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 light pressure 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 difficult, 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 ().
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 what 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 accurately. 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 have 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 percent 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:
- 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 from a solar sail is that solar impulses will be generated by an artificially created device, for example, a thermonuclear engine.
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 upon which light pressure occurs
Momentum of one photon
Planck's constant
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The physical phenomenon - the pressure of light on a surface - can be considered from two positions - the corpuscular and wave theories of light. According to the corpuscular (quantum) theory of light, a photon is a particle and has momentum, which, when the photon hits a surface, is fully or partially transferred to the surface. According to the wave theory, light is an electromagnetic wave, which, when passing through a material, has an effect on charged particles (Lorentz force), which explains the pressure of light in this theory.
Light of wavelength 620 nm is incident normally on a blackened surface and exerts a pressure of 0.1 μPa. How many photons fall on a surface with an area of 5 cm 2 in a time of 10 s?
Light falls normally on a mirror surface and exerts a pressure of 40 μPa on it. What is the irradiance of the surface?
Light of wavelength 600 nm is incident normally on a mirror surface and exerts a pressure of 4 μPa. How many photons hit a surface with an area of 1 mm 2 in a time of 10 s?
Light with a wavelength of 590 nm is incident on a mirror surface at an angle of 60 degrees. Luminous flux density 1 kW/m2. Determine the light pressure on the surface.
The source is located at a distance of 10 cm from the surface. The light pressure on the surface is 1 mPa. Find the power of the source.
A luminous flux of 0.8 W falls normally onto a mirror surface with an area of 6 cm2. Find the pressure and force of light pressure.
A luminous flux of 0.9 W falls normally on a mirror surface. Find the force of light pressure on this surface.
Light falls normally on a surface with a reflectance of 0.8. The light pressure exerted on this surface is 5.4 μPa. What energy will be brought by photons incident on a surface with an area of 1 m2 in a time of 1 s?
Find the light pressure exerted on the blackened surface of the incandescent lamp bulb from the inside. Consider the flask to be a sphere with a radius of 10 cm, and the lamp spiral to be a point light source with a power of 1 kW.
A luminous flux of 120 W/m2 falls normally on the surface and exerts a pressure of 0.5 μPa. Find the surface reflectance.
Light falls normally onto a perfectly reflective surface of area 5 cm2. In a time of 3 minutes, the energy of the incident light is 9 J. Find the light pressure.
Light falls on a mirror surface with an area of 4.5 cm2. Energy illumination of the surface 20 W/cm2. What impulse will the photons transmit to the surface in 5 s?
Light falls normally on a blackened surface and brings energy of 20 J in 10 minutes. The surface area is 3 cm2. Find the surface irradiance and light pressure.
Light with a flux power of 0.1 W/cm2 falls on a mirror surface at an incidence angle of 30 degrees. Determine the light pressure on the surface.
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). The 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 per $1$ perpendicular to a unit area with reflection coefficient $R$, then the light exerts pressure $p,$ expressed by the dependence: $p=\frac(E)(c)( 1+R)$ N/m 2 - 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, and for a long time it was not possible to verify his result experimentally. In mid-latitudes at solar noon, on a surface that fully reflects light rays, a pressure equal to only $4.7⋅10^(−6)$ N/m 2 is created. 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 the mirror surface, and its pressure on the mirror wing was twice as large ($R=1$) than on the blackened one ($R=0$). 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 momentum transmitted by individual molecules of black and shiny surfaces (due to a smaller temperature difference between them) and the total number of molecules falling on the surface (due to low gas pressure) decreased.
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 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 $1/r^2.$ Light pressure limits the maximum size of stars existing 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. In normal stars, a balance arises between the gravitational forces that stabilize the star and the light pressure forces that tend to destroy it. For stars of very large masses, such equilibrium does not occur; they are unstable, and they should not exist in the Universe. Astronomical observations have 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.
