Methods for measuring the speed of light. The speed of light and methods of its determination Physics laboratory work measuring the speed of light
With the discovery in the experiment of 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 which light exhibits both wave and corpuscular properties - the so-called corpuscular - wave dualism. (Max Karl Ernst Ludwig Planck - German theoretical physicist, 1858-1947, 1918 Nobel Prize for the discovery of the laws of radiation, Arthur Hotie Compton, American physicist, 1892-1962, 1927 Nobel Prize 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 experience. 4
1.2 Astronomical methods of determining the speed of light. 4
1.2.1. Eclipse of the moon of Jupiter - Io. 4
1.2.2. Light aberration. 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. nine
1.4.1. Arman Fizeau's experience. nine
1.4.3. Experiments by A. Michelson and Michelson - Morley. 12
1.4.4 Improvement of Michelson's experience. 13
2. Maximum speed of light. fourteen
2.1. Sade experience. fourteen
2.2. The Bertozzi 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. Acceleration instead of deceleration. eighteen
5. Superluminal speed. twenty
Conclusion 22
References 23
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Course work on the topic:
"The speed of light and methods of its determination"
Introduction 3
1. Experiments to determine the speed of light. 4
1.1. First experiments. 4
1.1.1. Galileo's experience. 4
1.2 Astronomical methods of determining the speed of light. 4
1.2.1. Eclipse of the moon of Jupiter - Io. 4
1.2.2. Light aberration. 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. nine
1.4.1. Arman Fizeau's experience. nine
1.4.2. Foucault's improvement. ten
1.4.3. Experiments by A. Michelson and Michelson - Morley. 12
1.4.4 Improvement of Michelson's experience. 13
2. Maximum speed of light. fourteen
2.1. Sade experience. fourteen
2.2. The Bertozzi 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. Acceleration instead of deceleration. eighteen
4.3. Negative energies. 19
5. Superluminal speed. twenty
Conclusion 22
References 23
Introduction
The nature of light has been thought about 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 propagates at very high speeds, almost instantly. In the XVI-XVII 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 propagation in space.
In 1801, T. Jung (Thomas Jung, English physicist, 1773-1829) observed the interference of light, which led to the development of 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. After establishing the general laws of the electromagnetic field, Maxwell came to the conclusion that light is electromagnetic waves. Further, the hypothesis of the "world ether" was put forward, that light is the propagation of electromagnetic waves in the medium - "ether". The famous experiments on checking the existence of the world ether were carried out by A.A. Michelson and E.W. Morley (1837-1923), and by the fascination of light with a moving medium - A.I. Fizeau. (Albert Abraham Michelson, American physicist, 1852-1931, 1907 Nobel Prize for the creation of precision instruments and the 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 motionless environment) does not exist.
With the discovery in the experiment of 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 which light exhibits both wave and corpuscular properties - the so-called corpuscular - wave dualism. (Max Karl Ernst Ludwig Planck - German theoretical physicist, 1858-1947, 1918 Nobel Prize for the discovery of the laws of radiation, Arthur Hotie Compton, American physicist, 1892-1962, 1927 Nobel Prize for the effect named after him).
They also tried to measure the speed of light in various ways, both in natural and in laboratory conditions.
1. Experiments to determine the speed of light.
1.1. First experiments.
1.1.1. Galileo's experience.
The first who tried to measure the speed of light experimentally was the Italian Galileo Galilei. The experiment consisted of the following: two people, standing on the tops of hills at a distance of several kilometers from each other, gave signals with the help of lanterns equipped with shutters. This experiment, which was subsequently carried out by the 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 Movement" (published in Leiden in 1638).
After the experiment, Galileo concluded that the speed of light propagates instantly, and if not instantly, then at an extremely high speed.
The means available then at Galileo's disposal, of course, did not allow this issue to be resolved so easily, and he was fully aware of this.
1.2 Astronomical methods of determining the speed of light.
1.2.1. Eclipse of the moon of Jupiter - Io.
O.K. Roemer (1676, Ole Christensen Roemer, Dutch astronomer, 1644-1710) observed the eclipse of Jupiter's moon (J) - Io, discovered by Galileo in 1610 (he also discovered 3 more moons of Jupiter). The radius of the orbit of Io's satellite around Jupiter is 421600 km, the satellite diameter is 3470 km (see Figures 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 propagation. The radius of Jupiter's orbit around the Sun Rj is much greater than the radius of the Earth's orbit R3, 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 fix 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 the Earth, and 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. Io's true orbital period 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 for six months, when the distance to the Earth changes to a maximum value. In this case, the true eclipse period can be determined as the average value for six months or a year. After that, you can determine the speed of light after two successive measurements of the time Io emerged from the shadow:
The values are found from astronomical calculations. However, this distance changes little over one eclipse. It is more convenient to take measurements in six months (when the Earth moves to the other side of its orbit) and obtain the total eclipse time:
where n is the number of eclipses during these six months. All other intermediate times of the propagation of light to the Earth have decreased, since the distance changes weakly in one eclipse. From here Roemer obtained the speed of light equal to c = 214300 km / s.
1.2.2. Light aberration.
In astronomy, aberration is a change in the apparent position of a star in the 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. Daily aberration is due to the rotation of the Earth; annual - the revolution of the Earth around the Sun;
secular - the movement of the solar system in space.
Rice. Star light aberration.
To understand this phenomenon, a simple analogy can be drawn. Raindrops falling vertically in calm weather leave an oblique trail 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. The figure shows that
where is the component of the Earth's motion velocity perpendicular to the direction to the star.
In practice, the phenomenon of aberration (annual) is observed as follows. During each observation, the telescope axis 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 throughout the year. Knowing the parameters of the ellipse and other data corresponding to the geometry of the experiment, it is possible to 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) applied the method of synchronous detection. He used a fast rotating disc with N teeth (Fig. 2.3), which are 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
The angular velocity of rotation was chosen so that the light, after being reflected from the mirror behind the disk, would enter the observer's eyes when passing through the adjacent hole. During the movement of light from the disk to the mirror and back:
turning the dial makes an angle
Knowing the distance L, the angular velocity of the disk ω and the angle △ φ at which light appears, one can obtain the speed of light. Fizeau obtained a speed value equal to c = (315300500) km / s. The experimenters obtained a refined value of the speed of light with approximately the same methods with = (298000500) km / s (1862), then with = (2997964) km / s (A. Michelson in 1927 and 1932). Later, Bergstrand received - s = (299793.10.3) km / s.
Let us note here one of the most accurate methods for measuring the speed of light - the cavity resonator method, the main idea of which is the formation of a standing light wave and the calculation of the number of half-waves along the resonator length. The basic relationships between the speed of light c, wavelength λ, period T and frequency ν are as follows:
The angular frequency is also introduced here, which is nothing more than the angular velocity of rotation ω of the amplitude, if the oscillations are represented as the projection of the rotational motion onto the axis. In the case of the formation of a standing light wave, an integer number of half-waves fit into the resonator length. 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. Arman Fizeau's experience.
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 interference patterns, by analyzing 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 semitransparent mirror (ray 1) and passing it (ray 2), pass twice through a pipe with water and then create an interference pattern on the screen. First, it is measured in stagnant water, and then in flowing water at a speed V.
In this case, one ray (1) moves with the flow, and the second (2) - against the flow of water. The interference fringes shift 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 propagation of light is found 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:
Experimentally, Fizeau established that there is a coefficient at the speed of water V and therefore the formula looks as follows:
where * is the coefficient of light entrainment by the moving medium:
Thus, Fizeau's experiment showed that the classical rule for the addition of velocities is inapplicable for the propagation of light in a moving medium, i.e. light is only partially carried away by the moving medium. Fizeau's experiment played an important role in the construction of the electrodynamics of moving media.
It served as a substantiation of SRT, where the coefficient * is obtained from the law of addition of velocities (if we restrict ourselves to the first order of accuracy with respect to the small value of ν / c). The conclusion that follows from this experience is that the classical (Galilean) transformations are not applicable to the propagation of light.
1.4.2. Foucault's improvement.
When Fizeau announced the result of his measurement, scientists questioned the reliability of this colossal figure, according to which light reaches from the Sun to the Earth in 8 minutes and can fly around the Earth in an eighth of a second. It seemed incredible that a person could measure such a tremendous speed with such primitive instruments. Does light travel more than eight kilometers between Fizeau mirrors in 1/36000 of a second? Impossible, many said. However, the figure obtained by Fizeau was very close to the result of Röhmer. This could hardly be a coincidence.
Thirteen years later, with skeptics still doubting and ironic, Jean Bernard Léon Foucault, the son of a Parisian publisher who was 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 cogwheel, Foucault used a rotating mirror.
Rice. 3. Installation of Foucault.
After some improvements, Michelson used this device to determine the speed of light. In this device, the cogwheel is replaced by a rotating flat mirror C. If the mirror C is stationary or rotates very slowly, the light is reflected to the translucent mirror B in the direction indicated by the solid line. When the mirror rotates rapidly, the reflected beam shifts 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 twice the value of the angle α, i.e. the angle of rotation of the mirror during the time while the light beam went from C to the concave mirror A and back to C. Knowing the speed of rotation of the mirror C, the distance from A to C and the angle of rotation of the mirror C during this time, it was possible to calculate the speed of light.
Long before scientists measured the speed of light, they had to work hard to define the very concept of "light". One of the first to think about this was Aristotle, 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.
By the 17th century, two main theories of the nature of light were formed - corpuscular and wave. Newton was among the adherents of the first. In his opinion, all light sources emit the smallest particles. In the process of "flight" they form luminous lines - rays. His opponent, the Dutch scientist Christian Huygens, insisted that light is a kind of wave motion.
As a result of centuries of disputes, scientists have come to a consensus: both theories have the right to life, and light is the spectrum of electromagnetic waves visible to the eye.
A bit of history. How the speed of light was measured
Most ancient scientists were convinced that the speed of light is infinite. However, the results of the studies of Galileo and Hooke admitted its limit, 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, a 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 at a distance equal to the diameter of the Earth's orbit, the lag time changed. The maximum value was 22 minutes. As a result of calculations, he received a speed of 220,000 km / s.
50 years later, in 1728, thanks to the discovery of aberration, the English astronomer J. Bradley "refined" this figure to 308,000 km / s. Later, the speed of light was measured by French astrophysicists François Argo and Leon Foucault, who received 298,000 km / s at the "exit". An even more accurate measurement technique was proposed by the creator of the interferometer, the famous American physicist Albert Michelson.
Michelson's experiment in determining 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. On Mount Wilson in the vicinity of Los Angeles, a light source, a mirror and a rotating octahedral prism were installed, and after 35 km, on Mount San Antonio, a reflecting mirror was installed. First, the light through the lens and the slit fell on a prism rotating with the help of a high-speed rotor (at a speed of 528 rps).
The participants in the experiments could adjust the speed of rotation so that the image of the light source was clearly visible in the eyepiece. Since the distance between the peaks and the rotation frequency were known, Michelson determined the value of the speed of light - 299796 km / s.
Scientists finally decided at 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 measurement error dropped to 1 km / s. 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 / s.
Is the speed of light achievable for us?
It is obvious that the exploration of the distant corners of the Universe is unthinkable without spaceships flying at great speed. Desirable at the speed of light. But is this possible?
The light speed barrier is one of the consequences of the theory of relativity. As you know, an increase in speed requires an increase in energy. The speed of light would require almost infinite energy.
Alas, the laws of physics are categorically against this. At a spacecraft speed of 300,000 km / s, particles flying towards it, for example, hydrogen atoms, turn into a deadly source of powerful radiation equal to 10,000 sievert / s. This is about the same as being inside the Large Hadron Collider.
According to scientists at Johns Hopkins University, while in nature there is no adequate protection from such a monstrous cosmic radiation. Erosion from the effects of interstellar dust will complete the destruction of the ship.
Another problem with light speed is time dilation. At the same time, old age will become much more prolonged. The visual field will also undergo a curvature, as a result of which the trajectory of the ship will pass, as it were, inside a tunnel, at the end of which the crew will see a shining flash. Absolute pitch darkness will remain behind the ship.
So in the near future, mankind will have to limit their high-speed "appetites" 10% of the speed of light. This means that the closest star to the Earth - Proxima Centauri (4.22 light years) will take about 40 years to fly.
There are various methods for measuring the speed of light, including astronomical and using various experimental techniques. Measurement accuracy WITH is constantly increasing. The table provides an incomplete list of experimental work on the determination of the speed of light.
|
date |
Experiment |
Experimental Methods |
Measurement results, km / s |
|
1676 1725 1849 1850 1857 1868 1875 1880 1883 1883 1901 1907 1928 1932 1941 1952 |
Roemer Bradley Fizeau Foucault Weber-Kohlrausch Maxwell Cornu Michelson Thomson Newcomb Perrotin Rose and dorsey Mittelyptedt Pease and Pearson Anderson Froome |
Eclipse of the moon of Jupiter Light aberration Propelling bodies Rotating mirrors Electromagnetic constants Electromagnetic constants Rotating mirrors Rotating mirrors Electromagnetic constants Rotating mirrors Rotating mirrors Electromagnetic constants Kerr shutter cell Rotating mirrors Kerr shutter cell Microwave interferometry |
214 459 308 000 313 290 298 000 310 000 288 000 299 990 299 910 282 000 299 880 299 777 299 784 299 778 299 774 299 782 299 792.45 |
The pictures show a reproduction of the picture itself Römer, as well as a schematic interpretation.
Roemer's astronomical method is based on measurement speed light from Earth observations of eclipses of Jupiter's satellites... Jupiter has severalabout satellites that are either visible from Earth near Jupiter, or
Let at a certain moment in time the EarthZ1 and Jupiter J1 are in opposition, and at this moment in time one of Jupiter's satellites, observed from Earth, disappears into the shadow of Jupiter (the satellite is not shown in the figure). Then, if we denote by R and r the radii of the orbits of Jupiter and the Earth and by c - the speed of the eta in in the coordinate system associated with the Sun C, on Earth, the satellite's departure into the shadow of Jupiter will be recorded (R-r) / s seconds later than it occurs in the time frame of reference associated with Jupiter.
After 0.545 years, Earth Z2 and Jupiter U2 are in conjunction. If at this time the n-th eclipse of the same satellite of Jupiter occurs, then on Earth it will be recorded with a delay of (R + r) / s seconds. Therefore, if the period of the satellite's revolution around Jupiter is t, then the time interval T1 between the first and nth eclipses observed from Earth is equal to
After another 0.545 year, Earth Z3 and Jupiter J3 will again be in opposition. During this time, (n-1) revolutions of the satellite around Jupiter and (n-1) eclipses took place, of which the first 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 last one with a delay (R-r) / s in relation to the moments when the satellite went into 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 = 4r / s, therefore c = 4r / 1980 m / s. Taking r, the average distance from the Earth to the Sun, equal to 1,500,000,000 km, we find the value of 3.01 * 10 6 m / s for the speed of light.
This result was the first measurement of the speed of light.
In 1725 g. James Bradley found that the star of the Dragon, located at the zenith (i.e. directly overhead), makes an apparent motion with a period of one year in an almost circular orbit with a diameter of 40.5 arc seconds. For stars visible elsewhere in the firmament, Bradley also observed a similar apparent motion — generally elliptical.
The phenomenon observed by Bradley is called aberration. It has nothing to do with the star's own motion. The reason for the aberration lies in the fact that the magnitude of the speed of light is finite, and the observation is carried out from the Earth, moving in its orbit at a certain speed v.
The opening angle of the cone, at which the apparent trajectory of the star is visible from the Earth, is determined by the expression: tgα = ν / c
Knowing the angle α and the speed of the Earth's orbit v, one can determine the speed of light c.
He got the value of the speed of light equal to 308,000 km / s.
In 1849, for the first time, the determination of the speed of light was carried out in laboratory conditions. A. Fizeau... His method was called the cogwheel method. A characteristic feature of his method is the automatic registration of the moments of starting and returning the signal, carried out by regularly interrupting the light flux (cogwheel).
Figure shows a diagram of an experiment to determine the speed of light by the cogwheel method.
The light from the source passed through the breaker (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, the speed of rotation, you can calculate the speed of light.
Knowing the distance D, the number of teeth z, the angular speed of rotation (number of revolutions per second) v, it is possible to determine the speed of light. He got it equal to 313,000 km / s.
American physicist throughout his life Albert Abraham Michelson(1852-1931) improved the method of measuring the speed of light. Creating more and more complex installations, he tried to obtain results with a minimum error. In 1924-1927, Michelson developed a scheme for an experiment in which a beam of light was sent from the top of Mount Wilson to the top of San Antonio (a distance of about 35 km). For the rotating shutter, a rotating mirror was used, manufactured with extreme precision and driven by a specially designed high-speed rotor that rotates up to 528 revolutions per second.
By changing the frequency of rotation of the rotor, the observer achieved the appearance of a stable image of the light source in the eyepiece. Knowing the distance between the installations and the frequency of rotation of the mirror made it possible to calculate the speed of light.
From 1924 to the beginning of 1927, five independent series of observations were carried out, the accuracy of measuring the distance and rotor speed was increased. The average measurement result was 299 798 km per second.
The results of all Michelson's measurements can be written as c = (299796 ± 4) km / s.
The upper figure shows a diagram of the Michelson experiment. The lower figure shows a simplified diagram of the experiment. The user can change the frequency of rotation of the octagonal prism, observing the movement of the light pulse and making it fall into the eyepiece of the observer.
The frequency can be changed from 0 to 1100 revolutions per second in 2 s –1 steps. To make it easier to set the frequency in the experiment, a coarse speed control knob was made, more precise settings can be set using additional keys to the right of the frequency window. Optimum results are achieved at 528 and 1056 rps. At 0 revolutions, a static light beam is drawn from the source to the observer.
An example of calculating the speed of light for an experiment in which the appearance of light is recorded by an observer at a mirror rotation frequency of 528 s –1.
Here ν and T are the frequency and period of rotation of the octahedral prism, τ 1 is the time during which the light beam has time to travel the distance L from one installation to another and return back, it is the time of rotation of one face of the mirror.
Based on materials from www.school-collection.edu.ru
Laboratory methods for determining the speed of light are essentially improvements to Galileo's method.
a) Interrupt method.
Fizeau (1849) performed for the first time the determination of the speed of light in laboratory conditions. A characteristic feature of his method is the automatic registration of the moments of start-up and return of the signal, carried out by regular interruption of the light flux (cogwheel). The scheme of the Fizeau 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 reflected back, must again pass between the teeth to the observer. For convenience, the 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, moreover, with such an angular velocity that during the movement of light from a To M and back in place of the teeth there will be slots, and vice versa, then the returned light will not be passed to the eyepiece and the observer will not see the light (first eclipse). As the angular velocity increases, the light will partially reach the observer. If the width of the teeth and gaps is the same, then at a double speed there will be a maximum of light, at a 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. The scheme of the experience of the interrupt method. |
Or with=2Dzn.
The main difficulty in determining lies in the exact determination of the moment of the eclipse. Accuracy increases with distance D and at interrupt rates allowing higher order eclipses to be observed. So, Perrotin conducted his observations at D= 46 km and observed an eclipse of the 32nd order. Under these conditions, high-aperture installations, clean air (observations in the mountains), good optics, and a strong light source are required.
Recently, instead of a rotating wheel, other, more advanced methods of interrupting light have been successfully used.
b) The rotating mirror method.
Foucault (1862) successfully implemented the second method, the principle of which was proposed by Arago even earlier (1838) in order to compare 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 time intervals using a rotating mirror. The scheme of the experiment is clear from Fig. 9.4. Light from source S guided by a lens L on a rotating mirror R, 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 whose rotation speed is precisely known; the angle of rotation is determined by measuring the displacement of the spot given by the returned light. Measurements are made using an eyepiece E and a translucent plate M which plays the same role as in the previous method; S 1 - the position of the bunny with a fixed mirror R, S " 1 - when the mirror rotates. An important feature of the Foucault installation was the 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 got back on R; in the case of using a flat mirror WITH this would only happen with a certain mutual orientation R and WITH when the axis of the reflected cone of rays is located normally to WITH.
Foucault, in accordance with the original plan of Arago, carried out with the help of his device also the determination of the speed of light in water, for 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.
The last (1926) Michelson installation was carried out between two mountain peaks, so that the result is a distance D»35.4 km (more precisely, 35,373.21 m). The mirror was an octahedral steel prism rotating at a speed of 528 rev / s.
The time it took for the light to make a full path was 0.00023 s, so that the mirror had time to turn 1/8 of a turn and the light fell on the face of the prism. Thus, the displacement of the spot was relatively insignificant, and the determination of its position played the role of a correction, and not the main measured value, as in the first experiments of Foucault, 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, radio-geodetic measurements were used, i.e. determination of the distance between two points using radio signals in parallel with accurate 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 by the method of standing waves generated in a cylindrical resonator. The theory makes it possible 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 no vacuum reduction was required. The best value obtained by this method is s = 299 792.5 ± 3.4 km / s.
c) Phase and group speeds of light.
Laboratory methods for determining the speed of light, which make it possible to make these measurements on a short basis, make it possible to determine the speed of light in various media and, therefore, to check the relations of the theory of refraction of light. As already mentioned many times, the refractive index of light in Newton's theory is n= sin i/ sin r=υ 2 /υ 1, and in 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 - the speed of light in the second medium. Arago also saw in this difference the possibility of experimentum crucis and proposed the idea of an experiment that was performed later by Foucault, who found a value for the ratio of the speeds of light in air and water close to, as follows from Huygens' theory, and not, as follows from Newton's theory.
Conventional definition 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 really realizable, since they would have to exist indefinitely in time and howl indefinitely in space.
In reality, we always have a more or less complex impulse, limited in time and space. When observing such an impulse, we can select some specific place of it, for example, the place of the maximum extent of that electric or magnetic field, which is an electromagnetic impulse. 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 pulse velocity becomes more complicated. If the dispersion is not very large, then the pulse deformation occurs slowly and we can follow the movement of a certain field amplitude in the wave pulse, for example, the maximum field amplitude. However, the speed of movement of the impulse, named by Rayleigh group speed, will differ from the phase velocity of any of its constituent monochromatic waves.
For simplicity of calculations, we will think of a pulse as a collection of two sinusoids of the same amplitude that are close in frequency, 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 taken to be equal, and the frequencies and wavelengths differ little from each other, i.e.
where and are small values. Impulse (wave group) at there is an amount at 1 and at 2, i.e.
Introducing the notation, we represent our momentum in the form, where A not constantly, but changes in time and space, however, it changes slowly, because δω and δk- small (compared to ω 0 and κ 0) values. Therefore, assuming a certain carelessness of speech, we can consider our impulse to be a sinusoid with a slowly varying amplitude.
Thus, the velocity of the impulse (group), which, according to Rayleigh, is called group speed, there is a speed of movement amplitudes and, consequently, energy carried by a moving pulse.
So, a monochromatic wave is characterized by a phase velocity υ=ω /κ , which means the speed of movement phase, and the impulse is characterized by the group velocity u = dω/dκ corresponding to the velocity of propagation of the field energy of this pulse.
It's not hard 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 variance dυ/dλ... In the absence of variance ( dυ/dλ= 0) we have u = υ... This case, as already mentioned, takes place only for vacuum.
Rayleigh showed that in the well-known methods of determining the speed of light, we, by the very essence of the technique, are not dealing with a continuously lasting wave, but we break it up into small segments. The cogwheel and other interrupters in the interrupt method give a weakening and increasing light excitation, i.e. a group of waves. The situation is similar in the Roehmer method, where the light is interrupted by periodic blackouts. 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, not the phase velocity, in a dispersive medium.
Rayleigh believed that in the method of light aberration, we measure the immediate phase velocity, because there the light is not artificially interrupted. However, Ehrenfest (1910) showed that the observation of light aberration is in principle indistinguishable from the Fizeau method, i.e. also gives group speed. Indeed, the aberration experience can be summarized as follows. Two discs with holes are rigidly fixed on a common axis. Light is sent along a line connecting these holes and reaches the observer. Let's bring the whole apparatus into fast rotation. Since the speed of light is finite, the 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 velocities of the disks and the light. This is a typical aberration experience; however, it is no different from the Fizeau experiment, in which, instead of two rotating disks with holes, there is one disk and a mirror for turning the beams, i.e. essentially two disks: a real one and its reflection in a fixed mirror. So, the aberration method gives the same as the interrupt 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.
There are various methods for measuring the speed of light, including astronomical and using various experimental techniques. Measurement accuracy with is constantly increasing. This table provides an incomplete list of experimental work to determine the speed of light.
|
Experiment |
Experimental Methods |
Measurement results, km / s |
Experimental error, |
|
|
Weber-Kohlrausch Maxwell Michelson Perrotin Rose and dorsey Mittelyptedt Pease and Pearson Anderson |
Eclipse of the moon of Jupiter Light aberration Propelling bodies Rotating mirrors Electromagnetic constants Electromagnetic constants Rotating mirrors Rotating mirrors Electromagnetic constants Rotating mirrors Rotating mirrors Electromagnetic constants Kerr shutter cell Rotating mirrors Kerr shutter 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 the progress in the field of science and technology.
The first successful measurement of the speed of light dates back to 1676.
The figures show a reproduction of a drawing by Röhmer himself, as well as a schematic interpretation.
Roemer's astronomical method is based on measurement the speed of light from Earth observations of eclipses of Jupiter's satellites... Jupiter has several satellites that are either visible from Earth near Jupiter or hidden in its shadow. Astronomical observations over the satellites of Jupiter show that the average time interval between two successive eclipses of any particular satellite of Jupiter depends on how far the Earth and Jupiter are from each other during observations. In the picture: Roemer's method. S - sun, U - Jupiter, W - earth
Let at a certain moment in time the Earth Z1 and Jupiter J1 are in opposition, and at this moment in time one of the satellites of Jupiter, 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 the radii of the orbits of Jupiter and the Earth and throughc is the speed of light in the coordinate system associated with the Sun C; on Earth, the satellite's departure into the shadow of Jupiter will be recorded at ( R- r) / s seconds later than it occurs in the time frame of reference associated with Jupiter.
After 0.545 years, Earth Z2 and Jupiter U2 are in conjunction. If at this time there isn-th eclipse of the same satellite of Jupiter, then on Earth it will be recorded with a delay by ( R + r) / s seconds. Therefore, if the period of revolution of the satellite around Jupitert, then the time intervalT1 flowing between the first andn-th eclipses observed from Earth is equal to
After another 0.545 year, Earth Z3 and Jupiter J3 will again be in opposition. During this time (n-1) revolutions of the satellite around Jupiter and (n-1) eclipses, of which the first 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) / с, and the latter with a delay ( R- r) / c in relation to the moments when the satellite leaves 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, equal to 1,500,000,000 km, we find the value of 3.01 * 10 for the speed of light 6 m / s.
Determination of the speed of light by observing aberration in 1725-1728. Bradley undertook observation in order to find out whether there is an annual parallax of stars, i.e. apparent displacement of stars in the firmament, reflecting the Earth's orbital motion and associated with the finiteness of the distance from the Earth to the star.
Bradley did find a similar bias. He explained the observed phenomenon, which he called light aberration, 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, one can determine the speed of light c.
He got the value of 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 over the course of a year. A constant velocity, no matter how great it may be, cannot be detected with the help of aberration, because with such a movement the direction to the star remains unchanged and there is no way to judge the presence of this velocity and what angle it makes with the direction to the star. The aberration of light allows us to judge only about 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. A characteristic feature of his method is the automatic registration of the moments of starting and returning the signal, carried out by regularly interrupting the light flux (cogwheel).
Fig 3. Scheme of the experiment to determine the speed of light by the cogwheel method.
The light from the source passed through the breaker (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, the speed of rotation, you can calculate the speed of light.
Knowing the distance D, the number of teeth z, angular velocity of rotation (number of revolutions per second)v, the speed of light can be determined. He got it equal to 313,000 km / s.
Many methods have been developed to further improve the accuracy of measurements. It soon even became necessary to take into account the refractive index in air. And soon in 1958, Froome obtained the value of the speed of light equal to 299792.5 km / s, using a microwave interferometer and an electro-optical shutter (Kerr cell).
