Light pressure on a completely absorbing surface. A. Light pressure. Formulas for determining the pressure of electromagnetic radiation when it falls at an angle
One of the experimental confirmations of the presence of momentum in photons is the existence of light pressure (Lebedev's experiments).
Wave explanation (according to Maxwell): interaction of induced currents with the magnetic field of the wave.
From a quantum point of view, the pressure of light on a surface is due to the fact that upon collision with this surface, each photon transfers its momentum to it. Since a photon can only move at the speed of light in a vacuum, the reflection of light from the surface of a body should be considered as a process of “re-emission” of photons - an incident photon is absorbed by the surface and then re-emitted by it with the opposite direction of momentum.
Let us consider the light pressure exerted on the surface of a body by a flux of monochromatic radiation incident perpendicular to the surface.
Let per unit time per unit surface area of the body fall P photons. If the coefficient of light reflection from the surface of the body is equal to R, That Rn photons are reflected and (1 –R) p- absorbed. Each reflected photon transfers to the wall an impulse equal to 2р f =2hv/c (upon reflection, the photon momentum changes to – r f). Each absorbed photon transfers its momentum to the wall r f =hv/c .The light pressure on the surface is equal to the impulse that all surfaces transmit in 1 s P photons:
, (11-12)
Where I=nhv – the energy of all photons incident on a unit surface per unit time, i.e. the intensity of light, and w=I/c – volumetric energy density of incident radiation. This formula was tested experimentally and was confirmed in Lebedev's experiments.
4. Photon gas. Bosons. Bose–Einstein distribution.
Let's consider light as a collection of photons that are inside a closed cavity with mirror walls. The pressure of light on a specularly reflecting surface should be the same as it would be if photons were specularly reflected from the surface like absolutely elastic balls.
Let's find the pressure exerted on ideally reflective walls| closed cavity.
For simplicity, we assume that the cavity is cube-shaped. Due to the isotropy of radiation, we can assume that all directions of photon motion are equally probable. There is no interaction between photons (their frequency does not change during collisions). Therefore, photons move like molecules of an ideal monatomic gas.
We find the pressure of an ideal gas on the walls of the cavity from the basic equation of the kinetic theory of gases:
But for photons m=hv i /c 2 , υ i=с and therefore mυ i 2 = hv i.Thus,
Where W is the total energy of all photons in the cavity, and the pressure on its walls
Here w- volumetric radiation energy density. If photons inside our cavity have frequencies from 0 to ∞, then w can be determined by the formula:
(11-14)
Here ρ(ν) - volumetric radiation energy density in the frequency range from ν to ν+dν.
Function ρ(ν) is found using a special quantum distribution of photons by energy (frequency), - distribution Bose-Einstein (B-E).
1. Unlike the Maxwell distribution, which characterizes the distribution of particles in velocity (momentum) space, the quantum distribution describes the energies of particles in the phase space formed by the momenta and coordinates of particles.
2. The elementary volume of the phase space is equal to (let’s multiply all coordinate increments):
3. The volume per state is equal to h 3 .
4. Number of states dg i radiation located in the elementary phase volume in quantum statistics is obtained by dividing the volume (11-15) by h 3:
5. Distribution B-E systems of particles with integer spin obey. They got the name bosons. These particles also include photons. Their spin takes integer values. The angular momentum of the photon takes on the value mh/2π, Where m = 1. 2,3… The Bose-Einstein distribution function for photons has the form:
, (11-16)
Where. ΔN – number of photons in volume dV, n i - average number of particles in one energy state with energy W i which is called k - Boltzmann constant, T– absolute temperature. Coefficient 2 appears due to the presence of two possible directions of polarization of light (left and right rotation of the plane of polarization).
Total number of states in volume V(after integrating over the volume and using the relationships between the photon momentum R and his energy W,νр =hv/c, W= hv ):
where ν is frequency, With - speed of light in vacuum.
Number of photons with energy from W before W+dW in volume V:
We find the volumetric radiation energy density in the frequency range from ν to ν +dν by multiplying (11-16) by the energy of one photon hν :
. (11-18)
We find the radiation pressure using formulas (11-13), (11-14) and (11-18):
Equation of state for radiation:
Radiation energy from volume V (Stefan-Boltzmann law):
The relationship between energetic luminosity and volumetric radiation energy density (follows from a comparison of Planck’s formula with formula (11-18):
R E (ν,T)= (c/4)ρ(ν,T).
Today we will devote a conversation to such a phenomenon as light pressure. Let us consider the premises of the discovery and the consequences for science.
Light and color
The mystery of human abilities has worried people since ancient times. How does the eye see? Why do colors exist? What is the reason that the world is the way we perceive it? How far can a person see? Experiments with the decomposition of a solar ray into a spectrum were carried out by Newton in the 17th century. He also laid a strict mathematical foundation for a number of disparate facts that were known about light at that time. And Newton’s theory predicted a lot: for example, discoveries that only quantum physics could explain (the deflection of light in a gravitational field). But the physics of that time did not know or understand the exact nature of light.
Wave or particle
Since scientists around the world began to understand the essence of light, there has been a debate: what is radiation, a wave or a particle (corpuscle)? Some facts (refraction, reflection and polarization) confirmed the first theory. Others (linear propagation in the absence of obstacles, light pressure) - the second. However, only quantum physics was able to calm this dispute by combining the two versions into one common one. states that any microparticle, including a photon, has both the properties of a wave and a particle. That is, a quantum of light has characteristics such as frequency, amplitude and wavelength, as well as momentum and mass. Let's make a reservation right away: photons have no rest mass. Being a quantum of the electromagnetic field, they carry energy and mass only in the process of movement. This is the essence of the concept of “light”. Physics has explained it in some detail these days.
Wavelength and energy
The concept of “wave energy” was mentioned just above. Einstein convincingly proved that energy and mass are identical concepts. If a photon carries energy, it must have mass. However, a quantum of light is a “cunning” particle: when a photon encounters an obstacle, it completely gives up its energy to the substance, becomes it and loses its individual essence. Moreover, certain circumstances (strong heating, for example) can cause the previously dark and calm interiors of metals and gases to emit light. The momentum of a photon, a direct consequence of the presence of mass, can be determined using the pressure of light. researchers from Russia have convincingly proven this amazing fact.
Lebedev's experience
The Russian scientist Pyotr Nikolaevich Lebedev performed the following experiment in 1899. He hung the crossbar on a thin silver thread. The scientist attached two plates of the same substance to the ends of the crossbar. These included silver foil, gold, and even mica. Thus, a kind of scales were created. Only they measured the weight not of a load that presses from above, but of a load that presses from the side on each of the plates. Lebedev placed this entire structure under a glass cover so that wind and random fluctuations in air density could not affect it. Further, I would like to write that he created a vacuum under the lid. But at that time it was impossible to achieve even an average vacuum. So we will say that he created under a glass cover strongly and alternately illuminated one plate, leaving the other in shadow. The amount of light directed onto the surfaces was predetermined. Based on the angle of deflection, Lebedev determined which impulse transmitted light to the plates.
Formulas for determining the pressure of electromagnetic radiation at normal beam incidence
Let us first explain what a “normal fall” is? Light falls on a surface normally if it is directed strictly perpendicular to the surface. This imposes restrictions on the problem: the surface must be perfectly smooth, and the radiation beam must be directed very precisely. In this case, the pressure is calculated:
k is the transmittance coefficient, ρ is the reflection coefficient, I is the intensity of the incident light beam, c is the speed of light in vacuum.
But, probably, the reader has already guessed that such an ideal combination of factors does not exist. Even if we do not take into account the ideality of the surface, it is quite difficult to organize the incidence of light strictly perpendicularly.
Formulas for determining the pressure of electromagnetic radiation when it falls at an angle
The light pressure on a mirror surface at an angle is calculated using another formula, which already contains vector elements:
p= ω ((1-k)i+ρi’)cos ϴ
The quantities p, i, i’ are vectors. In this case, k and ρ, as in the previous formula, are the transmittance and reflection coefficients, respectively. The new values mean the following:
- ω - volumetric radiation energy density;
- i and i’ are unit vectors that show the direction of the incident and reflected beam of light (they specify the directions along which the acting forces should be added);
- ϴ is the angle to the normal at which the light ray falls (and, accordingly, is reflected, since the surface is mirrored).
Let us remind the reader that the normal is perpendicular to the surface, so if the problem gives the angle of incidence of light to the surface, then ϴ is 90 degrees minus the given value.
Application of electromagnetic radiation pressure phenomenon
To a student studying physics, many formulas, concepts and phenomena seem boring. Because, as a rule, the teacher talks about theoretical aspects, but rarely can give examples of the benefits of certain phenomena. Let’s not blame school tutors for this: they are very limited by the program; during the lesson they need to cover extensive material and still have time to test the students’ knowledge.
Nevertheless, the object of our study has many interesting applications:
- Now almost every schoolchild in the laboratory of his educational institution can repeat Lebedev’s experiment. But then the coincidence of experimental data with theoretical calculations was a real breakthrough. The experiment, carried out for the first time with a 20% error, allowed scientists around the world to develop a new branch of physics - quantum optics.
- Producing high-energy protons (for example, for irradiating various substances) by accelerating thin films with a laser pulse.
- Taking into account the pressure of electromagnetic radiation from the Sun on the surface of near-Earth objects, including satellites and space stations, makes it possible to correct their orbit with greater accuracy and prevents these devices from falling to Earth.
The above applications exist in the real world now. But there are also potential opportunities that have not yet been realized, because humanity’s technology has not yet reached the required level. Among them:
- Solar sail. With its help it would be possible to move quite large loads in near-Earth and even near-solar space. The light gives a small impulse, but given the desired position of the sail surface, the acceleration would be constant. In the absence of friction, it is enough to gain speed and deliver cargo to the desired point in the solar system.
- Photon engine. This technology may allow a person to overcome the gravity of his native star and fly to other worlds. The difference is that solar impulses will be generated by an artificially created device, for example, a thermonuclear engine.
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A stream of photons (light) that upon impact with a surface exerts pressure.
Flux of photons incident on an absorbing surface:
Flux of photons incident on a mirror surface:
Flux of photons incident on the surface:
Physical meaning of Light Pressure:
Light is a stream of photons, then, according to the principles of classical mechanics, particles, when hitting a body, must transfer momentum to it, in other words, exert pressure
Device, measurements light pressure, was a very sensitive torsional dynamometer (torsion scale). This device was created by Lebedev. Its moving part was a light frame suspended on a thin quarry thread with wings attached to it - light and black disks up to 0.01 mm thick. The wings were made from metal foil. The frame was suspended inside a vessel from which the air was pumped out. The light falling on the wings exerted different pressures on the light and black disks. As a result, a torque acted on the frame, which twisted the suspension thread. The angle of twist of the thread was used to determine the light pressure.
In the Formula we used:
The force with which a photon presses
Surface area on which light pressure occurs
Momentum of one photon
This video lesson is dedicated to the topic “Light pressure. Lebedev's experiments. Lebedev's experiments made a huge impression on the scientific world, since thanks to them the pressure of light was measured for the first time and the validity of Maxwell's theory was proven. How did he do it? You can learn the answer to this and many other interesting questions related to the quantum theory of light from this fascinating physics lesson.
Topic: Light pressure
Lesson: Light pressure. Lebedev's experiments
The hypothesis about the existence of light pressure was first put forward by Johannes Kepler in the 17th century to explain the phenomenon of comet tails when they fly near the Sun.
Maxwell, based on the electromagnetic theory of light, predicted that light should exert pressure on an obstacle.
Under the influence of the electric field of the wave, electrons in bodies oscillate - an electric current is formed. This current is directed along the electric field strength. Orderly moving electrons are acted upon by the Lorentz force from the magnetic field, directed in the direction of wave propagation - this is light pressure force(Fig. 1).
Rice. 1. Maxwell's experiment
To prove Maxwell's theory, it was necessary to measure the pressure of light. The pressure of light was first measured by the Russian physicist Pyotr Nikolaevich Lebedev in 1900 (Fig. 2).
Rice. 2. Petr Nikolaevich Lebedev
Rice. 3. Lebedev device
Lebedev's device (Fig. 3) consists of a light rod on a thin glass thread, along the edges of which light wings are attached. The entire device was placed in a glass vessel, from which the air was pumped out. The light falls on the wings located on one side of the rod. The pressure value can be judged by the angle of twist of the thread. The difficulty of accurately measuring the pressure of light was due to the fact that it was impossible to pump out all the air from the vessel. During the experiment, the movement of air molecules began, caused by unequal heating of the wings and walls of the vessel. The wings cannot be hung completely vertically. Heated air flows rise upward and act on the wings, which leads to additional torques. Also, the twisting of the thread is affected by the non-uniform heating of the sides of the wings. The side facing the light source heats up more than the opposite side. Molecules reflected from the hotter side impart more momentum to the winglet.
Rice. 4. Lebedev device
Rice. 5. Lebedev device
Lebedev managed to overcome all difficulties, despite the low level of experimental technology at that time. He took a very large vessel and very thin wings. The wing consisted of two pairs of thin platinum circles. One of the circles of each pair was shiny on both sides. Other sides had one side covered with platinum niello. Moreover, both pairs of circles differed in thickness.
To exclude convection currents, Lebedev directed beams of light onto the wings from one side or the other. Thus, the forces acting on the wings were balanced (Fig. 4-5).
Rice. 6. Lebedev device
Rice. 7. Lebedev device
Thus, the pressure of light on solids was proven and measured (Fig. 6-7). The value of this pressure coincided with Maxwell's predicted pressure.
Three years later, Lebedev managed to perform another experiment - to measure the pressure of light on gases (Fig. 8).
Rice. 8. Installation for measuring the pressure of light on gases
Lord Kelvin: “You may know that all my life I fought with Maxwell, not recognizing his light pressure, and now your Lebedev forced me to surrender to his experiments.”
The emergence of the quantum theory of light made it possible to more simply explain the cause of light pressure.
Photons have momentum. When absorbed by the body, they transfer their impulse to it. Such an interaction can be considered as a completely inelastic impact.
The force exerted on the surface by each photon is:
Light pressure on the surface:
Interaction of a photon with a mirror surface
In the case of this interaction, an absolutely elastic interaction is obtained. When a photon falls on a surface, it is reflected from it with the same speed and momentum with which it fell on this surface. The change in momentum will be twice as large as when a photon falls on a black surface, the pressure of light will double.
There are no substances in nature whose surface would completely absorb or reflect photons. Therefore, to calculate the light pressure on real bodies, it is necessary to take into account that some photons will be absorbed by this body, and some will be reflected.
Lebedev's experiments can be considered as experimental proof that photons have momentum. Although light pressure is very low under normal conditions, its effect can be significant. Based on the pressure of the Sun, a sail was developed for spaceships, which will allow them to move in space under the pressure of light (Fig. 11).
Rice. 11. Spaceship sail
The pressure of light, according to Maxwell's theory, arises as a result of the action of the Lorentz force on electrons performing oscillatory movements under the influence of the electric field of an electromagnetic wave.
From the point of view of quantum theory, light pressure arises as a result of the interaction of photons with the surface on which they fall.
The calculations carried out by Maxwell coincided with the results produced by Lebedev. This clearly proves the quantum-wave dualism of light.
Crookes' experiments
Lebedev was the first to discover light pressure experimentally and was able to measure it. The experiment was incredibly complex, but there is a scientific toy - the Crookes experiment (Fig. 12).
Rice. 12. Crookes experiment
A small propeller, consisting of four petals, is located on a needle, which is covered with a glass cap. If you illuminate this propeller with light, it begins to rotate. If you look at this propeller in the open air when the wind blows on it, its rotation would not surprise anyone, but in this case the glass cover does not allow the air currents to act on the propeller. Therefore, the cause of its movement is light.
English physicist William Crookes accidentally created the first light spinner.
In 1873, Crookes decided to determine the atomic weight of the element Thallium and weigh it on a very precise balance. To prevent random air currents from distorting the weighing picture, Crookes decided to suspend the rocker arms in a vacuum. He did it and was amazed, since his thinnest scales were sensitive to heat. If the heat source was under the object, it reduced its weight; if above, it increased it.
Having improved this accidental experience, Crookes came up with a toy - a radiometer (light mill). The Crookes radiometer is a four-blade impeller balanced on a needle inside a glass bulb under a slight vacuum. When a light beam hits the blade, the impeller begins to rotate, which is sometimes incorrectly explained by light pressure. In fact, the cause of torsion is a radiometric effect. The emergence of a repulsive force due to the difference in the kinetic energies of gas molecules striking the illuminated (heated) side of the blade and the opposite unlit (colder) side.
- The pressure of light and the pressure of circumstances ().
- Pyotr Nikolaevich Lebedev ().
- Crookes radiometer ().
It turns out that pressure can be created not only by solids, liquids and gases. Falling on the surface of the body, light electromagnetic radiation also exerts pressure on it.
Light pressure theory
Johannes Kepler
For the first time the assumption that light pressure exists was made German scientist Johannes Kepler in the 17th century. While studying the behavior of comets flying near the Sun, he noticed that the comet's tail always deviates in the direction opposite to the Sun. Kepler theorized that somehow this deviation was caused by exposure to sunlight.
The theoretical existence of light pressure was predicted in the 19th century British physicist James Clerk Maxwell, who created the electromagnetic theory and argued that light is also electromagnetic vibrations, and it should exert pressure on obstacles.
James Clerk Maxwell
Light is an electromagnetic wave. It creates an electric field, under the influence of which electrons in a body encountered on its path oscillate. An electric current appears in the body, directed along the electric field strength. The magnetic field acts on electrons Lorentz force. Its direction coincides with the direction of propagation of the light wave. This power is light pressure force .
According to Maxwell's calculations, sunlight produces a pressure of a certain value on a black plate located on the Earth (p = 4 · 10 -6 N/m 2). And if instead of a black plate you take a reflective one, then the light pressure will be 2 times greater.
But this was just a theoretical assumption. To prove it, it was necessary to confirm the theory with a practical experiment, that is, measure the value of light pressure. But since its value is very small, it is extremely difficult to do this in practice.
Pyotr Nikolaevich Lebedev
In practice this was done Russian experimental physicist Pyotr Nikolaevich Lebedev. An experiment he conducted in 1899 confirmed Maxwell’s assumption that light pressure exists on solids.
Lebedev's experience
Schematic representation of Lebedev's experiment
To conduct his experiment, Lebedev created a special device, which was a glass vessel. A light rod on a thin glass thread was placed inside the vessel. Thin, light wings made of various metals and mica were attached to the edges of this rod. Air was pumped out of the vessel. Using special optical systems consisting of a light source and mirrors, the light beam was directed to the wings located on one side of the rod. Under the influence of light pressure, the rod rotated and the thread twisted at a certain angle. The magnitude of the light pressure was determined by the magnitude of this angle.
Lebedev device
But this experiment did not give accurate results. Carrying it out had its own difficulties. Since vacuum pumps did not exist in those days, they used ordinary mechanical ones. And with their help it was impossible to create an absolute vacuum in the vessel. Even after pumping it out, some air remained in it. The wings and walls of the vessel were heated differently. The side facing the light beam heated up faster. And this caused the movement of air molecules. Streams of warmer air rose upward. Since it is impossible to install the wings absolutely vertically, these flows created additional torques. In addition, the wings themselves did not heat up equally. The side facing the light source became hotter. As a result, there was an additional effect on the angle of rotation of the thread.
To make the experiment more accurate, Lebedev took a very large vessel. He made the wing from two pairs of very thin circles of platinum. Moreover, the thickness of the circles of one pair differed from the thickness of the circles of the other pair. On one side of the rod, the circles were shiny on both sides, on the other, one side was covered with platinum niello. Beams of light were directed at them from one side or the other to balance the forces acting on the wings. As a result, the light pressure on the wings was measured. The experimental results confirmed Maxwell's theoretical assumptions about the existence of light pressure. And its magnitude was almost the same as Maxwell predicted.
In 1907 - 1910 Using more accurate experiments, Lebedev measured the pressure of light on gases.
Light, like any electromagnetic radiation, has energy E .
Its momentum p = E v / c 2 ,
Where v - speed of electromagnetic radiation,
c - speed of light.
Because v = With , That p = E/s .
With the advent of quantum theory, light began to be considered as a stream of photons - elementary particles, quanta of light. When hitting a body, photons transfer their momentum to it, that is, they exert pressure.
Solar sail
Friedrich Arturovich Zander
Although the amount of light pressure is very small, nevertheless, it can be beneficial to a person.
Back in 1920 Soviet scientist and inventor Friedrich Arturovich Zander, one of the creators of the first liquid-fuel rocket, put forward the idea of flying into space using solar sail . She was very simple. Sunlight is made up of photons. And they create pressure, transferring their impulse to any illuminated surface. Therefore, pressure generated by sunlight or a laser on a mirror surface can be used to propel a spacecraft. Such a sail does not require rocket fuel, and its duration is unlimited. And this will make it possible to carry more cargo compared to a conventional spacecraft with a jet engine.
Solar sail
But so far these are only projects to create starships with a solar sail as the main engine.