Dr M. A. M. EL-Morsy Velocity of Light
Velocity of Light
1. INTRODUCTION
Determination of the velocity of light is of great importance. Einstein has shown that the energy released by the nucleus of an atom or otherwise is given by E=mc2 where m is the decrease in mass and c is the velocity of light.
But, before the 17th century, it was thought that velocity of light is infinite. The fact that the flash of lightening is seen instantaneously and the sound is heard after some time shows that velocity of light is greater than the velocity of sound.
The first attempt to find the velocity of light was made by Galileo in 1600.
2. GALELLEO’S EXPERIMENT
Two observers wore stationed at a distance of a few kilometres. One observer uncovered his lamp and the second observer uncovered his lamp after seeing light from the lamp of the first observer. The first observer tried to measure the time interval between the uncovering of his lamp and the light seen from the lamp of the second observer. If the distance between the two observers = x, then c = 2x/t.
But Galileo failed to find the velocity of light as the time interval t was small and could not be measured accurately. Romer, a Danish astronomer, made the first successful attempt in 1676.
3. ROMER'S ASTRONOMICAL METHOD
Romer observed the eclipses of the Jupiter's satellites at times when earth was at different positions with respect to Jupiter. He found that while the earth, in its orbital motion round the sun, receding from Jupiter, the mean period between two successive eclipses of a particular satellite is longer than that when the earth is moving nearer the Jupiter. This anomaly formed the basis for the calculation of velocity of light. He explained when the earth is receding from Jupiter, light has to travel a greater distance at each successive disappearance of the satellite whereas when the earth is approaching the Jupiter, light has to travel a shorter distance at each Successive disappearance of the satellite.
Fig. (1)
Jupiter has a number of satellites or moons revolving round it. Jupiter makes a complete revolution around the sun in 11.86 years whereas earth completes one revolution in one year. It is assumed for the sake of simplicity that the orbits of the earth and the Jupiter are circular.
The satellites which revolve round the Jupiter have their periods lying between 11 hours 58 minutes for the satellite nearest the planet and 16 days, 16 hours, 32 minutes and 11 seconds for the most remote satellite.
As the satellites revolve in orbits nearly parallel to the plane of the Jupiter's orbit, each satellite, once in every revolution, enters the shadow of the Jupiter and so becomes eclipsed (Fig.1). Romer studied the eclipses of the innermost satellite of Jupiter. At some time, Jupiter J1and the earth E1 are on the same side of the sun and are in conjunction. If light were transmitted instantaneously, the actual time of eclipse and its observation on the earth should be the same. If light has a velocity c, then light from the satellite at the time of eclipse has to travel a distance J1E1before reaching the earth. Thus, the eclipse will be observed at a time (J1E1 /c) later on the earth.
When the earth moves from opposition to conjunction, Romer observed that the time interval taken by the earth was 32 minutes 52 seconds.
Taking the diameter of the earth's orbit as 185 6 x 105 miles and the time interval is 1972 seconds, Romer calculated the value of c as
c =2 X 185.6 X 106 / 1972 miles/second
= 186,000 miles/second (approx.).
This method is not very accurate due to the following reasons:
(i) Orbits are not circular but they are elliptical.
(ii) Correct value of the diameter of the earth is not known.
(iii) It may not be possible to note the exact time when the eclipse occurs.
4. FIZEAU’S METHOD
The first terrestrial method for determining the velocity of light was performed by Fizeau in 1849. The experimental arrangement is shown in Fig. (2).
A bright source S emits light which after passing through a lens L and after reflection from the plate P is converged to a point H. The point H lies at the focus of the lens L1and in a space between the two teeth of the wheel W. Therefore, the light after passing through L1 is rendered parallel and after travelling a distance of few miles is allowed to fall on the lens L2. The light after refraction through the lens is brought to focus at A, which is also the pole of the concave mirror M. The radius of curvature of the mirror M is equal to twice the focal length of the lens L2. Due to this, the rays are reflected along their original path. The eye placed behind the eyepiece B (Fig 2) can thus observe an image of S.
Fig.(2)
The rim ofthe toothed wheel W is at H and the wheel is rotated about a horizontal axis. This is the important part of Fizeau's experiment. The teeth and spaces of the wheel are of equal width. Fizeau used a wheel with 720 teeth.
Working. When the wheel W is rotated, an image of the source is observed through E as long as light passes through the space of the wheel towards E. The wheel is rotated at such a speed that the rays passing the space fall on a tooth on their return. When this is adjusted, then no image of the source S is seen by the eye. If the speed of rotation of the wheel is doubled, again the image of the source S is seen by the eye because the rays on their return journey again pass through the next space. When the speed of the wheel is three times the first, the eye sees no image of the source because the rays on the return fall on the next tooth. In this way, if the speed of the wheel is continuously increased the image of the source S will be alternately blocked and seen.
If the distance between H and A is equal to d and the wheel makes n rotations per second when the first eclipse is observed, then the time taken by light to travel from H to A and back is
t = 2d/c
If the wheel has m teeth and m spaces, and in the time t, the wheel moves from the centre of the space to the centre of the tooth then,
t = 1/2mn
If n2 is the number of rotations/second of the wheel when the second eclipse is observed then
,
Because n2= 3n.
In Fizeau’s actual experiment
n = 12.6 rotations/second,
m = 720
d =8633 metres
c= 4mnd
= 4 x 720 x 12.6 x 8633
= 3.13 x 108 m/s
The main advantage of the method is that the principle involved is simple and Fizeau actually took the idea from the experiment attempted by Galileo (covering and uncovering the lamp).
It should be remembered that Fizeau's experiment is not free from criticism due to the following reasons:
(1) The complete eclipse or disappearance of light cannot be obtained due to scattering of light from the teeth.
(2) The image of the source is very faint because the intensity of light is considerably decreased due to refraction and reflection at various surfaces of the lenses and the mirror.
(3) Uniform speed of rotation of the wheel cannot he attained.
(4) The appearance or disappearance is not abrupt but it takes place gradually from maximum to minimum and vice versa.
Improvement.
(1) Cornu in 1874 determined the velocity of light by Fizeau's method with improved apparatus. He used a distance of 23 kilometres and instead of determining the velocity of rotation of the wheel for the disappearance of the image, he determined the velocity for which the brightness of the image appears to become minimum and where the image begins to increase in brightness. He took the mean of these velocities as the true velocity of rotation of the wheel for the purpose of calculation. His result for the velocity of light in air is 3.004 x 108 metre per second.
(2) Young and Forbes in 1881 determined the velocity of light by Fizeau's method and bevelled the teeth of the wheel so that light stopped by the teeth of the wheel was reflected to the sides. Moreover, they used the silvered plate having a small aperture for viewing the image instead of the glass plate P. They calculated the value of c as 3.013 x 108 m/s.
(3) Parrotin used Fizeau's method and kept the distance equal to 40 kilometres and calculated the value of velocity of light in air as 2.999 X 108 m/s.
5. MICHELSON’S METHOD ( ROTATING MIRORR NULL METHOD)
A. A. Michelson, an American Physicist, spent many years of his life in measuring the velocity of light. The method devised by him in the year 1926 at the Mount Wilson observatory is considered accurate.
The form of apparatus designed by him is shown in Fig. (3).
Light from an arc after passing through a narrow slit S is reflected
Fig. (3)
From one face of the octagonal rotating mirror R. Then it is reflected from the small fixed mirrors B and C to a large concave mirror M1. The point on the mirror C from where light is reflected is the focus of the concave mirror M1. The light then travels as a parallel beam to another concave mirror M2, and it is reflected to a planemirror D at the focus of the concave mirror M2. (The focal lengths of the concave mirrors M1, and M2 were nearly equal to 30 ft and aperture 2 ft. The distance between the two mirrors was about 22miles). The light is then reflected back to the concave mirror M2 travels back to M1 and is therefore reflected to a plane mirror E placed just below C. From E the light is reflected to a plane mirror F and is then incident on the face A' of the octagonal mirror opposite to A. The final image is viewed through a micrometer eyepiece T with the help of a total reflecting prism P. When the rotating octagonal mirror is stationary, the image is seen by light reflected from the top surface A'. When it is rotated the image disappears. The speed of rotation of R is suitably adjusted so that the image reappears and is seen in the same position as when R is stationary. The light reflected from A arrives at A' in the time taken by R to rotate through 45o or 1/8 of a revolution so that the next face is present at A. For this critical speed, the beam is reflected from the next face exactly along the same path as when the mirror was stationary.
If the distance travelled by light in its journey from A to A' is equal to d, then
c = d/t
If R makes n revolutions per second, then
Thus c can be calculated.
Michelson set-up M1 at an observing station on Mt. Wilson and M2 at Mt. St. Antonio in California, at a distance of 22 miles. The velocity of the revolving mirror R was measured by stroboscopic comparison with an electrically maintained tuning fork. He obtained the value of c = 2.99797 x 108 m/s.