There are various methods for measuring the speed of light, including astronomical ones and using various experimental techniques. Quantity measurement accuracy With is constantly increasing. This table provides an incomplete list of experimental works to determine the speed of light.
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Experiment |
Measurement results, km/sec |
Experimental error |
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Weber-Kohlrausch Maxwell Michelson Perrotine Rose and Dorsey Mittelyptedt Pease and Pearson Anderson |
Eclipse of Jupiter's moon Light aberration Moving bodies Rotating mirrors Electromagnetic constants Electromagnetic constants Rotating mirrors Rotating mirrors Electromagnetic constants Rotating mirrors Rotating mirrors Electromagnetic constants Kerr gate cell Rotating mirrors Kerr gate cell Microwave interferometry |
The figure graphically presents the numerical values of the speed of light obtained in different years(Figure Olimpusmicro.com).
You can trace how the accuracy of measurements has changed with progress in the field of science and technology.
The first successful measurement of the speed of light dates back to 1676.
The drawings show a reproduction of Roemer's own drawing, as well as a schematic interpretation.
Römer's astronomical method is based on the measurement speed of light based on observations from Earth of eclipses of Jupiter's satellites. Jupiter has several moons that are either visible from Earth near Jupiter or hidden in its shadow. Astronomical observations of the satellites of Jupiter show that the average time interval between two successive eclipses of any particular satellite of Jupiter depends on how far apart the Earth and Jupiter are at the time of observation. In the picture: Roemer's method. S - sun, S - jupiter, W - earth
Let at a certain moment in time Earth Z1 and Jupiter J1 be in opposition, and at this moment in time one of Jupiter’s satellites, observed from the Earth, disappears in the shadow of Jupiter (the satellite is not shown in the figure). Then, if we denote by R and r radii of the orbits of Jupiter and Earth and throughc is the speed of light in the coordinate system associated with the Sun C; on Earth, the departure of the satellite into the shadow of Jupiter will be recorded at ( R- r)/s seconds later than it occurs in the time reporting system associated with Jupiter.
After 0.545 years, Earth Z2 and Jupiter J2 are in conjunction. If at this time there isnth eclipse of the same satellite of Jupiter, then on Earth it will be registered with a delay of ( R+ r)/s seconds. Therefore, if the period of revolution of the satellite around Jupitert, then the time periodT1 flowing between the first andnth eclipses observed from Earth is equal to
After another 0.545 year, Earth 33 and Jupiter 3 will again be in opposition. During this time it happened (n-1) revolutions of the satellite around Jupiter and (n-1) eclipses, the first of which took place when the Earth and Jupiter occupied positions Z2 and Yu2, and the last - when they occupied positions Z3 and Yu3. The first eclipse was observed on Earth with a delay ( R+ r)/s, and the latter with a delay ( R-r)/ c in relation to the moments of the satellite leaving the shadow of the planet Jupiter. Therefore, in this case we have
Roemer measured the time intervals T1 and T2 and found that T1-T2 = 1980 s. But from the formulas written above it follows that T1-T2 = 4 r/c, so c=4 r/1980 m/s. Takingr, the average distance from the Earth to the Sun is equal to 1500000000 km, we find the value for the speed of light to be 3.01*10 6 m/s.
Determination of the speed of light from the observation of aberration in 1725-1728. Bradley undertook an observation to find out whether there is an annual parallax of stars, i.e. the apparent displacement of stars in the firmament, reflecting the movement of the Earth in its orbit and associated with the finite distance from the Earth to the star.
Bradley indeed found such a bias. He explained the observed phenomenon, which he called aberration of light, the finite value of the speed of propagation of light and used it to determine this speed.
Knowing the angle α and the speed of the Earth's orbit v, we can determine the speed of light c.
He obtained a value for the speed of light equal to 308,000 km/s.
It is important to note that the aberration of light is associated with a change in the direction of the Earth's speed throughout the year. A constant speed, no matter how great it may be, cannot be detected with the help of aberration, because with such movement the direction to the star remains unchanged and there is no way to judge the presence of this speed and what angle it makes with the direction to the star. The aberration of light allows us to judge only the change in the speed of the Earth.
In 1849, A. Fizeau was the first to determine the speed of light in laboratory conditions. His method was called the cogwheel method.Characteristic feature His method is the automatic registration of the start and return moments of the signal, carried out by regularly interrupting the light flow (gear wheel).
Figure 3. Scheme of an experiment to determine the speed of light using the gear wheel method.
The light from the source passed through the chopper (the teeth of the rotating wheel) and, reflected from the mirror, returned again to the gear wheel. Knowing the distance between the wheel and the mirror, the number of teeth of the wheel, and the speed of rotation, you can calculate the speed of light.
Knowing the distance D, the number of teeth z, angular velocity (rpm)v, you can determine the speed of light. He got it to be equal to 313,000 km/s.
Many methods have been developed to further improve the accuracy of measurements. Soon it even became necessary to take into account the refractive index in air. And soon in 1958, Frum obtained a value for the speed of light equal to 299792.5 km/s, using a microwave interferometer and an electro-optical shutter (Kerr cell).
The speed of light was first determined by the Danish astronomer Roemer in 1676. Until that time, there were two opposing opinions among scientists. Some believed that the speed of light is infinitely high. Others, although they considered it very large, were nevertheless finite. Roemer confirmed the second opinion. He correctly related the irregularities in the timing of eclipses of Jupiter's moons to the time it takes light to travel the diameter of the Earth's orbit around the Sun. He was the first to draw a conclusion about the finite speed of propagation of light and determine its value. According to his calculations, the speed of light was equal to 300870 km/s modern units. (Data taken from the book: G. Lipson. Great Experiments in Physics.)
Foucault method
A method for measuring the speed of light, which consists in sequentially reflecting a beam of light from a rapidly rotating mirror, then from a second stationary mirror located at a precisely measured distance, and then again from the first mirror, which has managed to rotate through a certain small angle. The speed of light is determined (given the known speed of rotation of the first mirror and the distance between the two mirrors) by changing the direction of the thrice reflected light beam. Using this method, the speed of light in air was first measured by J. B. L. Foucault in 1862.
In 1878–82 and 1924–26 he carried out measurements of the speed of light, which for a long time remained unsurpassed in accuracy. In 1881 he experimentally proved and, together with E. W. Morley (1885–87), confirmed with great accuracy the independence of the speed of light from the speed of the Earth.
The operation of corner reflectors of the optical range is based on the same principle, which is a small triangular prism made of transparent glass, the edges of which are covered with a thin layer of metal. Such a U. o. has a high Seff due to the high a/l ratio. To obtain omnidirectional U. o. use a system of several prisms. Optical U. o. became widespread after the advent of lasers. They are used in navigation, for measuring distances and the speed of light in the atmosphere, in experiments with the Moon, etc. Optical optical instruments. in the form of colored glass with many tetrahedral-shaped cavities, they are used as a means of signaling in the road sector and in everyday life.
The famous American scientist Albert Michelson devoted almost his entire life to measuring the speed of light.
One day, a scientist examined the expected path of a light beam along the canvas. railway. He wanted to build an even more advanced setup for an even more accurate method of measuring the speed of light. Before this, he had already worked on this problem for several years and achieved the most accurate values for that time. Newspaper reporters became interested in the scientist’s behavior and, perplexed, asked what he was doing here. Michelson explained that he was measuring the speed of light.
- What for? - followed the question.
“Because it’s damn interesting,” Michelson replied.
And no one could have imagined that Michelson’s experiments would become the foundation on which the majestic edifice of the theory of relativity would be built, giving a completely new understanding of the physical picture of the world.
Fifty years later, Michelson was still continuing his measurements of the speed of light.
Once the great Einstein asked him the same question:
– Because it’s devilishly interesting! - Michelson answered half a century later and Einstein.
Fizeau method
In 1849, A. Fizeau conducted a laboratory experiment to measure the speed of light. Light from source 5 passed through chopper K (teeth of a rotating wheel) and, reflected from mirror 3, returned again to the gear wheel. Let us assume that the tooth and slot of the gear wheel have the same width and the place of the slot on the wheel is taken by the adjacent tooth. Then the light will be blocked by the tooth and the eyepiece will become dark. This will occur provided that the round trip time of light t=2L/c is equal to the time of rotation of the gear through half the slot t2=T/(2N)=1/(2Nv). Here L is the distance from the gear to the mirror; T – period of rotation of the gear wheel; N – number of teeth; v=1/T – rotation frequency. From the equality t1=t2 follows the calculation formula for determining the speed of light using this method:
c=4LNv
Using the rotating shutter method, Fizeau in 1849 obtained the speed of light c = 3.13-10**5 km/s, which was not bad at all at that time. Subsequently, the use of various shutters made it possible to significantly refine the value of the speed of light. Thus, in 1950, the value of the speed of light (in vacuum) was obtained equal to:
s= (299,793.1 ±0.25) km/s.
An ingenious solution to the difficult problem of determining the speed of light was found in 1676 by the Danish astronomer Olaf Roemer.
Olaf Roemer, observing the movement of Jupiter's satellites, noticed that during an eclipse the satellite leaves the shadow region periodically with a delay. Roemer explained this by the fact that by the time of the next observation the Earth is at a different point in its orbit than the previous time, and, therefore, the distance between it and Jupiter is different. The maximum amount by which this distance increases is equal to the diameter of the earth's orbit. And it is precisely when the Earth is furthest away from Jupiter that the satellite emerges from the shadow with the greatest delay.
Comparing these data, Roemer came to the conclusion that light from the satellite travels a distance equal to the diameter of the earth's orbit - 299,106 thousand km in 1320 seconds. This conclusion not only convinces that the speed of propagation of light cannot be instantaneous, but also allows us to determine the magnitude of the speed; To do this, you need to divide the diameter of the Earth's orbit by the delay time of the satellite.
According to Roemer's calculations, the speed of light propagation turned out to be 215 thousand km/sec.
Subsequent, more advanced methods of observing the delay time of Jupiter's satellites made it possible to clarify this value. The speed of light, according to modern data, is 299,998.9 km/sec. For practical calculations, the speed of light in vacuum is taken to be 300 thousand km/sec. The enormous speed of light stunned not only Roemer's contemporaries, but also served as a reason to deny the corpuscular theory of light.
If light is a stream of corpuscles, then at such a speed of movement their energy should be very large. The impacts of corpuscles when falling on bodies must be perceptible, i.e. Light must exert pressure!
James Bradley was the next to measure the speed of light after Roemer.
While crossing the Thames River one day, Bradley noticed that while the boat was moving, the wind seemed to be blowing in a different direction than it actually was. This observation probably gave him the basis to explain by a similar phenomenon the apparent motion of the fixed stars, called aberration Sveta.
The light of a star reaches the Earth just as drops of vertically falling rain fall on the windows of a moving carriage. The movement of a light beam and the movement of the Earth add up.
Consequently, in order for the light from a star located perpendicular to the plane of motion of the Earth to fall into the telescope, it must be tilted by a certain angle, which does not depend on the distance to the star, but only on the speed of light and the speed of the Earth's motion (it was already at that time known – 30 km/sec).
Having measured the angle, Bradley found that the speed of light is 308 thousand km/sec. Bradley's measurements, like Roemer's, did not resolve the controversial issue of the value of the constant in the law of refraction, since Bradley and Roemer determined the set speed not in any medium, but in outer space.
The idea of a new method for measuring the speed of light was proposed by D. Arago. It was carried out in two different ways by I. Fizeau and L. Foucault.
Fizeau carefully measured the distance between two points in 1849. In the bottom of them he placed a light source, and in the other - a mirror, from which the light should be reflected and return to the source again.
In order to determine the speed of propagation of light, it was necessary to very accurately measure the period of time that light needed to travel twice the distance from the source to the mirror.
The distance from the source, located in the Paris suburb of Surenes, to the mirror installed on Montmartre, was 8633 m. This means that the double distance was 17,266 m. The time during which the light will travel this distance, if we use the results of Roemer's speed measurements, will be no more six hundred thousandths of a second.
There were no means to measure such short periods of time then.
This means that these measurements should have been excluded from the experiment.
A spotting scope was installed in Suresnes, aimed at Paris. On the side, light from the source entered through another tube. From the surface of a transparent glass plate located in the tube at an angle of 45, the light was partially reflected towards Paris.
In Paris, in Montmartre, another telescope was installed, into which the light reflected by a transparent plate entered.
Looking through the eyepiece, one could see the light source located behind the side tube. The eyepiece of the trumpet installed in Montmartre was replaced by a mirror, thanks to which the light returned to Suresnes.
The light reflected by the mirror in Montmartre, meeting a transparent glass plate on the way back inside the pipe, was partially reflected from its surface, and the light that passed through the plate and the eyepiece of the pipe entered the eye of the observer.
The telescope in Suresnes, in addition to the side tube through which light entered, had a slot in the place where the focus of the lens and eyepiece was located. A gear wheel passed through the slot, which was driven by a clock mechanism. When the wheel was stationary and positioned so that the light passed between the teeth, the light reflected from the mirror in Montmartre was visible in the eyepiece of the tube.
When the wheel was set in motion, the light disappeared. This happened at the moment when the light, passing between the teeth of the wheel towards Paris, met a tooth on the way back, and not a gap between the teeth.
In order for the light to reappear in the eyepiece, it was necessary to double the number of revolutions of the wheel.
As the speed increased further, the light disappeared again.
In Fizeau's experiments, the gear wheel had 720 teeth. The first set disappearance was observed when the wheel made 12.67 revolutions per second.
It made one revolution in a time equal to 1/12.67 seconds. In this case, the gap between the teeth was replaced by a tooth. If there are 720 teeth, then there are also 720 spaces. Therefore, the change occurs in a time equal to 1/12.67*2*720 = 1/18245 sec.
During this time, the light traveled twice the distance from Suresnes to Montmartre.
Consequently, its speed was equal to 315 thousand km/sec.
With this ingenious method, it was possible to avoid measuring short periods of time and still determine the speed of light.
The relatively large distance between the light source and the mirror did not allow any medium to be placed in the path of the light. Fizeau determined the speed of light in air.
The speed of light in other media was determined by Foucault in 1862. In Foucault's experiments, the distance from the source to the mirror was only a few meters. This made it possible to place a tube filled with water in the path of the light.
Foucault established that the speed of light propagation in various media is less than in air. In water, for example, it is equal to equal to the speed light in the air. The results obtained resolved a two-century dispute between the corpuscular and wave theories about the value of the constant in the law of refraction. The correct meaning in the law of refraction is given by the wave theory of light.
Measurements of the speed of light propagation in various media made it possible to introduce the concept of optical density of matter.
List of used literature
- Simulation modeling. – [Electronic resource] – Access mode: webcache.googleusercontent.com – Access date: April 2014. - Cap. from the screen.
Laboratory methods for determining the speed of light are essentially improvements on Galileo's method.
a) Interrupt method.
Fizeau (1849) was the first to determine the speed of light in laboratory conditions. A characteristic feature of his method is the automatic recording of the start and return moments of the signal, carried out by regularly interrupting the light flux (gear wheel). The scheme of Fizeau's experiment is shown in Fig. 9.3. Light from source S goes between the teeth of a rotating wheel W to the mirror M and, having been reflected back, must again pass between the teeth to the observer. For convenience, eyepiece E, serving for observation, is placed opposite A, and the light turns from S To W using a translucent mirror N. If the wheel rotates, and at such an angular speed that during the movement of light from A To M and back in place of the teeth there will be slits, and vice versa, then the returning light will not be transmitted to the eyepiece and the observer will not see the light (the first eclipse). As the angular velocity increases, the light will partially reach the observer. If the width of the teeth and gaps are the same, then at double speed there will be a maximum of light, at triple speed there will be a second eclipse, etc. Knowing the distance aM=D, number of teeth z, angular speed of rotation (number of revolutions per second) n, you can calculate the speed of light.
| Rice. 9.3. Scheme of the interruption method experiment. |
Or With=2Dzn.
The main difficulty of determination lies in the exact moment of the eclipse. Accuracy increases with increasing distance D and at interruption speeds that allow observation of higher order eclipses. Thus, Perrotin made his observations at D=46 km and observed a 32nd order eclipse. Under these conditions, high-aperture installations are required, fresh air(observations in the mountains), good optics, strong light source.
IN Lately Instead of a rotating wheel, other, more advanced methods of interrupting light are successfully used.
b) Rotating mirror method.
Foucault (1862) successfully implemented the second method, the principle of which had been proposed even earlier (1838) by Arago for the purpose of comparing the speed of light in air with the speed of light in other media (water). The method is based on very careful measurements of short periods of time using a rotating mirror. The experimental design is clear from Fig. 9.4. Light from source S guided by the lens L on a rotating mirror R, is reflected from it in the direction of the second mirror WITH and goes back, passing path 2 CR=2D during t. This time is estimated by the angle of rotation of the mirror R, the rotation speed of which is precisely known; the angle of rotation is determined from the measurement of the displacement of the bunny given by the returning light. Measurements are made using an eyepiece E and translucent plate M, playing the same role as in the previous method; S 1 – position of the bunny with a stationary mirror R, S" 1 – when the mirror rotates. An important feature of Foucault’s installation was its use as a mirror WITH concave spherical mirror, with the center of curvature lying on the axis of rotation R. Due to this, the light reflected from R To WITH, always ended up back on R; in the case of using a flat mirror WITH this would happen only with a certain mutual orientation R And WITH, when the axis of the reflected cone of rays is located normal to WITH.
Foucault, in accordance with Arago's original plan, also used his device to determine the speed of light in water, because he managed to reduce the distance RС up to 4 m, giving the mirror 800 revolutions per second. Foucault's measurements showed that the speed of light in water is less than in air, in accordance with the ideas of the wave theory of light.
Michelson's last (1926) installation was made between two mountain peaks, so the resulting distance D» 35.4 km (more precisely, 35,373.21 m). The mirror was an octagonal steel prism rotating at a speed of 528 rps.
The time it took for the light to travel the full way was 0.00023 s, so the mirror had time to rotate 1/8 of a revolution and the light fell on the edge of the prism. Thus, the bunny’s displacement was relatively insignificant, and the determination of its position played the role of a correction, and not the main measured value, as in Foucault’s first experiments, where the entire displacement reached only 0.7 mm.
Very accurate measurements of the speed of propagation of radio waves were also made. In this case, radiogeodetic measurements were used, i.e. determining the distance between two points using radio signals in parallel with precise triangulation measurements. The best value obtained by this method, reduced to vacuum, is c = 299,792 ± 2.4 km/s. Finally, the speed of radio waves was determined using the method of standing waves generated in a cylindrical resonator. The theory allows us to relate data on the dimensions of the resonator and its resonant frequency with the speed of the waves. The experiments were done with an evacuated resonator, so reduction to a vacuum was not required. Best value, obtained using this method, c = 299,792.5 ± 3.4 km/s.
c) Phase and group speeds of light.
Laboratory methods for determining the speed of light, which allow these measurements to be made on a short basis, make it possible to determine the speed of light in various media and, therefore, test the relationships of the theory of light refraction. As has already been mentioned several times, the refractive index of light in Newton’s theory is equal to n=sin i/sin r=υ 2 /υ 1, and in the wave theory n=sin i/sin r=υ 1 /υ 2 where υ 1 is the speed of light in the first medium, and υ 2 – speed of light in the second medium. Arago also saw in this difference the possibility of an experimentum crucis and proposed the idea of an experiment, which was carried out later by Foucault, who found for the ratio of the speeds of light in air and water a value close to , as follows from Huygens’ theory, and not, as follows from Newton’s theory.
Conventional determination of refractive index n=sin i/sin r=υ 1 /υ 2 from the change in the direction of the wave normal at the boundary of two media gives the ratio of the phase velocities of the wave in these two media. However, the concept of phase velocity is applicable only to strictly monochromatic waves, which are not realistically feasible, since they would have to exist indefinitely in time and howl infinitely extended in space.
In reality, we always have a more or less complex impulse, limited in time and space. When observing such a pulse, we can highlight some specific place, for example, the place of maximum extension of that electrical or magnetic field, which is an electromagnetic pulse. The speed of the pulse can be identified with the speed of propagation of any point, for example, the point of maximum field strength.
However, the medium (with the exception of vacuum) is usually characterized by dispersion, i.e. monochromatic waves propagate with different phase velocities depending on their length, and the pulse begins to deform. In this case, the question of the speed of the impulse becomes more complex. If the dispersion is not very large, then the pulse deformation occurs slowly and we can monitor the movement of a certain field amplitude in the wave pulse, for example, the maximum field amplitude. However, the speed of movement of the pulse, called by Rayleigh group velocity, will differ from the phase velocity of any of its constituent monochromatic waves.
For simplicity of calculations, we will imagine a pulse as a set of two sinusoids of equal amplitude that are close in frequency, and not as a set of an infinite number of close sinusoids. With this simplification, the main features of the phenomenon are preserved. So, our impulse, or, as they say, a group of waves, is composed of two waves.
where the amplitudes are assumed to be equal, and the frequencies and wavelengths differ little from each other, i.e.
where and are small quantities. Impulse (wave group) at there is a sum at 1 and at 2, i.e.
Introducing the notation, let us represent our momentum in the form where A not constantly, but changes in time and space, but changes slowly, because δω And δk– small (compared to ω 0 and κ 0) quantities. Therefore, allowing for a certain carelessness in speech, we can consider our impulse to be a sinusoid with a slowly changing amplitude.
Thus, the speed of the impulse (group), which, according to Rayleigh, is called group velocity, is the speed of movement amplitudes, and, consequently, energy, carried by a moving impulse.
So, monochromatic wave characterized by phase velocity υ=ω /κ , indicating the speed of movement phases, and the impulse is characterized by the group velocity u=dω/dκ, corresponding to the speed of propagation of the field energy of this pulse.
It is not difficult to find a connection between u And υ . Indeed,
or, since and therefore,
those. finally
(Rayleigh formula).
Difference between u And υ the more significant the greater the dispersion dυ/dλ. In the absence of dispersion ( dυ/dλ=0) we have u=υ. This case, as already said, occurs only for vacuum.
Rayleigh showed that in the known methods for determining the speed of light, by the very essence of the method, we are not dealing with a continuously lasting wave, but breaking it into small segments. The gear wheel and other interrupters in the interruption method provide weakening and increasing light excitation, i.e. group of waves. The same thing happens in Roemer's method, where the light is interrupted by periodic darkening. In the rotating mirror method, light also stops reaching the observer when the mirror is rotated sufficiently. In all these cases, we measure the group velocity in a dispersive medium, not the phase velocity.
Rayleigh believed that in the light aberration method we measure the direct phase velocity, because there the light is not interrupted artificially. However, Ehrenfest (1910) showed that the observation of light aberration is in principle indistinguishable from Fizeau’s method, i.e. also gives group velocity. Indeed, the aberration experience can be reduced to the following. Two disks with holes are rigidly fixed on a common axis. Light is sent along a line connecting these holes and reaches the observer. Let's put the whole apparatus into rapid rotation. Since the speed of light is finite, light will not pass through the second hole. To transmit light, it is necessary to rotate one disk relative to the other by an angle determined by the ratio of the speeds of the disks and light. This is a typical aberration experience; however, it is no different from Fizeau’s experiment, in which instead of two rotating disks with holes, there is one disk and a mirror for turning the rays, i.e. essentially two disks: the real one and its reflection in a fixed mirror. So, the aberration method gives the same as the interruption method, i.e. group speed.
Thus, in Michelson's experiments with both water and carbon disulfide, the ratio of group rather than phase velocities was measured.
Long before scientists measured the speed of light, they had to work hard to define the very concept of “light.” Aristotle was one of the first to think about this, who considered light to be a kind of mobile substance spreading in space. His ancient Roman colleague and follower Lucretius Carus insisted on the atomic structure of light.
TO XVII century Two main theories of the nature of light were formed - corpuscular and wave. Newton was one of the adherents of the first. In his opinion, all light sources emit tiny particles. In the process of “flight” they form luminous lines - rays. His opponent, the Dutch scientist Christiaan Huygens, insisted that light is a type of wave motion.
As a result of centuries-old disputes, scientists have come to a consensus: both theories have the right to life, and light is visible to the eye spectrum of electromagnetic waves.
A little history. How was the speed of light measured?
Most ancient scientists were convinced that the speed of light is infinite. However, the results of research by Galileo and Hooke allowed for its extreme nature, which was clearly confirmed in the 17th century by the outstanding Danish astronomer and mathematician Olaf Roemer.
He made his first measurements by observing the eclipses of Io, the satellite of Jupiter, at a time when Jupiter and the Earth were located on opposite sides relative to the Sun. Roemer recorded that as the Earth moved away from Jupiter by a distance equal to the diameter of the Earth's orbit, the delay time changed. The maximum value was 22 minutes. As a result of calculations, he received a speed of 220,000 km/sec.
50 years later in 1728, thanks to the discovery of aberration, the English astronomer J. Bradley “refined” this figure to 308,000 km/sec. Later, the speed of light was measured by French astrophysicists François Argot and Leon Foucault, obtaining an output of 298,000 km/sec. An even more accurate measurement technique was proposed by the creator of the interferometer, the famous American physicist Albert Michelson.
Michelson's experiment to determine the speed of light
The experiments lasted from 1924 to 1927 and consisted of 5 series of observations. The essence of the experiment was as follows. A light source, a mirror and a rotating octagonal prism were installed on Mount Wilson in the vicinity of Los Angeles, and a reflecting mirror was installed 35 km later on Mount San Antonio. First, light through a lens and a slit hit a prism rotating with a high-speed rotor (at a speed of 528 rps).
Participants in the experiments could adjust the rotation speed so that the image of the light source was clearly visible in the eyepiece. Since the distance between the vertices and the rotation frequency were known, Michelson determined the speed of light - 299,796 km/sec.
Scientists finally decided on the speed of light in the second half of the 20th century, when masers and lasers were created, characterized by the highest stability of the radiation frequency. By the beginning of the 70s, the error in measurements had dropped to 1 km/sec. As a result, on the recommendation of the XV General Conference on Weights and Measures, held in 1975, it was decided to assume that the speed of light in a vacuum is now equal to 299792.458 km/sec.
Is the speed of light achievable for us?
Obviously, exploration of the far corners of the Universe is unthinkable without spaceships flying at enormous speed. Preferably at the speed of light. But is this possible?
The speed of light barrier is one of the consequences of the theory of relativity. As you know, increasing speed requires increasing energy. The speed of light would require virtually infinite energy.
Alas, the laws of physics are categorically against this. At speed spaceship At 300,000 km/sec, particles flying towards him, for example, hydrogen atoms, turn into a deadly source of powerful radiation equal to 10,000 sieverts/sec. This is about the same as being inside the Large Hadron Collider.
According to scientists at Johns Hopkins University, there is no adequate protection in nature from such monstrous cosmic radiation. The destruction of the ship will be completed by erosion from the effects of interstellar dust.
Another problem with light speed is time dilation. Old age will become much longer. The visual field will also be distorted, as a result of which the ship’s trajectory will pass as if inside a tunnel, at the end of which the crew will see a shining flash. Behind the ship there will be absolute pitch darkness.
So in the near future, humanity will have to limit its speed “appetites” to 10% of the speed of light. This means that it will take about 40 years to fly to the closest star to Earth, Proxima Centauri (4.22 light years).
Literature
Myakishev G.Ya. Bukhovtsev B.B. Physics 11. Textbook. M.: Education, 2004.
Lesson Objectives
Consider different ways to measure the speed of light.
In this lesson, computer models are used to explain new material.
| No. | Lesson steps | Time, min | Techniques and methods |
| 1 | Organizing time | 2 | |
| 2 | Survey on the topic “Porpucular and wave theories of light” | 10 | Oral survey |
| 3 | Explanation of new material on the topic “The speed of light” | 30 | Working with the “Fizeau experiment” and “Michelson experiment” models |
| 4 | Homework explanation | 3 |
Homework: § 59.
When explaining new material, a demonstration of interactive models “Fizeau's Experience” and “Michelson's Experience” is used. Demonstration method is determined technical capabilities used classroom. The following options are possible:
- Demonstration of the model by the teacher using multimedia projection equipment.
- Demonstration of the model by a teacher using a system for remote control of students’ personal computers, for example NetOp School.
- Students work with the model directly on educational PCs while the teacher explains new material and under his control.
Theory for the lesson
Fizeau's experience
In 1849, the French physicist Armand Hippolyte Louis Fizeau (11/23/1819–9/18/1896, Paris, France) was the first to conduct a laboratory experiment to measure the speed of light using the rotating shutter method. In the Fizeau installation, a narrow beam of light was split into pulses, passing through the gaps between the protrusions on the circumference of a rapidly rotating disk. The pulses hit a mirror located at a distance L = 8.66 km from the source and oriented perpendicular to the path of the beam. The experimenter, by changing the speed of rotation of the wheel, ensured that the reflected light fell into the gap between the teeth. There were 720 projections on the Fizeau disk. Knowing the distance between the teeth and the speed of rotation of the wheel at which light enters the next gap, we can calculate the speed of light.
Fizeau's result for the speed of light was 313,247,304 m/s. Subsequently, a number of researchers improved the method using various shutter options. In particular, the American physicist A. Michelson developed a very advanced method for measuring the speed of light using rotating mirrors. This made it possible to significantly clarify the value of the speed of light.
An example of a calculation operation for the option in which the experimenter makes the light disappear in the eyepiece of the device
Let us assume that the tooth and slot of the gear wheel have the same width and during the movement of the light pulse to the mirror and back, the place of the slot on the wheel is taken by the adjacent tooth. Then the light will be blocked by the tooth and the eyepiece will become dark. This will occur provided that the time it takes for light to travel there and back is:
Here L is the distance from the gear to the mirror, T 1 is the period of rotation of the gear, ν 1 = 1 / T 1 is the rotation frequency at which the light flux in the eyepiece disappears for the first time, N is the number of teeth. Since t = t 1, we obtain a calculation formula for determining the speed of light using this method:| c = 4LN ν 1 . |
An example of a calculation operation for the option in which the experimenter makes light appear after it has disappeared in the eyepiece of the device
Let us assume that the tooth and slot of the gear wheel have the same width and that during the movement of the light pulse to the mirror and back, the place of the first slot on the wheel is taken by the slot following it. Then the light will be able to pass through to the eyepiece again and the eyepiece will become light again. This will occur provided that the time it takes for light to travel there and back is:
We obtain a calculation formula for determining the speed of light using this method: c = 2LN ν 2, where ν 2 = 1 / T 2 is the rotation frequency at which light appears in the eyepiece again after the first disappearance.Michelson experiment
Throughout his life, the American physicist Albert Abraham Michelson (12/19/1852–05/09/1931) improved the technique for measuring the speed of light. Creating increasingly complex installations, he tried to obtain results with minimal error. In 1924–1927, he developed a design for an experiment in which a beam of light was sent from the top of Mount Wilson to the top of San Antonio. The rotating shutter was a rotating mirror, manufactured with extreme precision and driven by a specially designed device.
“The preparation of the experiment was carried out with great care. A site was selected for two installations. One of them was located on the top of Mount Wilson, already familiar to him, and the other was on the top of Mount San Antonio, known by the nickname “Old Baldness,” at an altitude of 5800 m above sea level and at a distance of 35 km from Mount Wilson. The United States Coast and Geodetic Survey was tasked with accurately measuring the distance between two reflecting planes, a rotating prismatic mirror on Mount Wilson and a fixed mirror on San Antonio. The possible error in measuring the distance was one seven-millionth, or a fraction of a centimeter, per 35 km. A rotating prism of nickel-plated steel with eight mirror surfaces polished to one part in a million was manufactured for the experiment by the Sperry Gyroscope Company of Brooklyn, whose president, engineer-inventor Elmer A. Sperry, was a friend of Michelson. In addition, several more glass and steel prisms were made. The octagonal high-speed rotor made up to 528 revolutions per second. It was driven by an air stream, and its speed, as in previous experiments, was regulated using an electric tuning fork. (The tuning fork is used not only by musicians to determine the pitch of a sound. With its help, you can very accurately determine short equal periods of time. You can create an instrument with the desired frequency, which, under the influence electric current will vibrate like an electric bell).”
(Bernard Jeff. Michelson and the speed of light. Translation from English by R. S. Bobrova. M.: Publishing House foreign literature, 1963. Electronic version– http://n-t.ru/ri/dj/mc.htm).
Beginning in 1924 and ending in early 1927, five independent series of observations were carried out. The average result was 299,798 km per second.
The results of all Michelson’s measurements can be written as c = (299796 ± 4) km/s.
Calculation of the speed of light
The experiment uses an octagonal prism. Therefore, the time of rotation of the prism on one face is τ 1 = T / 8, τ 1 = 1/ 8ν 1, where ν 1 is the frequency of rotation of the prism at which light appears for the first time. Thus, c = 2L / τ 1 = 16L ν 1.