sometimes false suns are not inferior in brightness to the Sun itself. Observing them, the ancient chroniclers wrote about three suns, about severed fiery heads, and so on.
In connection with this phenomenon, a curious fact has been recorded in the history of mankind. In 1551, the German city of Magdeburg was besieged by the troops of the Spanish king Charles V. The defenders of the city held firm, the siege had lasted for more than a year. Finally, the irritated king gave the order to prepare for a decisive attack. But then an unprecedented thing happened: a few hours before the assault, three suns shone over the besieged city. The mortally frightened king decided that heaven was protecting Magdeburg and ordered the siege to be lifted.
Rainbow - This is an optical phenomenon that occurs in the atmosphere and has the form of a multi-colored arc in the firmament.
In the religious ideas of the peoples of antiquity, the role of a bridge between earth and sky was attributed to the rainbow. In Greco-Roman mythology, even the special goddess of the rainbow, Irida, is known. The Greek scientists Anaximenes and Anaxagoras believed that a rainbow is formed by the reflection of the Sun in a dark cloud. Aristotle set forth ideas about the rainbow in a special section of his Meteorology. He believed that the rainbow occurs due to the reflection of light, but not just from the whole cloud, but from its drops.
In 1637, the famous French philosopher and scientist Descartes gave a mathematical theory of the rainbow based on the refraction of light. Subsequently, this theory was supplemented by Newton on the basis of his experiments on the decomposition of light into colors using a prism. Descartes' theory, supplemented by Newton, could not explain the simultaneous existence of several rainbows, their different widths, the obligatory absence of certain colors in the color bands, the influence of the size of cloud drops on appearance phenomena. The exact theory of the rainbow based on the concepts of light diffraction was given in 1836 by the English astronomer D. Erie. Considering the rain veil as a spatial structure that provides the occurrence of diffraction, Airy explained all the features of the rainbow. His theory has fully retained its significance for our time.
A rainbow is an optical phenomenon that occurs in the atmosphere and has the form of a multi-colored arc on the vault of heaven. It is observed in those cases when the sun's rays illuminate the curtain of rain, located on the opposite side of the sky from the Sun. The center of the rainbow arc is in the direction of a straight line passing through the solar disk (even if hidden from observation by clouds) and the observer's eye, i.e. at a point opposite the sun. The arc of the rainbow is part of a circle circumscribed around this point with a radius of 42°30" (in angular measurement).
Interesting arrangement of colors in the rainbow. It is always constant. The red color of the main rainbow is located on its upper edge, purple - on the lower one. Between these extreme colors, the remaining colors follow each other in the same sequence as in solar spectrum. In principle, the rainbow never contains all the colors of the spectrum. Most often, blue, dark blue and saturated pure red colors are absent or weakly expressed in it. With the increase in the size of raindrops, the color bands of the rainbow narrow, and the colors themselves become more saturated. The predominance of green tones in the phenomenon usually indicates a subsequent transition to good weather. The overall picture of the colors of the rainbow is blurry, as it is formed by an extended light source.
With the artificial reproduction of the phenomenon in the laboratory, it was possible to obtain up to 19 rainbows. Additional rainbows can be observed above the reservoir, located non-concentrically relative to each other. For one of them, the source of light is the Sun, for the other - its reflection from water surface. Under these conditions, rainbows located "upside down" can also be found. At night, under moonlight and foggy weather in the mountains and on the shores of the seas, you can observe white rainbow. This type of rainbow can also occur when sunlight is exposed to fog. It has the appearance of a brilliant white arc, on the outside it is painted yellowish and orange red colors, and from the inside - in blue-violet. The rainbow is observed not only on the veil of rain. On a smaller scale, it can be seen on drops of water near waterfalls, fountains and in the surf. At the same time, not only the Sun and the Moon, but also a searchlight can serve as a light source.
Polar Lights - glow (luminescence) of the upper atmosphere of a planet with a magnetosphere due to its interaction with charged particles of the solar wind. In most cases, auroras are green or blue-green in color, with occasional patches or borders of pink or red. Auroras are observed in two main forms - in the form of ribbons and in the form of cloud-like spots. Intense flashes of radiance are often accompanied by sounds resembling noise, crackling. Auroras cause strong changes in the ionosphere, which in turn affects radio conditions. In most cases, radio communication deteriorates significantly. There is strong interference, and sometimes a complete loss of reception.
Mirage - any of us has seen the simplest. For example, when driving on a heated paved road, far ahead it looks like a water surface. And this has not surprised anyone for a long time, because a mirage is nothing more than an atmospheric optical phenomenon, due to which images of objects appear in the visibility zone, which under normal conditions are hidden from observation. This happens because light is refracted when passing through layers of air of different densities. In this case, distant objects may turn out to be raised or lowered relative to their actual position, and may also be distorted and acquire irregular, fantastic shapes.
Ghosts of the Brocken - in some regions of the globe, when the shadow of an observer on a hill at sunrise or sunset falls behind him on clouds located at a short distance, a striking effect is revealed: the shadow acquires colossal dimensions. This is due to the reflection and refraction of light by the smallest water droplets in the fog. The described phenomenon is named after the peak in the Harz mountains in Germany.
Saint Elmo's fire- Luminous pale blue or purple brushes from 30 cm to 1 m or more in length, usually on the tops of masts or the ends of the yards of ships at sea. Sometimes it seems that the entire rigging of the ship is covered with phosphorus and glows. Elmo's fires sometimes appear on mountain peaks, as well as on spiers and sharp corners of tall buildings. This phenomenon is brush electrical discharges at the ends of electrical conductors, when the electric field strength is greatly increased in the atmosphere around them.
Conclusion
The physical nature of light has interested people since time immemorial. But before being established modern look on the nature of light, and the light beam has found its application in human life, many optical phenomena that occur everywhere in the Earth's atmosphere, from the well-known rainbow to complex, periodic mirages, have been identified, described, scientifically substantiated and experimentally confirmed. But, despite this, the bizarre play of light has always attracted and still attracts a person. Neither the contemplation of the winter halo, nor the bright sunset, nor the wide, half-sky strip of the northern lights, nor the modest moonlit path on the water surface leaves anyone indifferent. A light beam, passing through the atmosphere of our planet, not only illuminates it, but also gives it a unique look, making it beautiful.
Of course, much more optical phenomena occur in the atmosphere of our planet, which are discussed in this work. Among them there are both well-known to us and solved by scientists, and those who are still waiting for their discoverers. And we can only hope that, over time, we will witness more and more new discoveries in the field of optical atmospheric phenomena, indicating the versatility of an ordinary light beam.
Literature
Bludov M.I. "Conversations on Physics, Part II" - M .: Education, 1985
Bulat V.L. "Optical phenomena in nature" - M .: Education, 1974
Gershenzon E.M., Malov N.N., Mansurov A.N. "Course of General Physics"- M.: Enlightenment, 1988
Korolev F.A. "Physics course" M., "Enlightenment" 1988
Myakishev G.Ya. Bukhovtsev B.B. "Physics 10 - M .: Education, 1987
Tarasov L.V. "Physics in nature" - M .: Education, 1988
Tarasov L.V. "Physics in nature"- M.: Enlightenment, 1988
Trubnikov P.R. Pokusaev N.V. "Optics and Atmosphere - St. Petersburg: Enlightenment, 2002
Shakhmaev N.M. Chodiev D.Sh. "Physics 11 - M .: Education, 1991
Internet resources
Appendix
The shape of the arc, the brightness of the colors, the width of the stripes depend on the size of the water droplets and their number. Large drops create a narrower rainbow, with sharply prominent colors, small drops create an arc that is blurry, faded and even white.
One of the most beautiful optical phenomena of nature is the aurora borealis.
Lake, or lower mirages - the most common
mirage, a well-known natural phenomenon for a long time ...
photograph, the ghost of Brocken, the shadow of the mountain, observed against the background of evening clouds:
Halo is one of the most beautiful and unusual phenomena of nature.
The atmosphere of our planet is a rather interesting optical system, the refractive index of which decreases with height due to a decrease in air density. Thus, earth's atmosphere can be considered as a "lens" of gigantic dimensions, repeating the shape of the Earth and having a monotonically changing refractive index.
This circumstance gives rise to a whole a number of optical phenomena in the atmosphere due to refraction (refraction) and reflection (reflection) of rays in it.
Let us consider some of the most significant optical phenomena in the atmosphere.
atmospheric refraction
atmospheric refraction- phenomenon curvature light rays as light passes through the atmosphere.
With height, the air density (and hence the refractive index) decreases. Imagine that the atmosphere consists of optically homogeneous horizontal layers, the refractive index in which varies from layer to layer (Fig. 299).
Rice. 299. Change in the refractive index in the Earth's atmosphere
When a light beam propagates in such a system, it will, in accordance with the law of refraction, “press” against the perpendicular to the layer boundary. But the density of the atmosphere does not decrease in jumps, but continuously, which leads to a smooth curvature and rotation of the beam through an angle α when passing through the atmosphere.
As a result of atmospheric refraction, we see the Moon, the Sun, and other stars somewhat higher than where they actually are.
For the same reason, the duration of the day increases (in our latitudes by 10-12 minutes), the disks of the Moon and the Sun near the horizon are compressed. Interestingly, the maximum refraction angle is 35" (for objects near the horizon), which exceeds the apparent angular size of the Sun (32").
From this fact it follows: at the moment when we see that the lower edge of the star touched the horizon line, in fact the solar disk is already below the horizon (Fig. 300).
Rice. 300. Atmospheric refraction of rays at sunset
twinkling stars
twinkling stars also associated with the astronomical refraction of light. It has long been noticed that twinkling is most noticeable in stars near the horizon. Air currents in the atmosphere change the density of the air over time, resulting in an apparent twinkling of the heavenly body. Astronauts in orbit do not observe any flicker.
Mirages
In hot desert or steppe regions and in the polar regions, strong heating or cooling of the air near the earth's surface leads to the appearance mirages: due to the curvature of the rays, objects that are actually located far beyond the horizon become visible and appear close.
Sometimes this phenomenon is called terrestrial refraction. The appearance of mirages is explained by the dependence of the refractive index of air on temperature. There are inferior and superior mirages.
inferior mirages can be seen on a hot summer day on a well-heated asphalt road: it seems to us that there are puddles ahead on it, which in fact are not. AT this case we take for "puddles" the specular reflection of rays from non-uniformly heated layers of air located in the immediate vicinity of the "hot" asphalt.
superior mirages differ in considerable variety: in some cases they give a direct image (Fig. 301, a), in others - inverted (Fig. 301, b), they can be double and even triple. These features are associated with different dependences of air temperature and refractive index on altitude.
Rice. 301. Formation of mirages: a - direct mirage; b - reverse mirage
Rainbow
Atmospheric precipitation leads to the appearance of spectacular optical phenomena in the atmosphere. So, during the rain, education is an amazing and unforgettable sight. rainbows, which is explained by the phenomenon of different refraction (dispersion) and reflection of sunlight on the smallest droplets in the atmosphere (Fig. 302).
Rice. 302. Formation of a rainbow
In particularly successful cases, we can see several rainbows at once, the order of the colors in which is mutually inverse.
The light beam involved in the formation of a rainbow experiences two refractions and multiple reflections in each raindrop. In this case, somewhat simplifying the mechanism of rainbow formation, we can say that spherical raindrops play the role of a prism in Newton's experiment on the decomposition of light into a spectrum.
Due to spatial symmetry, the rainbow is visible in the form of a semicircle with an opening angle of about 42 °, while the observer (Fig. 303) must be between the Sun and the raindrops, with his back to the Sun.
The variety of colors in the atmosphere is explained by patterns light scattering on particles of various sizes. Due to the fact that blue is scattered more than red, during the day, when the Sun is high above the horizon, we see the sky blue. For the same reason, near the horizon (at sunset or sunrise), the Sun becomes red and not as bright as at zenith. The appearance of colored clouds is also associated with the scattering of light by particles of various sizes in the cloud.
Literature
Zhilko, V.V. Physics: textbook. allowance for the 11th grade. general education institutions with Russian. lang. training with a 12-year term of study (basic and advanced) / V.V. Zhilko, L.G. Markovich. - Minsk: Nar. Asveta, 2008. - S. 334-337.
Introduction.
Within the framework of traditional approaches, a number of anomalous optical phenomena in the circumlunar space have not yet been explained. We will note a couple of the most notorious of them - links to testimonies of which are given below. Firstly, this is the phenomenon of loss of color: objects are observed not in natural colors, and, practically, in shades of gray. Secondly, this is the phenomenon of backscattering of light: at whatever angle the light falls on the scattering surface, most of the reflected light goes to reverse direction where the light came from.
We believe that the reason for these amazing phenomena is the special organization of lunar gravity - according to a different principle than the gravity of the planets. Planetary gravity is due, in our terminology, to a planetary frequency funnel. In the volume of a free test body, the local section of the frequency slope directly sets the gradient of the own energies of the particles of matter, which generates an unsupported force effect on the body. There are no signs of the presence of a lunar frequency funnel. We have presented a model of the organization of lunar gravity - through the imposition, on the local area of the earth's frequency slope, of specific vibrations of "inertial space" in the circumlunar region. Being in the resulting "unsteady space", the test body has, in its volume, a gradient of local absolute velocities - and, therefore, through quadratic Doppler shifts quantum levels energy , also has an energy gradient, i.e., again, it experiences an unsupported force effect.
The vibrations of "inertial space" have a dual effect on optical phenomena. First, these vibrations affect the molecules, i.e. on emitters and absorbers of light - why their emission and absorption spectra change. Secondly, phase velocity light, as we believe, is tied, in a local-absolute sense, to a local section of "inertial space", therefore its vibrations affect the process of light propagation.
In this article, we will give a refined model of the circumlunar "unsteady space" and explain the origin of these anomalous optical phenomena.
Refined model of the circumlunar "unsteady space".
An early model of the circumlunar "unsteady space" is set out in. It is appropriate to note that the very first flights of Soviet and American spacecraft to the Moon showed that its gravity acts only in a small near-lunar region, up to about 10,000 km from the surface of the Moon - and, thus, does not reach the Earth far. Therefore, the Earth does not have a dynamic response to the Moon: contrary to popular belief, the Earth does not apply, in antiphase with the Moon, near their common "center of mass" - and, contrary to another common misconception, lunar gravity has nothing to do with the tides in the oceans.
According to the model, in the area of lunar gravity, harmonic vibrations of "inertial space" are set, purely by software, in directions along the local lunar verticals. For these radial vibrations, the amplitude values of velocities and equivalent linear displacements decrease as the distance from the center increases, and at the boundary of the lunar gravity region they become practically zero. If spherically symmetric gravity is simulated, obeying the inverse square law, then the dependence of the velocity amplitude V vibrations from the length of the radius vector r there is
where K\u003d 4.9 × 10 12 m 3 / s 2 - the gravitational parameter of the Moon, r max is the radius of the boundary of the lunar gravity region. If we substitute in (1) the values of the average radius of the Moon r L = 1738 km, and also r max = 11738 km, then for the amplitude of the velocity of vibrations of the "unsteady space" on the surface of the Moon, we get V(r L)" 3.10 km/s. If we assume that on the surface of the Moon the amplitude of equivalent linear displacements is d(r A) = 5 μm, then for the frequency of vibrations, which we assume to be the same in the entire region of lunar gravitation, we obtain V(r L)/2p d(r L) » 100 MHz. These figures are, of course, indicative.
The key refinement of the model of the circumlunar "unsteady space" is connected with the question of the phases of the radial vibrations of the "inertial background". Previously, we believed that the area of lunar gravity is divided into radial sections, in which the phases of radial vibrations are organized "in a checkerboard pattern." Now, however, such an organization of the phases of radial vibrations seems to us to be unreasonably complicated and completely unnecessary. Radial shifts of "inertial space" can occur synchronously in the entire area of lunar gravity: "all together from the center - all together towards the center." With such globally synchronous vibrations, "unsteady space" will communicate centripetal acceleration a free body is no worse than according to the model, and programmatically organizing globally synchronous vibrations is incomparably easier.
The propagation of light in a vibrating "unsteady space" has fundamental features, since the conditions under which the Quantum Energy Transfer Navigator operates are unusual here. This is a program that individually for each excited atom searches for the recipient atom to which the excitation energy will be transferred. Light propagation effects, including wave phenomena, are determined by the calculation algorithms that the Navigator performs - identifying the recipient atom, to which the probability of a quantum energy transfer is maximum. These Navigator algorithms are described in . Now it is important for us that the speed of the search waves, with which the Navigator informationally scans the space, is equal to the speed of light and is tied, in the local-absolute sense, to the local section of the "inertial space". Therefore, the vibrations of the "inertial space" affect the movement of the search waves of the Navigator. With the orientation of these vibrations along the local lunar verticals, the local horizontal light beam will move not in a straight line, but along a sinusoid - with a period determined by the vibration frequency. At their frequency of 100 MHz (see above), the period of the sinusoid will be about 3 m. In this case, the vertical angular spread of the directions of the beam movement can be estimated through the ratio of the amplitude of the vibration velocity to the speed of light - near the surface of the Moon, this spread will be approximately one arc second.
Accounting for this vertical spread in the directions of motion of a light beam traveling near the surface of the Moon easily explains, in our opinion, the following optical effects. First, it is impossible predict the occurrences and duration of occultations of stars by the Moon with such accuracy with which many other celestial phenomena are predicted» . Secondly, this is a decrease in the quality of the image of the Moon's surface near the edges of the disk (see, for example, photographs in). Blurring at the edges of the lunar disk would be unsurprising if the moon had an atmosphere—but it doesn't. Both of these effects have not found a reasonable explanation within the framework of traditional approaches.
The phenomenon of loss of color in the circumlunar "unsteady space".
As we stated earlier, the process of light propagation is a chain of quantum transfers of excitation energy from atom to atom. Successive links in this chain, i.e. pairs of atom-sender and atom-receiver are set, according to certain algorithms, by the Navigator. The distance between the peaks of the Navigator's search waves is what in optics is called the wavelength of "radiation" (we put this word in quotation marks, because the Navigator's search waves are not of a physical nature, but of a software nature). In the conditions of ordinary, non-vibrating space, the wavelength is completely determined by the excitation energy of the atom, if this atom is at rest - in a locally absolute sense. If the vector of its local-absolute velocity is not equal to zero, then the lengths of the search waves coming from it in different directions have the corresponding linear Doppler shifts. We emphasize that, when an excited atom moves, only search waves are subject to the linear Doppler effect - the energy of the transferred quantum remains unchanged. Thus, a search wave with some linear Doppler shift can successfully overcome a narrow-band filter, and an energy quantum can be transferred to an atom located behind this filter, but the energy of this transferred quantum will still be the same excitation energy as in the case of an excited excited object at rest. atom - when the search wave would not pass through the filter.
Now let's return to the case of "unsteady space". Its radial vibrations can produce linear Doppler shifts in the Navigator's search wavelengths of the order of up to V(r L)/ c~ 10 -5 . Effects of this order - given that the visible range occupies an octave - could not lead to radical changes in colors. But note that the vast majority of the color palette, including on the Moon, is provided by a substance that forms molecular compounds. Could it be that "unsteady space" affects the molecular emission-absorption spectra?
As we stated earlier, a chemical bond is a process of cyclic switching of the compositions of the “proton-electron” valence bonds of the bonded atoms, in which each of the two electrons involved alternately enters into the composition of one or another atom. This cyclic process is stabilized by transfers of the excitation energy quantum from one atom to another and vice versa. At thermal equilibrium, the most probable energy of this quantum corresponds to the maximum of the equilibrium spectrum, i.e. equals 5 kT, where k – Boltzmann's constant, T is the absolute temperature. As we tried to show in, the so-called. oscillatory and rotational molecular lines do not correspond to different binding energies of atoms in a molecule: they correspond to certain resonances in the cyclic process of chemical bonding - at a suitable quantum energy, which the bound atoms cyclically transfer to each other. A typical feature of molecular absorption spectra are the bands of the continuous spectrum - the dissociation bands. For most molecules, the lower edge of the first dissociation band is 4–5 eV away from the ground state level, i.e. the energies of excitation quanta corresponding to the entire visible range fall within the gap between the ground state and the first dissociation band. Under "usual" conditions, this gap is more or less densely filled with discrete energy levels. Little known is the fact that the corresponding molecular lines, unlike atomic lines, are not characteristic - their positions "float" depending on temperature and pressure. Vibrations of the "unsteady space", in our opinion, should lead to a strong broadening of molecular lines; let's explain it.
Recall that, under the conditions of "ordinary" gravitation, a change in the local-absolute velocity of a free body uniquely corresponds to a change in the gravitational potential. In the circumlunar "unsteady space" the situation is different: free bodies there they experience harmonic changes in the local-absolute velocity (measured in the geocentric coordinate system), being, practically, in the same gravitational potential (the earth's gravitational region). We believe that this anomalous, from the point of view of energy transformations, situation is resolved as follows. Buffer for the periodic component kinetic energy molecule is the energy of its excitation - i.e. the same quantum that the bound atoms transfer to each other. Then, for molecules from light elements with single bonds, the amplitude value of the kinetic energy on the surface of the Moon ( V(r A)» 3 km/s) should correspond to the amplitude value of the excitation energy ~ 1 eV per bond. Because of this periodic component of the excitation energy, the "vibrational" and "rotational" molecular lines must experience such significant broadenings that the gap from the ground state to the first dissociation band should occupy a continuous spectrum . And there is: " The lunar spectrum is almost devoid of bands that could give information about the composition of the moon.» .
Let us clarify why the phenomenon of loss of color should take place in the case of continuous molecular spectra. It is known that in the retina of the human eye there are three types of light-sensitive cells responsible for color perception - which differ in the positions of the absorption band maxima: in the red-orange, green and blue-violet regions. The color sensation is not determined by the energy of monochromatic light quanta - it is determined by the ratio of the number of "operations" of the cells named three types for some "color reaction time". If, under conditions of “unsteady space”, molecular absorption lines spread over the entire visible range, then for each of the three types of cells, the probabilities of “triggering” for a quantum from any region of the visible range become the same.
It immediately follows from this that all objects on the Moon should be seen with a loss of color - practically, in shades of gray scale. Loss of color should take place not only during live visual observation on the Moon, but also when photographing there on color film, and even through light filters. Really, " color filters on board...["Surveyors"] were used to produce color photographs of the lunar landscape... It is surprising that there is no color in any part of these images, especially when compared with the variety of colors of typical terrestrial desert or mountain landscapes.» . Maybe the author is confusing something? Not at all, the official NASA report on Surveyor-1 states the same thing. The transmission curves of the three light filters were close to standard - we reproduce the corresponding diagram from the Fig.1. What are
were the results? In the section “Photometry and Colorimetry”, only three phrases are given to colorimetry proper. Namely: " Pre-processing of colorimetric measurements based on photographic film data shows that only minor color differences can be present in materials of the lunar surface. Lack of rich colors for surface lunar materials, this is something striking given the observed differences in albedo. Everywhere the color of the lunar surface is dark gray"(Our translation). However, the amazement of NASA specialists did not last long. The author already writes: The surveyor had a sharper and more uncomplicated look. And, for the first time, he saw in color. Three separate photographs taken through orange, green and blue filters, when combined, gave a completely natural reproduction of color. As scientists expected, this color turned out to be nothing but gray - a uniform, neutral gray."(Our translation). We reproduce one of these gray photomosaics from Surveyor-1 on Fig.2.
It may be suspected that only lunar materials have a natural gray color, and terrestrial objects delivered to the Moon look there in the same colors as on Earth. Not at all, we are reproducing a fragment of another photo with “natural color reproduction” - see below. Fig.3. This is a very remarkable document. Against the background of the "pancake" of the supporting "paw" of the device, in the right part of the image, a section of the disk with sector markings is visible. This is just a color calibration disk: on Earth, its four sectors were white,
Fig.3.
red, green and blue colors. But, instead of them, we see only shades of gray scale.
We add that the loss of color occurs even when the Moon is observed from outside its gravitational region. True, in this case, a shade of brown is mixed with gray colors: “ In a telescope, the moon has a uniform brownish-gray hue and is almost devoid of color differences.» . Attempts have been made to obtain color photographs of the Moon when photographing from outside the region of its gravitation through light filters, with the subsequent combination of images. By this technique, indeed, magnificent color pictures are obtained - but, in view of the foregoing, it is naive to believe that the colors in them demonstrate the real color scheme of the Moon.
It should be clarified that the phenomenon of color loss in the circumlunar space is in no way refuted when photographing and video filming with digital equipment - which allows you to "make" any desired colors "out of nothing". With traditional photography, i.e. with natural color reproduction, the phenomenon of loss of color in the circumlunar space is an indisputable fact. Moreover, according to NASA officials, experts even expected the absence of a rich color scheme on the Moon in advance. Let's remember it!
The phenomenon of backscattering of light in the circumlunar "unsteady space".
The albedo of the lunar surface, i.e. its ability to reflect sunlight is small: it averages 7%. And for this small amount of reflected light, the phenomenon of backscattering takes place. Namely: at whatever angle the light falls on the scattering surface - up to an almost grazing incidence! Most of the reflected light goes back to where the light came from.
Evidence of this amazing phenomenon for the terrestrial observer is the well-known fact that " the brightness of all areas of the lunar disk reaches a sharp maximum at the full moon, when the light source is exactly behind the observer» . The integral curve of the brightness of the moon glow, as a function of the phase angle, is shown in Fig.4(, the zero phase corresponds to the full moon).
Fig.4
The backscattering phenomenon cannot be explained by ordinary scattering on the roughness of the Moon's surface. A rough surface would scatter light according to Lambert's law, and then on a full moon darkening would be observed towards the edges of the lunar disk - which is not the case. The brightness of the full moon increases anomalously for each region of the lunar disk, " regardless of its position on the lunar sphere, surface inclination and morphological type» . Due to the lack of darkening to the edges, the full moon appears "flat as a pancake". The phenomenon of backscattering of light takes place not only for the side of the Moon visible from the Earth, but also for the opposite one, as evidenced by photographs of the latter taken with the help of spacecraft. The indicatrices of the backscattering of light by the Moon are given, for example, in.
Sometimes the phenomenon of backscattering is confused with the so-called. oppositional effect, which is simply that " the brightness increase rate is especially high at small phase angles' - as this well illustrates Fig.4. The opposition effect characterizes the rate of change in brightness - and not the change in brightness itself - with a change in phase angle. The oppositional effect only emphasizes the sharpness of the action of the backscattering effect - because of which, in an abnormally bright moonlight on a full moon, you can read a book.
It was believed that the phenomenon of backscattering is due to some unusual properties lunar soil- and this despite the fact that the phenomenon is equally manifested for all regions of the lunar disk, although the morphologies of the lunar seas and continents differ. Many attempts have been made to find a mineral or material that gives the lunar scattering law. A variety of samples of terrestrial and cosmic origin were investigated " in various forms: solid, pulverized, melted and resolidified, irradiated with ultraviolet light, X-rays and protons ...» None scattered the light back as much as the Moon. Finally, it was found that a scattering law similar to the lunar one gives finely dispersed structures with extremely developed porosity. But one could hardly expect that the existence of such a "fluff" is supported in the real conditions of the surface of the Moon. Not to mention the frequent weak "moonquakes", electrostatic erosion and "slumping" of the surface material play a significant role there. Studies of the lunar soil - both "on the ground", with the help of "Surveyers", and in terrestrial laboratories - showed that there are no "fluffy structures" in it. The soil of the moon fine-grained, weakly cohesive with an admixture of gravel and small stones» . Lunar " regolith easily sticks together into separate loose lumps and is easily molded. Despite noticeable stickiness, it has an unstable, easily broken structure.» . On top of these discouraging discoveries, in terrestrial laboratories, lunar samples did not at all exhibit the lunar scattering law. Research on the phenomenon has come to a standstill.
Meanwhile, this phenomenon finds a simple natural explanation - as a result of the vibrations of the "unsteady space". Recall that, under "ordinary" conditions, specular reflection is explained as follows. The section of the flat wave front falls on flat surface- whose points, to which this front has reached, immediately become sources of secondary spherical waves, according to the Huygens-Fresnel principle. The envelope of secondary spherical wave fronts is a section of a flat front - which is a mirror image. Note that this classical explanation implies the interference of secondary wave fronts - and for this it is necessary that the coherence area be larger than the section of the reflecting surface on which the original section of the front falls. But in the "unsteady space", in view of the foregoing, the concept of "coherence" loses all meaning. For each channel of the Navigator that calculates the transfer address of one quantum, already with a characteristic size of the “coherence area” smaller than the wavelength, there will not be a set of secondary spherical waves emanating from various points of the scattering surface - secondary spherical waves will come from one points on this surface. According to the logic of the Navigator's algorithms, calculations are continued only for the most probable directions of the search for the destination atom - and those are those that overlap with different peaks of the search waves (of the same Navigator channel). In the case under consideration, secondary spherical waves emerging from one point can only overlap the peaks of the incident wave - giving bursts of probabilities on the line along which this incident wave goes. Thus, if the quantum of light is not absorbed by the surface, and the Navigator is forced to continue searching for the destination for its transfer, then the "reflection" from the surface will most likely be the opposite - regardless of the angle of incidence.
What are the physical consequences of the backscattering phenomenon? If the Moon only reflects about 7% of the incoming sunlight, and if almost all of that reflected light is going in the direction it came from, then an observer on the Moon will by no means see the sunlit scenery. For an observer, even on the side of the Moon illuminated by the Sun, twilight reigns - which is demonstrated, for example, by the very first photographic panoramas made on the surface of the Moon by Soviet devices, starting with Luna-9 (see, for example,), as well as a large archive of television images transmitted "Lunokhod-1". An observer on the Moon will be able to see brightly illuminated either those objects that are close to an imaginary straight line drawn from the Sun through his head, or those that he illuminates himself by holding a light source near his eyes. In addition to twilight, which reigns even on the side of the Moon illuminated by the Sun, due to the phenomenon of backscattering, completely black shadows are observed there - and not gray, as on Earth, since on the Moon the shadow regions are not illuminated by scattered light either from illuminated areas or from the atmosphere, which not on the moon. Fig.5 reproduces one of the panoramas taken by Lunokhod-1 - immediately rushes into
Fig.5
eyes characteristic blackness from the anti-solar side - on the platform from which Lunokhod-1 moved out, as well as on the irregularities of the lunar surface. Fig.5 well conveys the typical signs of real moonlight.
Small discussion.
Above, we tried to explain the phenomena of loss of color and backscattering of light that take place in the circumlunar space. Perhaps someone will be able to explain these phenomena better than we did, but the very existence of these phenomena is indisputable. scientific fact- which is confirmed even by the first NASA reports on the lunar program.
Accounting for the existence of these phenomena provides new, deadly arguments in support of those who believe that film and photographic materials, which allegedly testify to the presence of American astronauts on the surface of the Moon, are fakes. After all, we give the keys to conduct a simple and merciless independent examination. If we are shown, against the background of lunar landscapes flooded with sunlight (!) Astronauts, on whose spacesuits there are no black shadows from the anti-solar side, or a well-lit figure of an astronaut in the shadow "lunar module", or color (!) frames with a colorful rendering of the colors of the American flag - then these are all irrefutable evidence screaming about falsification. In fact, we are not aware of any film or photographic document depicting astronauts on the Moon under real lunar lighting and with a real lunar color "palette".
The physical conditions on the Moon are too abnormal - and it cannot be ruled out that the circumlunar space is detrimental to terrestrial organisms. To date, we know the only model that explains the short-range effect of lunar gravity, and at the same time the origin of the accompanying anomalous optical phenomena - this is our model of "unsteady space". And if this model is correct, then the vibrations of the "unsteady space", below a certain height above the surface of the Moon, are quite capable of breaking weak bonds in protein molecules - with the destruction of their tertiary and, possibly, secondary structures. As far as we know, turtles returned alive from circumlunar space aboard the Soviet Zond-5 spacecraft, which circled the Moon with a minimum distance of about 2000 km from its surface. It is possible that, with the passage of the apparatus closer to the Moon, the animals would have died as a result of the denaturation of proteins in their organisms. If it is very difficult to protect yourself from cosmic radiation, but still possible, then there is no physical protection from the vibrations of the “unsteady space”.
The author thanks Ivan, the author of the sitehttp://ivanik3.narod.ru, for kind assistance in accessing primary sources, and also to O.Yu. Pivovar for helpful discussions.
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21. Web resource
Volgograd Municipal Gymnasium No. 1
in physics on the topic:
"Optical phenomena in nature"
Completed
9th grade students "B"
Pokusaeva V.O.
Trubnikova M.V.
Plan
1. Introduction
a) What is optics?
b) Types of optics
c) The role of optics in the development of modern physics
2. Phenomena associated with the reflection of light
a) The object and its reflection
b) The dependence of the reflection coefficient on the angle of incidence of light
c) Protective glasses
e) Total reflection of light
f) Cylindrical light guide
g) Diamonds and Gems
3. Phenomena associated with the refraction of light
b) rainbow
4. Auroras
Introduction
What is optics?
The first ideas of ancient scientists about light were very naive. It was believed that special thin tentacles come out of the eyes and visual impressions arise when they feel objects. At that time, optics was understood as the science of vision. This is the exact meaning of the word "optics". In the Middle Ages, optics gradually turned from the science of vision into the science of light, this was facilitated by the invention of lenses and the camera obscura. AT modern times Optics is a branch of physics that studies the emission of light, its propagation in various media and interaction with matter. As for issues related to vision, the structure and functioning of the eye, they stood out in a special scientific direction called physiological optics.
Types of optics
When considering many optical phenomena, one can use the concept of light rays - geometric lines along which light energy propagates. In this case one speaks of geometric (ray) optics.
Geometric optics is widely used in lighting engineering and when considering the operation of numerous instruments and devices, from magnifiers and glasses to the most complex optical microscopes and telescopes.
AT early XIX century, intensive studies of the previously discovered phenomena of interference, diffraction and polarization of light unfolded. These phenomena have not been explained in terms of geometric optics, it was necessary to consider the light in the form shear waves. This is how wave optics. Initially, it was believed that light is elastic waves in a certain medium (world ether), which supposedly fills the entire world space.
In 1864, the English physicist James Maxwell created the electromagnetic theory of light, according to which the waves of light are electromagnetic waves with the appropriate length range.
Studies carried out at the beginning of the 20th century showed that in order to explain some phenomena, such as the photoelectric effect, it is necessary to present a light beam as a stream of peculiar particles - light quanta (photons). As early as 200 years ago, Isaac Newton held a similar view of the nature of light in his "theory of the emission of light." Now the concept of light quanta is studied by quantum optics.
The role of optics in the development of modern physics.
The role of optics in the development of modern physics is great. The emergence of two of the most important and revolutionary theories of the twentieth century (quantum mechanics and the theory of relativity) is largely associated with optical research. Optical methods for analyzing matter at the molecular level have given rise to a special scientific direction - molecular optics. Closely adjacent to it is optical spectroscopy, which is used in modern materials science, plasma research, and astrophysics. There are also electron and neutron optics; created an electron microscope and a neutron mirror. Optical models of atomic nuclei have been developed.
Contributing to the development of various areas of modern physics, optics itself is currently experiencing a period of rapid development. The main impetus to this development was given by the invention of intense sources of coherent light - lasers. As a result, wave optics has risen to a higher level, corresponding to coherent optics. It is even difficult to enumerate all the latest scientific and technical areas that are developing due to the advent of lasers. Among them are nonlinear optics, holography, radio optics, picosecond optics, adaptive optics, and others. Radio optics arose at the intersection of radio engineering and optics; she explores optical methods transmission and processing of information. These methods are usually combined with traditional electronic methods; as a result, a scientific and technical direction called optoelectronics has developed. The transmission of light signals along dielectric fibers is the subject of fiber optics. Using the achievements of nonlinear optics, it is possible to correct the wavefront of a light beam, which is distorted when light propagates in a particular medium, for example, in the atmosphere or in water. As a result, the so-called adoptive optics has emerged and is being intensively developed. Closely adjacent to it is the photoenergetics that is emerging before our eyes, dealing, in particular, with the efficient transmission of light energy along a beam of light. Modern laser technology allows you to receive light pulses with a duration of the order of only a picosecond. Such pulses turn out to be a unique "tool" for studying a number of fast processes in matter, and in particular in biological structures. A special direction arose and is developing - picosecond optics; photobiology closely adjoins it. It can be said without exaggeration that the wide practical use of the achievements of modern optics is an indispensable condition for scientific and technological progress. Optics opened the way to the microworld for the human mind, it also allowed him to penetrate the secrets of the stellar worlds. Optics covers all aspects of our practice.
Phenomena associated with the reflection of light.
The object and its reflection
What is reflected in standing water the landscape does not differ from the real one, but only turned “upside down” is far from being the case.
If a person looks late in the evening at how the lamps are reflected in the water or how the shore descending to the water is reflected, then the reflection will seem shortened to him and will completely “disappear” if the observer is high above the surface of the water. Also, you can never see the reflection of the top of a stone, part of which is immersed in water.
The landscape is seen by the observer as if it were viewed from a point as much deeper than the surface of the water as the observer's eye is above the surface. The difference between the landscape and its image decreases as the eye approaches the surface of the water, as well as as the object moves away.
It often seems to people that the reflection of bushes and trees in a pond is distinguished by greater brightness of colors and saturation of tones. This feature can also be noticed by observing the reflection of objects in the mirror. Here the psychological perception plays a greater role than the physical side of the phenomenon. The frame of the mirror, the banks of the pond limit a small section of the landscape, protecting a person’s peripheral vision from excessive scattered light coming from the entire sky and blinding the observer, that is, he looks at a small section of the landscape as if through a dark narrow pipe. Reducing the brightness of reflected light compared to direct light makes it easier for people to see the sky, clouds, and other brightly lit objects that are too bright for the eye when viewed directly.
Coefficient dependency reflections from the angle of incidence of light.
At the boundary of two transparent media, light is partially reflected, partially passes into another medium and is refracted, partially absorbed by the medium. The ratio of the reflected energy to the incident energy is called the reflection coefficient. The ratio of the energy of light passing through a substance to the energy of incident light is called the transmittance.
The reflection and transmission coefficients depend on the optical properties, the media adjacent to each other, and the angle of incidence of the light. So, if light falls on a glass plate perpendicularly (angle of incidence α = 0), then only 5% of the light energy is reflected, and 95% passes through the interface. As the angle of incidence increases, the fraction of reflected energy increases. At the angle of incidence α=90˚ it is equal to one.
The dependence of the intensity of light reflected and passing through a glass plate can be traced by placing the plate at different angles to the light rays and estimating the intensity by eye.
It is also interesting to estimate by eye the intensity of the light reflected from the surface of the reservoir, depending on the angle of incidence, to observe the reflection of the sun's rays from the windows of the house at different angles of incidence during the day, at sunset, at sunrise.
Protective glasses
Ordinary window panes partially transmit heat rays. It is good for using them in northern areas as well as for greenhouses. In the south, the premises are so overheated that it is difficult to work in them. Protection from the sun comes down to either darkening the building with trees, or choosing a favorable orientation for the building during restructuring. Both are sometimes difficult and not always feasible.
In order for the glass not to transmit heat rays, it is covered with thin transparent films of metal oxides. Thus, a tin-antimony film does not transmit more than half of the thermal rays, and coatings containing iron oxide completely reflect ultraviolet rays and 35-55% of thermal ones.
Solutions of film-forming salts are applied from a spray gun to a hot glass surface during its heat treatment or molding. At high temperatures, the salts turn into oxides, which are firmly bound to the glass surface.
Glasses for light-protective glasses are made in a similar way.
Total internal light reflection
A beautiful sight is a fountain, in which the ejected jets are illuminated from the inside. This can be depicted under normal conditions by doing the following experiment (Fig. 1). In a high tin can, at a height of 5 cm from the bottom, a round hole must be drilled ( a) with a diameter of 5-6 mm. An electric light bulb with a cartridge must be carefully wrapped with cellophane paper and placed opposite the hole. You need to pour water into the jar. Opening a hole a , we get a jet that will be illuminated from the inside. In a dark room, it glows brightly and looks very impressive. The jet can be given any color by placing colored glass in the path of the light rays. b. If you put your finger in the path of the jet, then the water is sprayed and these droplets glow brightly.
The explanation for this phenomenon is quite simple. The light beam passes along the water jet and hits the curved surface at an angle greater than the limit, experiences total internal reflection, and then again hits the opposite side of the jet at an angle again greater than the limit. So the beam passes along the jet, bending along with it.
But if the light were completely reflected inside the jet, then it would not be visible from the outside. Part of the light is scattered by water, air bubbles and various impurities present in it, as well as due to the uneven surface of the jet, so it is visible from the outside.
Cylindrical light guide
If you direct a light beam at one end of a solid curved glass cylinder, you can see that the light will come out of its other end (Fig. 2); almost no light escapes through the side surface of the cylinder. The passage of light through a glass cylinder is explained by the fact that, falling on the inner surface of the cylinder at an angle greater than the limit, the light repeatedly experiences total reflection and reaches the end.
The thinner the cylinder, the more often the beam will be reflected and the greater part of the light will fall on the inner surface of the cylinder at angles greater than the limit.
Diamonds and Gems
There is an exhibition of Russia's diamond fund in the Kremlin.
The lights in the hall are slightly dimmed. Jewelers' creations sparkle in the shop windows. Here you can see such diamonds as "Orlov", "Shah", "Maria", "Valentina Tereshkova".
The secret of the beautiful play of light in diamonds lies in the fact that this stone has a high refractive index (n=2.4173) and, as a result, a small angle of total internal reflection (α=24˚30′) and has a greater dispersion, causing the decomposition of white light for simple colors.
In addition, the play of light in a diamond depends on the correctness of its cut. The facets of a diamond repeatedly reflect light within the crystal. Due to the high transparency of high-class diamonds, the light inside them almost does not lose its energy, but only decomposes into simple colors, the rays of which then break out in various, most unexpected directions. When the stone is turned, the colors emanating from the stone change, and it seems that the stone itself is the source of many bright multi-colored rays.
There are diamonds painted in red, bluish and lilac colors. The brilliance of a diamond depends on its cut. When viewed through a well-cut water-clear diamond in the light, the stone appears completely opaque, and some of its facets look just black. This is because the light, undergoing total internal reflection, exits in the opposite direction or to the sides.
When you look at the top cut from the side of the world, it shines in many colors, and in places it glitters. The bright sparkle of the upper facets of a diamond is called diamond brilliance. The underside of the diamond from the outside seems to be silver-plated and casts with a metallic sheen.
The most transparent and large diamonds serve as decoration. Small diamonds are widely used in technology as a cutting or grinding tool for machine tools. Diamonds are used to reinforce the heads of drilling tools for drilling wells in hard rocks. This use of diamond is possible because of the great hardness that distinguishes it. Other precious stones in most cases are aluminum oxide crystals with an admixture of oxides of coloring elements - chromium (ruby), copper (emerald), manganese (amethyst). They are also hard, durable and have a beautiful color and "play of light". At present, they are able to artificially obtain large crystals of aluminum oxide and paint them in the desired color.
The phenomena of light dispersion are explained by the variety of colors of nature. A whole complex of optical experiments with prisms in the 17th century was carried out by the English scientist Isaac Newton. These experiments showed that white light is not the main one, it must be considered as a composite ("non-uniform"); the main ones are different colors (“homogeneous” rays, or “monochromatic” rays). The decomposition of white light into different colors occurs for the reason that each color has its own degree of refraction. These conclusions made by Newton are consistent with modern scientific ideas.
Along with the dispersion of the refractive index, there is a dispersion of the coefficients of absorption, transmission, and reflection of light. This explains the various effects in the illumination of bodies. For example, if there is some body transparent to light, in which the transmittance is large for red light, and the reflection coefficient is small, for green light it is the other way around: the transmittance is small, and the reflectance is large, then in transmitted light the body will appear red, and green in reflected light. Such properties are possessed, for example, by chlorophyll, a green substance contained in the leaves of plants and causing green color. A solution of chlorophyll in alcohol when viewed through the light is red. In reflected light, the same solution appears green.
If some body has a large absorption coefficient, and the transmission and reflection coefficients are small, then such a body will appear black and opaque (for example, soot). A very white, opaque body (such as magnesium oxide) has a reflectance close to unity for all wavelengths, and very low transmittance and absorption. A body (glass) that is completely transparent to light has low reflection and absorption coefficients and a transmittance close to unity for all wavelengths. For colored glass, for some wavelengths, the transmission and reflection coefficients are practically equal to zero and, accordingly, the value of the absorption coefficient for the same wavelengths is close to unity.
Phenomena associated with the refraction of light
Mirage
Some types of mirages. From the greater variety of mirages, we single out several types: “lake” mirages, also called inferior mirages, superior mirages, double and triple mirages, ultra-long-range vision mirages.
Inferior ("lake") mirages occur over a strongly heated surface. Superior mirages, on the contrary, arise over a strongly cooled surface, for example, over cold water. If the lower mirages are observed, as a rule, in deserts and steppes, then the upper ones are observed in northern latitudes.
Superior mirages are diverse. In some cases they give a direct image, in other cases an inverted image appears in the air. Mirages can be double when two images are observed, a simple one and an inverted one. These images may be separated by a strip of air (one may be above the horizon, the other below it), but may directly merge with each other. Sometimes there is another - the third image.
Especially amazing are the mirages of ultra-long vision. K. Flammarion in his book “Atmosphere” describes an example of such a mirage: “Based on the testimony of several credible persons, I can report a mirage that was seen in the city of Verviers (Belgium) in June 1815. One morning, the inhabitants of the city saw in the sky army, and it is so clear that it was possible to distinguish the suits of artillerymen and even, for example, a cannon with a broken wheel, which is about to fall off ... It was the morning of the Battle of Waterloo! The described mirage is depicted in the form of a colored watercolor by one of the eyewitnesses. The distance from Waterloo to Verviers in a straight line is more than 100 km. There are cases when such mirages were observed at large distances - up to 1000 km. The "Flying Dutchman" should be attributed precisely to such mirages.
Explanation of the lower ("lake") mirage. If the air at the very surface of the earth is very hot and, therefore, its density is relatively low, then the refractive index at the surface will be less than in higher air layers. Changing the refractive index of air n with height h near the earth's surface for the case under consideration is shown in Figure 3, a.
In accordance with the established rule, light rays near the surface of the earth will in this case be bent so that their trajectory is convex downward. Let an observer be at point A. Light beam from some area blue sky hits the eye of the observer, experiencing the specified curvature. And this means that the observer will see the corresponding section of the sky not above the horizon line, but below it. It will seem to him that he sees water, although in fact he has an image of a blue sky in front of him. If we imagine that there are hills, palm trees or other objects near the horizon, then the observer will see them upside down due to the marked curvature of the rays, and will perceive them as reflections of the corresponding objects in non-existent water. So there is an illusion, which is a "lake" mirage.
Simple superior mirages. It can be assumed that the air at the very surface of the earth or water is not heated, but, on the contrary, noticeably cooled compared to higher air layers; the change in n with height h is shown in Figure 4, a. Light rays in the case under consideration are bent so that their trajectory is convex upwards. Therefore, now the observer can see objects hidden from him beyond the horizon, and he will see them at the top, as if hanging above the horizon line. Therefore, such mirages are called superior.
An superior mirage can produce both upright and inverted images. The direct image shown in the figure occurs when the refractive index of air decreases relatively slowly with height. With a rapid decrease in the refractive index, an inverted image is formed. This can be verified by considering a hypothetical case - the refractive index at a certain height h decreases abruptly (Fig. 5). The rays of the object, before reaching the observer A, experience total internal reflection from the boundary BC, below which, in this case, there is denser air. It can be seen that the superior mirage gives an inverted image of the object. In reality, there is no jump-like boundary between the layers of air, the transition takes place gradually. But if it is done sharply enough, then the superior mirage will give an inverted image (Fig. 5).
Double and triple mirages. If the refractive index of air changes first rapidly and then slowly, then the rays in region I will be bent faster than in region II. As a result, two images appear (Fig. 6, 7). The light rays 1 propagating within the air region I form an inverted image of the object. Beams 2, which propagate mainly within region II, are curved to a lesser extent and form a straight image.
To understand how a triple mirage appears, one must imagine three consecutive air regions: the first (near the surface itself), where the refractive index decreases slowly with height, the next, where the refractive index decreases rapidly, and the third region, where the refractive index decreases slowly again. The figure shows the considered change in the refractive index with height. The figure shows how a triple mirage occurs. Rays 1 form the lower image of the object, they propagate within the air region I. Rays 2 form an inverted image; I fall into the air region II, these rays experience a strong curvature. Beams 3 form the upper direct image of the object.
Mirage of ultra-long vision. The nature of these mirages is the least studied. It is clear that the atmosphere must be transparent, free from water vapor and pollution. But this is not enough. A stable layer of cooled air should form at some height above the ground. Below and above this layer, the air should be warmer. A light beam that has fallen inside a dense cold layer of air is, as it were, “locked” inside it and propagates in it like a kind of light guide. The ray trajectory in Figure 8 is convex all the time towards the less dense regions of the air.
The emergence of ultra-distant mirages can be explained by the propagation of rays inside such "light guides", which are sometimes created by nature.
Rainbow
The rainbow is a beautiful celestial phenomenon that has always attracted the attention of man. In the old days, when people still knew little about the world around them, the rainbow was considered a "heavenly sign." So, the ancient Greeks thought that the rainbow is the smile of the goddess Irida.
The rainbow is observed in the direction opposite to the Sun, against the background of rain clouds or rain. A multi-colored arc is usually located at a distance of 1-2 km from the observer, and sometimes it can be observed at a distance of 2-3 m against the background of water drops formed by fountains or water sprays.
The center of the rainbow is on the continuation of the straight line connecting the Sun and the eye of the observer - on the anti-solar line. The angle between the direction to the main rainbow and the antisolar line is 41-42º (Fig. 9).
At the time of sunrise, the antisolar point (point M) is on the horizon line and the rainbow looks like a semicircle. As the sun rises, the antisolar point falls below the horizon and the size of the rainbow decreases. It is only part of a circle.
Often there is a secondary rainbow, concentric with the first, with an angular radius of about 52º and an inverse arrangement of colors.
At a Sun height of 41º, the main rainbow ceases to be visible and only a part of the secondary rainbow appears above the horizon, and at a Sun height of more than 52º, the secondary rainbow is not visible either. Therefore, in the middle equatorial latitudes, this natural phenomenon is never observed during the near noon hours.
The rainbow has seven primary colors that smoothly transition from one to another.
The shape of the arc, the brightness of the colors, the width of the stripes depend on the size of the water droplets and their number. Large drops create a narrower rainbow, with sharply prominent colors, small drops create an arc that is blurry, faded and even white. That is why a bright narrow rainbow is visible in the summer after a thunderstorm, during which large drops fall.
The rainbow theory was first given in 1637 by René Descartes. He explained the rainbow as a phenomenon associated with the reflection and refraction of light in raindrops.
The formation of colors and their sequence were explained later, after unraveling the complex nature of white light and its dispersion in a medium. The diffraction theory of the rainbow was developed by Airy and Partner.
Can be considered simplest case: let a beam of parallel solar rays fall on drops having the shape of a ball (Fig. 10). A beam incident on the surface of a drop at point A is refracted inside it according to the law of refraction:
n sin α=n sin β, where n=1, n≈1.33 –
refractive indices of air and water, respectively, α is the angle of incidence, and β is the angle of refraction of light.
Inside the drop, the ray AB goes in a straight line. At point B, the beam is partially refracted and partially reflected. It should be noted that the smaller the angle of incidence at point B, and hence at point A, the lower the intensity of the reflected beam and the greater the intensity of the refracted beam.
Beam AB after reflection at point B occurs at an angle β`=β b hits point C, where partial reflection and partial refraction of light also occur. The refracted beam leaves the drop at an angle γ, while the reflected one can go further, to point D, etc. Thus, the light beam in the drop undergoes multiple reflections and refractions. With each reflection, some of the rays of light come out and their intensity inside the drop decreases. The most intense of the rays emerging into the air is the ray that emerged from the drop at point B. But it is difficult to observe it, since it is lost against the background of bright direct sunlight. The rays refracted at point C, together, create a primary rainbow against the background of a dark cloud, and rays refracted at point D give a secondary rainbow, which is less intense than the primary one.
When considering the formation of a rainbow, one more phenomenon must be taken into account - the unequal refraction of light waves of different lengths, that is, light rays different color. This phenomenon is called dispersion. Due to dispersion, the angles of refraction γ and the angle of deflection of rays Θ in a drop are different for rays of different colors.
Most often we see one rainbow. It is not uncommon for two rainbow stripes to appear simultaneously in the sky, located one after the other; an even greater number of celestial arcs are observed - three, four and even five at the same time. This interesting phenomenon was observed by Leningraders on September 24, 1948, when four rainbows appeared among the clouds over the Neva in the afternoon. It turns out that a rainbow can arise not only from direct rays; often it appears in the reflected rays of the sun. This can be seen on the shores of the sea bays, big rivers and lakes. Three or four rainbows - ordinary and reflected - sometimes create a beautiful picture. Since the rays of the Sun reflected from the water surface go from bottom to top, the rainbow formed in the rays can sometimes look completely unusual.
You should not think that a rainbow can be observed only during the day. It happens at night, however, always weak. You can see such a rainbow after a night rain, when the moon looks out from behind the clouds.
Some semblance of a rainbow can be obtained from this experience: You need to light a flask filled with water sunlight or a lamp through a hole in the whiteboard. Then a rainbow will become clearly visible on the board, and the angle of divergence of the rays compared to the initial direction will be about 41-42 °. Under natural conditions, there is no screen, the image appears on the retina of the eye, and the eye projects this image onto the clouds.
If a rainbow appears in the evening before sunset, then a red rainbow is observed. In the last five or ten minutes before sunset, all the colors of the rainbow, except for red, disappear, it becomes very bright and visible even ten minutes after sunset.
A beautiful sight is a rainbow on the dew. It can be observed at sunrise on the grass covered with dew. This rainbow is shaped like a hyperbola.
auroras
One of the most beautiful optical phenomena of nature is the aurora borealis.
In most cases, auroras are green or blue-green in color, with occasional patches or borders of pink or red.
Auroras are observed in two main forms - in the form of ribbons and in the form of cloud-like spots. When the radiance is intense, it takes on the form of ribbons. Losing intensity, it turns into spots. However, many ribbons disappear before they break into spots. The ribbons seem to hang in the dark space of the sky, resembling a giant curtain or drapery, usually stretching from east to west for thousands of kilometers. The height of this curtain is several hundred kilometers, the thickness does not exceed several hundred meters, and it is so delicate and transparent that stars can be seen through it. The lower edge of the curtain is quite sharply and distinctly outlined and often tinted in red or pinkish color, reminiscent of the border of the curtain, the upper one is gradually lost in height and this creates a particularly spectacular impression of the depth of space.
There are four types of auroras:
Homogeneous arc - the luminous strip has the simplest, calmest form. It is brighter from below and gradually disappears upward against the background of the glow of the sky;
Radiant arc - the tape becomes somewhat more active and mobile, it forms small folds and streams;
Radiant band - with increasing activity, larger folds are superimposed on small ones;
With increased activity, the folds or loops expand to huge size, the bottom edge of the ribbon glows brightly with a pink glow. When the activity subsides, the wrinkles disappear and the tape returns to a uniform shape. This suggests that homogeneous structure is the main form of the aurora, and the folds are associated with an increase in activity.
Often there are aurora of a different kind. They capture the entire polar region and are very intense. They occur during an increase solar activity. These lights appear as a whitish-green cap. Such auroras are called squalls.
According to the brightness of the aurora, they are divided into four classes, differing from each other by one order of magnitude (that is, 10 times). The first class includes aurora, barely noticeable and approximately equal in brightness Milky Way, the radiance fourth grade illuminate the earth as brightly as the full moon.
It should be noted that the aurora that has arisen propagates to the west at a speed of 1 km/sec. The upper layers of the atmosphere in the area of aurora flares heat up and rush upwards, which has affected the enhanced deceleration of artificial satellites of the Earth passing through these zones.
During auroras, vortexes appear in the Earth's atmosphere. electric currents covering large areas. They excite additional unstable magnetic fields, the so-called magnetic storms. During aurora, the atmosphere emits X-rays, which appear to be the result of electron deceleration in the atmosphere.
Intense flashes of radiance are often accompanied by sounds resembling noise, crackling. Auroras cause strong changes in the ionosphere, which in turn affects radio conditions. In most cases, radio communication deteriorates significantly. There is strong interference, and sometimes a complete loss of reception.
How auroras occur. The earth is a huge magnet South Pole which is located near the northern geographic pole, and the northern one is close to the southern one. The lines of force of the Earth's magnetic field, called geomagnetic lines, come out of the area adjacent to the north magnetic pole of the Earth, covers Earth and enter it in the area of the south magnetic pole, forming a toroidal lattice around the Earth.
It has long been believed that the location of the magnetic lines of force symmetrical about earth's axis. Now it turned out that the so-called "solar wind" - a stream of protons and electrons emitted by the Sun - hits the geomagnetic shell of the Earth from a height of about 20,000 km, pulls it back, away from the Sun, forming a kind of magnetic "tail" near the Earth.
An electron or a proton that has fallen into the Earth's magnetic field moves in a spiral, as if winding itself on a geomagnetic line. Electrons and protons that have fallen from the solar wind into the Earth's magnetic field are divided into two parts. Some of them flow down the magnetic field lines immediately into the polar regions of the Earth; others get inside the teroid and move inside it, as it is possible according to the left hand rule, along the closed curve ABC. These protons and electrons eventually flow along geomagnetic lines to the region of the poles, where their increased concentration occurs. Protons and electrons produce ionization and excitation of atoms and molecules of gases. To do this, they have enough energy, since protons arrive at the Earth with energies of 10000-20000 eV (1 eV = 1.6 10 J), and electrons with energies of 10-20 eV. For the ionization of atoms, it is necessary: for hydrogen - 13.56 eV, for oxygen - 13.56 eV, for nitrogen - 124.47 eV, and even less for excitation.
Excited gas atoms give back the received energy in the form of light, just as it happens in tubes with a rarefied gas when currents are passed through them.
A spectral study shows that the green and red glow belongs to excited oxygen atoms, infrared and violet - to ionized nitrogen molecules. Some emission lines of oxygen and nitrogen are formed at an altitude of 110 km, and the red glow of oxygen is formed at an altitude of 200-400 km. Another weak source of red light is hydrogen atoms formed in the upper atmosphere from protons arriving from the Sun. Having captured an electron, such a proton turns into an excited hydrogen atom and emits red light.
Aurora flares usually occur a day or two after solar flares. This confirms the connection between these phenomena. A study using rockets showed that in places of greater aurora intensity there is a more significant ionization of gases by electrons.
AT recent times scientists have found that the auroras are more intense near the coasts of the oceans and seas.
But the scientific explanation of all the phenomena associated with polar lights, encounters a number of difficulties. For example, the exact mechanism of particle acceleration to the indicated energies is unknown, their trajectories in the near-Earth space are not quite clear, not everything converges quantitatively in the energy balance of ionization and excitation of particles, the mechanism of luminescence formation is not quite clear. various kinds, the origin of sounds is unclear.
Literature:
5. "Encyclopedic dictionary of a young physicist", compiled by V. A. Chuyanov, publishing house "Pedagogy", Moscow, 1984.
6. "Handbook of a schoolboy in physics", compiler -, philological society "Slovo", Moscow, 1995.
7. "Physics 11", N. M. Shakhmaev, S. N. Shakhmaev, D. Sh. Shodiev, Prosveshchenie publishing house, Moscow, 1991.
8. "Solution of problems in physics", V. A. Shevtsov, Nizhne-Volzhskoe book publishing house, Volgograd, 1999.
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