>> Light pressure

§ 91 LIGHT PRESSURE

Maxwell based electromagnetic theory light predicted that light should exert pressure on obstacles.

Under the influence of the electric field of a wave incident on the surface of a body, for example a metal, a free electron moves in the direction opposite to the vector(Fig. 11.7). A moving electron is acted upon by a Lorentz force directed in the direction of wave propagation. Total force, acting on the electrons of the metal surface, and determines the force of light pressure.

To prove the validity of Maxwell's theory, it was important to measure the pressure of light. Many scientists have tried to do this, but without success, since the light pressure is very low. On a bright sunny day, a force equal to only 4 10 -6 N acts on a surface with an area of ​​1 m 2. The pressure of light was first measured by the Russian physicist Pyotr Nikolaevich Lebedev in 1900.

Lebedev Petr Nikolaevich (1866-1912)- Russian physicist who was the first to measure the pressure of light on solids and gases. These works quantitatively confirmed Maxwell's theory. In an effort to find new experimental evidence of the electromagnetic theory of light, he obtained electromagnetic waves of millimeter wavelength and studied all their properties. Created the first in Russia physical school. Many outstanding Soviet scientists were his students. Lebedev's name is physical institute USSR Academy of Sciences (FIAN).

Lebedev's device consisted of a very light rod on a thin glass thread, but the edges of which had light wings glued to them (Fig. 11.8). The entire device was placed in a vessel from which the air was pumped out. The light fell on the wings located on one side of the rod. The pressure value could be judged by the angle of twist of the thread. Difficulties precise measurement light pressures were associated with the inability to pump all the air out of the vessel (the movement of air molecules caused by unequal heating of the wings and walls of the vessel leads to additional torques). In addition, the twisting of the thread is affected by unequal heating of the sides of the wings (the side facing the light source heats up more than opposite side). Molecules reflected from the hotter side transfer more momentum to the winglet than molecules reflected from the less heated side.

Lebedev managed to overcome all these difficulties, despite low level experimental technique of that time, taking a very large vessel and very thin wings. Eventually the existence of light pressure on solids was proven and measured. The obtained value coincided with that predicted by Maxwell. Subsequently, after three years of work, Lebedev managed to carry out an even more subtle experiment: to measure the pressure of light on gases.

The emergence of the quantum theory of light made it possible to more simply explain the cause of light pressure. Photons, like particles of matter that have a rest mass, have momentum. When absorbed by the body, they transfer their impulse to it. According to the law of conservation of momentum, the momentum of the body becomes equal to impulse absorbed photons. Therefore, a body at rest comes into motion. A change in the momentum of a body means, according to Newton's second law, that a force acts on the body.

Lebedev's experiments can be considered as experimental proof that photons have momentum.

Although the light pressure is very low in normal conditions, its effect may nevertheless be significant. Inside stars, at temperatures of several tens of millions of Kelvin, the pressure of electromagnetic radiation should reach enormous values. Light pressure forces along with gravitational forces play a significant role in stellar processes.

According to Maxwell's electrodynamics, the pressure of light arises due to the action of the Lorentz force on the electrons of the medium, oscillating under the influence of an electric field electromagnetic wave. From the point of view of quantum theory, pressure appears as a result of the transfer of photon impulses to the body when they are absorbed.

Myakishev G. Ya., Physics. 11th grade: educational. for general education institutions: basic and profile. levels / G. Ya. Myakishev, B. V. Bukhovtsev, V. M. Charugin; edited by V. I. Nikolaeva, N. A. Parfentieva. - 17th ed., revised. and additional - M.: Education, 2008. - 399 p.: ill.

Textbooks for all subjects download, development of lesson plans for teachers, Physics and astronomy for grade 11 online

Lesson content lesson notes supporting frame lesson presentation acceleration methods interactive technologies Practice tasks and exercises self-test workshops, trainings, cases, quests homework controversial issues rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures, graphics, tables, diagrams, humor, anecdotes, jokes, comics, parables, sayings, crosswords, quotes Add-ons abstracts articles tricks for the curious cribs textbooks basic and additional dictionary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in a textbook, elements of innovation in the lesson, replacing outdated knowledge with new ones Only for teachers perfect lessons calendar plan for a year guidelines discussion programs Integrated Lessons

48. Elements quantum optics. Energy, mass and momentum of a photon. Derivation of the formula for light pressure based on quantum ideas about the nature of light.

Thus, the propagation of light should not be considered as a continuous wave propagation

process, but as a stream of discrete particles localized in space, moving at the speed of light propagation in a vacuum. Subsequently (in 1926) these particles were called photons. Photons have all the properties of a particle (corpuscle).

The development of Planck's hypothesis led to the creation of ideas about quantum properties Sveta. Light quanta are called photons. According to the law of proportionality of mass and energy and Planck's hypothesis, the photon energy is determined by the formulas

.

Equating the right-hand sides of these equations, we obtain an expression for the photon mass

or taking into account that,

The photon momentum is determined by the formulas:

The rest mass of the photon is zero. Quantum electromagnetic radiation exists only by propagating at the speed of light, while possessing finite values ​​of energy and momentum. In monochromatic light with frequency ν, all photons have the same energy, momentum and mass.

Light pressure

Light radiation can transfer its energy to the body in the form of mechanical pressure.

He proved that light completely absorbed by a blackened plate exerts a force on it. Light pressure manifests itself in the fact that a distributed force acts on the illuminated surface of the body in the direction of light propagation, proportional to the density of light energy and depending on optical properties surfaces.

As a result of applying the laws of mechanics to Lebedev’s optical measurements, an extremely important relationship was obtained, which showed that energy is always equivalent to mass. Einstein was the first to point out that the equation mc 2 =E is universal and should be valid for any type of energy.

This phenomenon can be explained from the standpoint of both wave and corpuscular concepts of the nature of light. In the first case, this is the result of interaction electric current induced in the body electric field light wave, with its magnetic field according to Ampere's law. The electric and magnetic fields of a light wave, periodically changing in space and time, when interacting with the surface of a substance, exert a force on the electrons of the atoms of the substance. The electric field of the wave causes the electrons to oscillate. Lorentz force from the side magnetic field wave is directed along the direction of wave propagation and represents light pressure force. Quantum theory explains the pressure of light by the fact that photons have a certain momentum and, when interacting with matter, they transfer part of the momentum to particles of the substance, thereby exerting pressure on its surface (an analogy can be drawn with the impacts of molecules on the wall of a vessel, in which the momentum transferred to the wall determines gas pressure in the vessel).

When absorbed, photons transfer their momentum to the body with which they interact. This is the cause of light pressure.

Let us determine the pressure of light on a surface using the quantum theory of radiation.

Let radiation with frequency ν fall perpendicular to some surface (Fig. 5). Let this radiation, consisting of N photons, fall on the surface of a flat

spare ∆ S for time ∆ t. The surface absorbs N 1 photons and reflects

Xia N 2, i.e. N = N 1 + N 2.

	Continued 48
Each absorbed photon (inelastic impact) transfers momentum to the surface				And everyone from-
the affected photon (elastic impact) transfers momentum to it			Then all incident photons are transmitted
blow an impulse equal to
In this case, the light will act on the surface with force
those. exert pressure

Multiply and divide the right side of this equality by N, we get

Finally

where is the energy of all N photons incident per unit area per unit time, size-

ity; – reflection coefficient.

For a black surface ρ = 0 and the pressure will be equal.

represents bulk density energy, its dimension .

Then the concentration of n photons in a beam incident on the surface will be

.

Substituting (2.2) into the equation for light pressure, we obtain

The pressure produced by light when falling on a flat surface can be calculated using the formula

where E is the intensity of surface irradiation (or illumination), c is the speed of propagation of electromagnetic waves in vacuum, α, is the fraction of incident energy absorbed by the body (absorption coefficient

tion), ρ is the fraction of the incident energy reflected by the body (reflection coefficient), θ is the angle between the direction of radiation and the normal to the irradiated surface. If the body is not transparent, that is, everything

incident radiation is reflected and absorbed, then α +ρ =1.

49 Elements of quantum optics. Compton effect. Particle-wave dualism of light (radiation).

3) Wave-corpuscle dualism of electromagnetic radiation

So, study thermal radiation, photoelectric effect, Compton effect showed that electromagnetic radiation (in particular, light) has all the properties of a particle (corpuscle). However large group optical phenomena- interference, diffraction, polarization indicates wave properties electromagnetic radiation, in particular light.

What constitutes light - continuous electromagnetic waves emitted by a source or a stream of discrete photons, randomly for an electromagnetic wave, does not exclude the discrete properties characteristic of photons.

Light (electromagnetic radiation) simultaneously has the properties of continuous electromagnetic waves and the properties of discrete photons. This is the particle-wave dualism (duality) of electromagnetic radiation.

2) Compton effect Consists of increasing the wavelength x-ray radiation when it is scattered by matter. Wavelength change

K (1-cos)=2k sin2 (/2),(9) "

where k =h/(mc) is the Compton wavelength, m is the rest mass of the

throne. k =2.43*10 -12 m=0.0243 A(1 A=10-10 m).

All features of the Compton effect were explained by considering scattering as a process elastic collision X-ray photons with free electrons, in which the law of conservation of energy and the law of conservation of momentum are observed.

According to (9), the change in wavelength depends only on the scattering angle and does not depend on either the X-ray wavelength or the type of substance.

1) Elements of quantum optics. Photons, energy, mass and momentum of a photon

To explain the distribution of energy in the spectrum of thermal radiation, Planck assumed that electromagnetic waves are emitted in portions (quanta). Einstein in 1905 came to the conclusion that radiation is not only emitted, but also propagates and is absorbed in the form of quanta. This conclusion made it possible to explain all the experimental facts (photoelectric effect, Compton effect, etc.) that could not be explained by classical electrodynamics, based on wave concepts of the properties of radiation. Thus, the propagation of light should not be considered as continuous wave process, but as a stream of discrete particles localized in space, moving at the speed of light propagation in a vacuum. Subsequently (in 1926) these particles were called photons. Photons have all the properties of a particle (corpuscle).

1. Photon energy

Therefore, Planck's constant is sometimes called the quantum of action. The dimension coincides, for example, with the dimension of angular momentum (L=r mv).

As follows from (1), the photon energy increases with increasing frequency (or decreasing wavelength),

2. The photon mass is determined based on the law on the relationship between mass and energy (E=mc 2)

3.Photon impulse. For any relativistic particle its energy Since photons have m 0 =0, then the photon momentum

those. wavelength is inversely proportional to momentum

50. Nuclear model of the atom according to Rutherford. Spectrum of a hydrogen atom. Generalized Balmer formula. Spectral series of the hydrogen atom. The concept of terma.

1) Rutherford suggested nuclear model atom. According to this model, an atom consists of a positive nucleus having a charge Ze (Z - serial number element in the periodic table, e - elementary charge), size 10 -5 -10 -4 A (1A = 10 -10 m) and the mass is almost equal to mass atom. Electrons move around the nucleus in closed orbits, forming electron shell atom. Since the atoms are neutral, Z electrons should rotate around the nucleus, the total charge of which is Zе. The dimensions of the atom are determined by the dimensions of the outer orbits of the electrons and are on the order of units of A.

The mass of electrons makes up a very small fraction of the mass of the nucleus (0.054% for hydrogen, less than 0.03% for other elements). The concept of “electron size” cannot be formulated consistently, although ro 10-3 A is called the classical electron radius. So, the nucleus of an atom occupies an insignificant part of the volume of the atom and almost the entire (99.95%) mass of the atom is concentrated in it. If the nuclei of atoms were located close to each other, then Earth would have a radius of 200 m and not 6400 km (density of matter

atomic nuclei 1.8

2) Line spectrum of a hydrogen atom

The emission spectrum of atomic hydrogen consists of individual spectral lines, which are located in in a certain order. In 1885, Balmer discovered that the wavelengths (or frequencies) of these lines can be represented by the formula.

, (9)

where R =1.0974 7 m -1 is also called the Rydberg constant.

In Fig. Figure 1 shows a diagram of the energy levels of the hydrogen atom, calculated according to (6) at z=1.

When an electron moves from higher energy levels to the n = 1 level, ultraviolet radiation or Lyman series (SL) radiation occurs.

When electrons move to the n = 2 level, visible radiation or Balmer series radiation (SB).

When electrons move from more high levels per level n =

3 arises infrared radiation, or Paschen series radiation (SP), etc.

The frequencies or wavelengths of the radiation arising in this case are determined by formulas (8) or (9) with m = 1 for the Lyman series, m = 2 for the Balmer series and m = 3 for the Paschen series. The energy of photons is determined by formula (7), which, taking into account (6), can be reduced for hydrogen-like atoms to the form:

eV (10)

50 continued

4) Spectral series of hydrogen- a set of spectral series that make up the spectrum of a hydrogen atom. Since hydrogen is the simplest atom, its spectral series are the most studied. They obey the Rydberg formula well:

,

where R = 109,677 cm−1 is the Rydberg constant for hydrogen, n′ is the main level of the series. Spectral lines, arising during transitions to the main energy level,

are called resonant, all others are called subordinate.

Lyman series

Discovered by T. Lyman in 1906. All lines in the series are in the ultraviolet range. The series corresponds to the Rydberg formula with n′ = 1 and n = 2, 3, 4,

Balmer series

Discovered by I. Ya. Balmer in 1885. The first four lines of the series are in the visible range. The series corresponds to the Rydberg formula with n′ = 2 and n = 3, 4, 5

5) Spectral term or electronic termatom, molecule or ion - configuration

walkie-talkie (state) electronic subsystem, which determines the energy level. Sometimes the word term is understood as energy itself. this level. Transitions between terms determine the emission and absorption spectra of electromagnetic radiation.

The terms of an atom are usually denoted in capital letters S,P,D,F, etc., corresponding to the value of the quantum number orbital angular momentum L =0, 1, 2, 3, etc. Quantum number The total angular momentum J is given by the subscript at the bottom right. The small number at the top left indicates the multiplicity ( multiplicity) terma. For example, ²P 3/2 is a doublet P. Sometimes (as a rule, for one-electron atoms and ions) the term symbol is indicated principal quantum number(for example, 2²S 1/2).

CBETA PRESSURE, the pressure exerted by light on reflecting and absorbing bodies, particles, and individual molecules and atoms; one of the ponderomotive actions of light associated with the transfer of impulse electromagnetic field substance. The hypothesis about the existence of light pressure was first put forward by I. Kepler in the 17th century to explain the deviation of the tails of comets from the Sun. Light pressure theory within classical electrodynamics given by J.C. Maxwell in 1873. In it, the pressure of light is explained by the scattering and absorption of electromagnetic waves by particles of matter. Within the framework of quantum theory, light pressure is the result of the transfer of momentum by photons to the body.

With normal incidence of light on the surface of a solid body, the light pressure p is determined by the formula:

р = S(1 + R)/с, where

S is the energy flux density (light intensity), R is the coefficient of light reflection from the surface, c is the speed of light. Under normal conditions, light pressure is barely noticeable. Even in a powerful laser beam (1 W/cm 2 ), the light pressure is about 10 -4 g/cm 2 . A laser beam with a wide cross-section can be focused, and then the force of light pressure at the focus of the beam can hold a milligram particle suspended.

The pressure of light on solids was first studied experimentally by P. N. Lebedev in 1899. The main difficulties in the experimental detection of light pressure were in isolating it against the background of radiometric and convective forces, the magnitude of which depends on the pressure of the gas surrounding the body and, in case of insufficient vacuum, can exceed the light pressure by several orders of magnitude. In Lebedev's experiments, in an evacuated (pressure of the order of 10 -4 mm Hg) glass vessel, the rocker arms of a torsion balance with thin disk-wings attached to them were suspended on a thin silver thread, which were irradiated. The wings were made of various metals and mica with identical opposing surfaces. By sequentially irradiating the front and rear surfaces of wings of various thicknesses, Lebedev was able to neutralize the residual effect of radiometric forces and obtain satisfactory (with an error of ± 20%) agreement with Maxwell's theory. In 1907-10 Lebedev investigated the pressure of light on gases.

The light pressure is playing big role in astronomical and atomic phenomena. The pressure of light in stars, along with the pressure of gas, ensures their stability, counteracting the forces of gravity. The action of light pressure explains some of the shapes of cometary tails. When a photon is emitted by atoms, so-called luminous recoil occurs, and the atoms receive the momentum of the photon. In condensed matter, light pressure can cause a current of charge carriers (see Entrainment of electrons by photons). Pressure solar radiation They are trying to use it to create a type of space propulsion device - the so-called solar sail.

Specific features of light pressure are detected in rarefied atomic systems during resonant scattering of intense light, when the frequency laser radiation equal to frequency atomic transition. Having absorbed a photon, the atom receives an impulse in the direction of the laser beam and goes into an excited state. Further, spontaneously emitting a photon, the atom acquires momentum (luminous output) in an arbitrary direction. With subsequent absorption and spontaneous emission of photons, the atom constantly receives impulses directed along the light beam, which creates light pressure.

The force F of the resonant pressure of light on an atom is defined as the momentum transferred by a flux of photons with density N per unit time: F = Nћkσ, where ћk = 2πћ/λ is the momentum of one photon, σ ≈ λ 2 is the absorption cross section of the resonant photon, λ is the wavelength light, k - wave number, ћ - Planck's constant. At relatively low radiation densities, the resonant pressure of light is directly proportional to the light intensity. At high densities In the photon flux N, absorption saturation and resonant light pressure saturate (see Saturation effect). In this case, light pressure is created by photons spontaneously emitted by atoms with an average frequency γ (reverse to the lifetime of an excited atom) in a random direction. The strength of light pressure ceases to depend on intensity, but is determined by the speed of spontaneous emission events: F≈ћkγ. For typical valuesγ ≈ 10 8 s -1 and λ ≈0.6 μm light pressure force. F≈5·10 -3 eV/cm; when saturated, the resonant pressure of light can create an acceleration of atoms up to 10 5 g (g is the acceleration free fall). Such large forces make it possible to selectively control atomic beams, varying the frequency of light and differently affecting atoms with slightly different resonant absorption frequencies. In particular, it is possible to compress the Maxwellian velocity distribution by removing high-speed atoms from the beam. The laser light is directed towards the atomic beam, while selecting the frequency and shape of the radiation spectrum so that the light pressure slows down fast atoms with a large displacement resonant frequency(see Doppler effect). The resonant pressure of light can be used to separate gases: when a two-chamber vessel filled with a mixture of two gases, the atoms of one of which are in resonance with the radiation, is irradiated, the resonant atoms, under the influence of light pressure, will move into the far chamber.

The resonant pressure of light on atoms placed in an intense field has some features. standing wave. WITH quantum dot In view, a standing wave formed by counter flows of photons causes shocks to the atom due to the absorption of photons and their stimulated emission. Average strength, acting on the atom, is not equal to zero due to the inhomogeneity of the field at the wavelength. From the classical point of view, the force of light pressure is due to the action of a spatially inhomogeneous field on the atomic dipole induced by it. This force is minimal at nodes where the dipole moment is not induced, and at antinodes where the field gradient vanishes. The maximum light pressure force is equal in order of magnitude to F≈ ±Ekd (the signs refer to the in-phase and anti-phase motion of dipoles with moment d relative to the field with strength E). This force can reach gigantic values: d≈ 1 debye, λ≈0.6 μm and E≈ 10 6 V/cm force F≈5∙10 2 eV/cm. The field of a standing wave stratifies a beam of atoms passing through a beam of light, since the dipoles, oscillating in antiphase, move along different trajectories, like the atoms in the Stern-Gerlach experiment. Atoms moving along the laser beam are affected by the radial light pressure force caused by the radial inhomogeneity of density light field. In both a standing and traveling wave, not only the deterministic movement of atoms occurs, but also their diffusion in phase space, since the absorption and emission of photons are quantum random processes. Quasiparticles in solids: electrons, excitons, etc.

Lit.: Lebedev P. N. Collection. op. M., 1963; Ashkin A. Pressure of laser radiation // Advances physical sciences. 1973. T. 110. Issue. 1; Kazantsev A.P. Resonant light pressure // Ibid. 1978. T. 124. Issue. 1; Letokhov V. S., Minogin V. G. Pressure of laser radiation on atoms. M., 1986.

S. G. Przhibelsky.

The quantum theory of light explains light pressure as a result of photons transferring their momentum to atoms or molecules of matter.

Let on the surface of the area S normally falls to her every second

N photons frequency v . Every photon has momentum hv/c . If

R is the surface reflectance, then pN photons will be reflected from the surface, ( 1-p) N photons will be absorbed.

Each absorbed quantum of light will transfer an impulse to the surface hv/c , and each reflected impulse [(hv/c) - (-hv/c)] = 2hv/c , since upon reflection the direction of the photon momentum changes to the opposite and the momentum transferred by it to particles of matter is 2hv/c . Full the impulse received by the surface of the body will be

Let's calculate the light pressure. To do this, we divide (20.18) by the area S of the “wing”: (20.19)

If we take into account that hvN/S = Ee, then formula (20.19) will take the form

(20.20)

Expressions (20.17) and (20.20), derived within the framework of electromagnetic and quantum theories, match up.

The validity of these results was experimentally proven by the experiments of P.N. Lebedeva.

Pressure natural light very little. If the surface absorption coefficient is close to unity, then the pressure exerted sun rays to such surfaces found on Earth is approximately

5 10 Pa (i.e. 3.7 10 mmHg) . This pressure is ten orders of magnitude less atmospheric pressure at the surface of the Earth.

P. N. Lebedev was able to measure such low pressure only by demonstrating exceptional ingenuity and skill in setting up and conducting the experiment.

Light pressure plays no role in the phenomena we encounter in life. But in cosmic and microscopic systems its role is significant.

In the microcosm, the pressure of light is manifested in the luminous output that an excited atom experiences when it emits light. Gravitational attraction the outer layers of stellar matter towards its center is balanced by a force, a significant contribution to which is made by the pressure of light coming from the depths of the star outward.

Chemical action Sveta

As a result of the action of light, chemical transformations occur in some substances - photochemical reactions . Photochemical transformations are very diverse. Under the influence of light complex molecules can decompose into component parts (for example, silver bromide into silver and bromine) or. on the contrary, complex molecules are formed (for example, if you illuminate a mixture of chlorine and hydrogen, then the formation reaction hydrogen chloride proceeds so violently that it is accompanied by an explosion).

Many of the photochemical reactions play a large role in nature and technology. The main one is photochemical decomposition of carbon dioxide , occurring under the influence of light in the green parts of plants. This reaction has great value, because it ensures the carbon cycle, without which long-term existence is impossible organic life on the ground. As a result of the vital activity of animals and plants (respiration), continuous process carbon oxidation (formation CO2 ). Reverse process carbon reduction occurs under the influence of light in the green parts of plants. This reaction proceeds according to the scheme 2СО2 2СО + О2

The photochemical reaction of the decomposition of silver bromide underlies photography and all its scientific and technical applications, the phenomenon of paint fading, which comes down mainly to the photochemical oxidation of these paints, has a very great importance to understand the processes occurring in the eye of humans and animals and underlying visual perception. Many photochemical reactions are now used in chemical production and thus acquire direct industrial significance.

Light is not only absorbed and reflected by the substance, but also creates pressure on the surface of the body. Back in 1604, the German astronomer J. Kepler explained the shape of the comet's tail by the action of light pressure (Fig. 1). English physicist J. Maxwell 250 years later calculated the light pressure on bodies, using the theory of the electromagnetic field he developed. According to Maxwell's calculations, it turned out that if light energy E falls perpendicular to a unit area with reflection coefficient R in 1 s, then the light exerts pressure, expressed by the dependence: where c is the speed of light.

This formula can also be obtained by considering light as a stream of photons interacting with a surface (Fig. 2). Some scientists doubted Maxwell's theoretical calculations, but experimentally verified his result for a long time it didn't work out. In mid-latitudes at solar noon on a fully reflective surface light rays, a pressure equal to only . For the first time, light pressure was measured in 1899 by the Russian physicist P. N. Lebedev. He hung two pairs of wings on a thin thread: the surface of one of them was blackened, and the other was mirrored (Fig. 3). The light was almost completely reflected from mirror surface, and its pressure on the mirrored wing was twice as great as on the blackened one. A moment of force was created that rotated the device. By the angle of rotation one could judge the force acting on the wings, and therefore measure the light pressure.

The experiment is complicated by extraneous forces that arise when the device is illuminated, which are thousands of times greater than the light pressure unless special precautions are taken. One of these forces is associated with the radiometric effect. This effect occurs due to the temperature difference between the illuminated and dark sides of the wing. The light-heated side reflects the residual gas molecules at a faster rate than the cooler, unlit side. Therefore, the gas molecules transfer a greater impulse to the illuminated side and the wings tend to turn in the same direction as under the influence of light pressure - a false effect occurs. P. N. Lebedev reduced the radiometric effect to a minimum by making wings from thin foil that conducts heat well and placing them in a vacuum. As a result, both the difference in impulses transmitted by individual molecules of black and shiny surfaces (due to a smaller temperature difference between them) and total number molecules falling on the surface (due to low gas pressure).

Lebedev's experimental studies supported Kepler's assumption about the nature of cometary tails. As the radius of a particle decreases, its attraction to the Sun decreases in proportion to the cube, and the light pressure decreases in proportion to the square of the radius. Small particles will experience repulsion from the Sun regardless of the distance r from it, since the radiation density and gravitational attractive forces decrease according to the same law. Light pressure limits the maximum size of stars that exist in the Universe. As the mass of a star increases, the gravity of its layers toward the center increases. Therefore, the inner layers of stars are greatly compressed, and their temperature increases to millions of degrees. Naturally, this significantly increases the outward light pressure of the inner layers. U normal stars a balance arises between the gravitational forces that stabilize the star and the forces of light pressure that tend to destroy it. Very for the stars large mass such equilibrium does not occur, they are unstable, and they should not exist in the Universe. Astronomical observations confirmed: the “heaviest” stars have exactly the maximum mass that is still allowed by the theory, which takes into account the balance of gravitational and light pressure inside the stars.