Experimental methods for measuring the speed of light. Methods for determining the speed of light. Modern methods for measuring the speed of light

28.08.2022

Really, how? How to measure the highest speed in Universe in our modest, Earthly conditions? We no longer need to rack our brains over this - after all, over several centuries, so many people have worked on this issue, developing methods for measuring the speed of light. Let's start the story in order.

Speed of light– propagation speed electromagnetic waves in a vacuum. It is designated Latin letter c. The speed of light is approximately 300,000,000 m/s.

At first, no one thought about the issue of measuring the speed of light. There is light - that’s great. Then, in the era of antiquity, the prevailing opinion among scientific philosophers was that the speed of light is infinite, that is, instantaneous. Then it happened Middle Ages with the Inquisition, when the main question of thinking and progressive people was “How to avoid getting caught in the fire?” And only in epochs Renaissance And Enlightenment The opinions of scientists multiplied and, of course, were divided.

So, Descartes, Kepler And Farm were of the same opinion as the scientists of antiquity. But he believed that the speed of light is finite, although very high. In fact, he made the first measurement of the speed of light. More precisely, he made the first attempt to measure it.

Galileo's experiment

Experience Galileo Galilei was brilliant in its simplicity. The scientist conducted an experiment to measure the speed of light, armed with simple improvised means. At a large and well-known distance from each other, on different hills, Galileo and his assistant stood with lit lanterns. One of them opened the shutter on the lantern, and the second had to do the same when he saw the light of the first lantern. Knowing the distance and time (the delay before the assistant opens the lantern), Galileo expected to calculate the speed of light. Unfortunately, for this experiment to succeed, Galileo and his assistant had to choose hills that were several million kilometers apart. I would like to remind you that you can order an essay by filling out an application on the website.

Roemer and Bradley experiments

The first successful and surprisingly accurate experiment in determining the speed of light was that of a Danish astronomer Olaf Roemer. Roemer used the astronomical method of measuring the speed of light. In 1676, he observed Jupiter's satellite Io through a telescope, and discovered that the time of the eclipse of the satellite changes as the Earth moves away from Jupiter. The maximum delay time was 22 minutes. Calculating that the Earth is moving away from Jupiter at a distance of the diameter of the Earth's orbit, Roemer divided the approximate value of the diameter by the delay time, and received a value of 214,000 kilometers per second. Of course, such a calculation was very rough, the distances between the planets were known only approximately, but the result turned out to be relatively close to the truth.

Bradley's experience. In 1728 James Bradley estimated the speed of light by observing the aberration of stars. Abberation is a change in the apparent position of a star caused by the movement of the earth in its orbit. Knowing the speed of the Earth and measuring the aberration angle, Bradley obtained a value of 301,000 kilometers per second.

Fizeau's experience

As a result of the experience of Roemer and Bradley, the then scientific world reacted with disbelief. However, Bradley's result was the most accurate for over a hundred years, right up to 1849. That year, a French scientist Armand Fizeau measured the speed of light using the rotating shutter method, without observing celestial bodies, but here on Earth. In fact, this was the first laboratory method for measuring the speed of light since Galileo. Below is a diagram of its laboratory setup.

The light, reflected from the mirror, passed through the teeth of the wheel and was reflected from another mirror, 8.6 kilometers away. The speed of the wheel was increased until the light became visible in the next gap. Fizeau's calculations gave a result of 313,000 kilometers per second. A year later, a similar experiment with a rotating mirror was carried out by Leon Foucault, who obtained a result of 298,000 kilometers per second.

With the advent of masers and lasers, people have new opportunities and ways to measure the speed of light, and the development of the theory also made it possible to calculate the speed of light indirectly, without making direct measurements.

The most accurate value of the speed of light

Humanity has accumulated vast experience in measuring the speed of light. Today, the most accurate value for the speed of light is considered to be 299,792,458 meters per second, received in 1983. It is interesting that further, more accurate measurement of the speed of light turned out to be impossible due to errors in the measurement meters. Currently, the value of a meter is tied to the speed of light and is equal to the distance that light travels in 1/299,792,458 of a second.

Finally, as always, we suggest watching an educational video. Friends, even if you are faced with such a task as independently measuring the speed of light using improvised means, you can safely turn to our authors for help. You can order a test paper online by filling out an application on the Correspondence Student website. We wish you a pleasant and easy study!

With the experimental discovery of the corpuscular properties and manifestations of light (photoelectric effect, Compton effect and other phenomena), the quantum nature of light was developed by M. Planck and A. Einstein, within the framework of which light exhibits both wave and corpuscular properties - the so-called corpuscular - wave dualism. (Max Karl Ernst Ludwig Planck - German theoretical physicist, 1858-1947, Nobel Prize 1918 for the discovery of the laws of radiation, Arthur Hotey Compton, American physicist, 1892-1962, Nobel Prize 1927 for the effect named after him).

Introduction 3
1. Experiments to determine the speed of light. 4
1.1. First experiments. 4
1.1.1. Galileo's experiment. 4
1.2 Astronomical methods for determining the speed of light. 4
1.2.1. Eclipse of Jupiter's satellite Io. 4
1.2.2. Aberration of light. 6
1.3. Laboratory methods for measuring the speed of light. 7
1.3.1. Synchronous detection method. 7
1.4. Experiments on the propagation of light in a medium. 9
1.4.1. The experience of Armand Fizeau. 9

1.4.3. Experiments by A. Michelson and Michelson - Morley. 12
1.4.4.Improving the Michelson experiment. 13
2. Maximum speed of light. 14
2.1. Sade's experience. 14
2.2. Bertozzi's experience. 15
3. The speed of light in matter. 17
4. Tachyons. Particles moving at speeds greater than the speed of light. 17
4.1. Imaginary masses. 17
4.2. Speeding up instead of slowing down. 18

5. Superluminal speed. 20
Conclusion 22
References 23

The work contains 1 file

Coursework on the topic:

“The speed of light and methods for determining it”

Introduction 3

1. Experiments to determine the speed of light. 4

1.1. First experiments. 4

1.1.1. Galileo's experiment. 4

1.2 Astronomical methods for determining the speed of light. 4

1.2.1. Eclipse of Jupiter's satellite Io. 4

1.2.2. Aberration of light. 6

1.3. Laboratory methods for measuring the speed of light. 7

1.3.1. Synchronous detection method. 7

1.4. Experiments on the propagation of light in a medium. 9

1.4.1. The experience of Armand Fizeau. 9

1.4.2. An improvement on Foucault. 10

1.4.3. Experiments by A. Michelson and Michelson - Morley. 12

1.4.4.Improving the Michelson experiment. 13

2. Maximum speed of light. 14

2.1. Sade's experience. 14

2.2. Bertozzi's experience. 15

3. The speed of light in matter. 17

4. Tachyons. Particles moving at speeds greater than the speed of light. 17

4.1. Imaginary masses. 17

4.2. Speeding up instead of slowing down. 18

4.3. Negative energies. 19

5. Superluminal speed. 20

Conclusion 22

References 23

Introduction

The nature of light has been speculated on since ancient times. Ancient thinkers believed that light is the outflow of “atoms” from objects into the eyes of the observer (Pythagoras - about 580 - 500 BC). At the same time, the straightness of the propagation of light was determined; it was believed that it spreads at very high speeds, almost instantly. In the 16th-17th centuries, R. Descartes (René Descartes, French physicist, 1596-1650), R. Hooke (Robert Hooke, English physicist, 1635-1703), H. Huygens (Christian Huygens, Dutch physicist, 1629-1695) proceeded from the fact that the propagation of light is the propagation of waves in a medium. Isaac Newton (Isaac Newton, English physicist, 1643 - 1727) put forward the corpuscular nature of light, i.e. believed that light is the emission of certain particles by bodies and their distribution in space.

In 1801, T. Young (Thomas Young, English physicist, 1773-1829) observed the interference of light, which served to develop experiments with light on interference and diffraction. And in 1818 O.Zh. Fresnel (Augustin Jean Fresnel, French physicist, 1788-182 7) revived the wave theory of light propagation. D.K. Maxwell after establishing the general laws of electricity magnetic field came to the conclusion that light is electromagnetic waves. Next, the “world ether” hypothesis was put forward, that light is the propagation of electromagnetic waves in a medium - “ether”. Famous experiments to test the existence of the world ether were carried out by A.A. Michelson and E.W. Morley (1837-1923), and on the entrainment of light by a moving medium - A.I. Physo. (Albert Abraham Michelson, American physicist, 1852-1931, Nobel Prize 1907 for the creation of precision instruments and spectroscopic and metrological studies performed with their help; Armand Hippolyte Louis Fizeau, French physicist, 1819-1896). As a result, it was shown that the world ether (at least in the sense that physicists believed at that time - some absolute stationary medium) does not exist.

They have also tried to measure the speed of light in various ways, both in natural and laboratory conditions.

1. Experiments to determine the speed of light.

1.1. First experiments.

1.1.1. Galileo's experiment.

The first person to try to measure the speed of light experimentally was the Italian Galileo Galilei. The experiment was as follows: two people standing on the tops of hills at a distance of several kilometers from each other gave signals using lanterns equipped with shutters. This experiment, subsequently carried out by scientists of the Florentine Academy, he expressed in his work “Conversations and mathematical proofs concerning two new branches of science, relating to mechanics and local motion” (published in Leiden in 1638).

After the experiment, Galileo concluded that the speed of light travels instantly, and if not instantly, then at an extremely high speed.

The means available to Galileo at that time, of course, did not allow this issue to be resolved so easily, and he was fully aware of this.

1.2 Astronomical methods for determining the speed of light.

1.2.1. Eclipse of Jupiter's satellite Io.

O.K. Roemer (1676, Ole Christensen Roemer, Dutch astronomer, 1644-1710) observed the eclipse of the satellite of Jupiter (J) - Io, discovered by Galileo in 1610 (he also discovered 3 more satellites of Jupiter). The radius of the orbit of the satellite Io around Jupiter is 421600 km, the diameter of the satellite is 3470 km (see Fig. 2.1 and 2.2). The eclipse time was = 1.77 days = 152928 s. O.K. Roemer observed a violation of the periodicity of eclipses, and Roemer associated this phenomenon with the finite speed of light. The radius of Jupiter's orbit around the Sun Rj is significantly greater than the radius of the Earth's orbit Rз, and the orbital period is approximately 12 years. That is, during the half-revolution of the Earth (six months), Jupiter will move in orbit a certain distance and, if we record the time of arrival of the light signal from the moment Io appears from the shadow of Jupiter, then the light must travel a greater distance to the Earth in case 2 than in case 1 ( see Fig. 2.2). Let be the moment in time when Io emerges from the shadow of Jupiter according to the clock on Earth, and let be the real moment in time when this happens. Then we have:

where is the distance that light travels to the Earth. In the next Io output we have similarly:

where is the new distance that light travels to the Earth. The true period of Io's orbit around Jupiter is determined by the time difference:

Of course, in one period of time, when one eclipse occurs, it is difficult to determine these times with great accuracy. Therefore, it is more convenient to conduct observations over six months, when the distance to the Earth changes by its maximum value. In this case, the true period of the eclipse can be defined as the average value over six months or a year. After this, you can determine the speed of light after two consecutive measurements of the time when Io leaves the shadow:

The values are found from astronomical calculations. However, during one eclipse this distance changes little. It is more convenient to take measurements over six months (when the Earth moves to the other side of its orbit) and obtain the total time of the eclipse:

where n is the number of eclipses during these six months. All other intermediate times of light propagation to the Earth have been shortened, since the distance changes little during one eclipse. From here Roemer obtained the speed of light equal to c = 214300 km/s.

1.2.2. Aberration of light.

In astronomy, aberration is a change in the apparent position of a star by celestial sphere, that is, the deviation of the apparent direction to the star from the true one, caused by the finiteness of the speed of light and the movement of the observer. The diurnal aberration is caused by the rotation of the Earth; annual – the revolution of the Earth around the Sun;

century - the movement of the solar system in space.

Rice. Aberration of star light.

To understand this phenomenon, we can draw a simple analogy. Raindrops falling vertically in windless weather leave an inclined mark on the side window of a moving car.

As a result of light aberration, the apparent direction to the star differs from the true direction by an angle called the aberration angle. From the figure it is clear that

where is the component of the Earth's velocity perpendicular to the direction to the star.

In practice, the phenomenon of aberration (annual) is observed as follows. During each observation, the axis of the telescope is oriented in space in the same way relative to the starry sky, and the image of the star is fixed in the focal plane of the telescope. This image describes an ellipse over the course of a year. Knowing the parameters of the ellipse and other data corresponding to the geometry of the experiment, one can calculate the speed of light. In 1727, from astronomical observations, J. Bradley found 2* = 40.9" and received

s = 303000 km/s.

1.3. Laboratory methods for measuring the speed of light.

1.3.1. Synchronous detection method.

To measure the speed of light, Armand Fizeau (1849) used the synchronous detection method. He used a rapidly rotating disk with N teeth (Fig. 2.3), which were opaque sectors. Between these sectors (teeth), light passed from the source to the reflecting mirror and back to the observer. In this case, the angle between the midpoints of the sectors is equal to

The angular velocity of rotation was selected so that the light, after being reflected from the mirror behind the disk, entered the observer’s eyes when passing through an adjacent hole. During the movement of light from the disk to the mirror and back:

the rotation of the disk makes an angle

Knowing the distance L, the angular speed of the disk ω and the angle △φ at which light appears, we can obtain the speed of light. Fizeau obtained a speed value equal to c = (315300500) km/s. Using approximately the same methods, experimenters obtained a refined value for the speed of light with = (298,000,500) km/s (1862), then with = (2997,964) km/s (A. Michelson in 1927 and 1932). Later Bergstrand received - c = (299793.10.3) km/s.

Let us note here one of the most accurate ways of measuring the speed of light - the cavity resonator method, the main idea of which is the formation of a standing light wave and calculating the number of half-waves along the length of the resonator. The basic relationships between the speed of light c, wavelength λ, period T and frequency ν have the form:

Circular frequency is also introduced here, which is nothing more than the angular velocity of rotation ω amplitude, if the oscillations are represented as a projection of rotational motion onto the axis. In the case of the formation of a light standing wave, an integer number of half-waves fits along the length of the resonator. By finding this number and using the relations (*), you can determine the speed of light.

Recent advances (1978) gave the following value for the speed of light: c = 299792.458 km/s = (299792458 1.2) m/s.

1.4. Experiments on the propagation of light in a medium.

1.4.1. The experience of Armand Fizeau.

The experiment of Armand Fizeau (1851). Fizeau considered the propagation of light in a moving medium. To do this, he passed a beam of light through standing and flowing water and, using the phenomenon of light interference, compared the interference patterns, by analysis of which it was possible to judge the change in the speed of light propagation (see Figure 2.4). Two rays of light, reflected from a translucent mirror (beam 1) and passing through it (beam 2), pass twice through a pipe with water and then create an interference pattern on the screen. First, they measure in still water, and then in flowing water at a speed V.

In this case, one beam (1) moves with the flow, and the second (2) moves against the flow of water. A shift in the interference fringes occurs due to a change in the path difference between the two beams. The difference in the path of the rays is measured and the change in the speed of light propagation is determined from it. The speed of light in a stationary medium ĉ depends on the refractive index of the medium n:

According to Galileo's principle of relativity, for an observer relative to whom light moves in a medium, the speed should be equal to:

Fizeau experimentally established that there is a coefficient for the water speed V and therefore the formula looks like this:

where * is the coefficient of light entrainment by the moving medium:

Thus, Fizeau’s experiment showed that the classical rule of adding velocities is not applicable when light propagates in a moving medium, i.e. light is only partially entrained by the moving medium. Fizeau's experience played a role important role when constructing the electrodynamics of moving media.

It served as a justification for SRT, where the coefficient * is obtained from the law of addition of velocities (if we limit ourselves to the first order of accuracy for the small value of ν/c). The conclusion that follows from this experiment is that classical (Galilean) transformations are not applicable in the propagation of light.

1.4.2. An improvement on Foucault.

When Fizeau announced the result of his measurement, scientists doubted the reliability of this colossal figure, according to which light reaches the Earth from the Sun in 8 minutes and can circle the Earth in an eighth of a second. It seemed incredible that man could measure such enormous speed with such primitive instruments. Light travels more than eight kilometers between the Fizeau mirrors in 1/36000 of a second? Impossible, many said. However, the figure obtained by Fizeau was very close to Roemer's result. This could hardly be a mere coincidence.

Thirteen years later, while skeptics were still doubting and making ironic remarks, Jean Bernard Leon Foucault, the son of a Parisian publisher and at one time preparing to become a doctor, determined the speed of light in a slightly different way. He worked with Fizeau for several years and thought a lot about how to improve his experience. Instead of a gear wheel, Foucault used a rotating mirror.

Rice. 3. Foucault's installation.

After some improvements, Michelson used this device to determine the speed of light. In this device, the gear wheel is replaced by a rotating plane mirror C. If mirror C is stationary or rotates very slowly, light is reflected onto the translucent mirror B in the direction indicated by the solid line. When the mirror rotates rapidly, the reflected beam moves to the position indicated by the dotted line. By looking through the eyepiece, the observer could measure the displacement of the beam. This measurement gave him double the value of the angle α, i.e. the angle of rotation of the mirror during the time the light ray went from C to the concave mirror A and back to C. Knowing the speed of rotation of mirror C, the distance from A to C and the angle of rotation of mirror C during this time, it was possible to calculate the speed of light.

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. Characteristic feature His method is the automatic registration 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 when 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.

Recently, instead of a rotating wheel, other, more advanced methods of interrupting light have been 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 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 standing waves, formed in a cylindrical resonator. The theory makes it possible to relate data on the dimensions of the resonator and its resonant frequency to 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 identify a specific place, for example, the place of maximum extent of the electric or magnetic field that represents the 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 combination of two sinusoids close in frequency same amplitude, and not as a collection 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, a monochromatic wave is characterized by a 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 method of light aberration 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 the Fizeau 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.

Speed of light and methods of measuring it. The astronomical method of measuring the speed of light was first carried out by the Dane Olaf Roemer in 1676. When the Earth came very close to Jupiter (at a distance of L 1), the time interval between the two appearances of the satellite Io turned out to be 42 hours 28 minutes; when the Earth moved away from Jupiter at a distance of L 2, the satellite began to emerge from Jupiter’s shadow for 22 minutes. later. Roemer's explanation: this delay occurs due to the fact that the light travels an additional distance Δ l= l 2 – l 1.

Laboratory method for measuring the speed of light Fizeau's method (1849). Light falls on a translucent plate and is reflected as it passes through a rotating gear wheel. The beam reflected from the mirror can reach the observer only by passing between the teeth. If you know the speed of rotation of the gear, the distance between the teeth, and the distance between the wheel and the mirror, you can calculate the speed of light. Foucault's method - instead of a gear wheel, a rotating mirror octagonal prism.

C= km/s.

You can measure the oscillation frequency of the wave and, independently, the wavelength (especially convenient in the radio range), and then calculate the speed of light using the formula. с=λں According to modern data, in vacuum с=(.2 ± 0.8) m/s.

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. During the “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. 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).