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 SPEED OF LIGHT One of the earliest references of the velocity of light are given in the ancient Indian Rigveda, where a particular hymn pays respect to the sunlight by mentioning its speed in ancient units of distance and time, "2202 yojanas in one nimish". When calculated to SI units, this value comes out to be about 3.0 x 108 ms-1, which is very close to the exact value. This exact value was defined in 1983 to be 299,792,458 ms-1, and the unit of distance, metre was defined from this constant. This value of the speed of light is a fundamental concept in physics. Almost every of Einstein's equations in his special theory of relativity has this constant, which he used to denote with the letter 'c'. It was shown by him that the speed of light is the same in all inertial frames, i.e. the speed of light measured by a person in a stationary laboratory, and one measured by a person in a frame moving at a very high velocity is the same, no matter how fast is the frame moving. The speed of light has also been defined as an ultimate barrier, one which cannot be broken by any massive particle (particle carrying some mass). It was proved that as the velocity of a body increases, so does its mass, according to the expression mv = ms ( 1 - (v/c)2 )-1/2 where, mv is the mass of the moving body, is the mass of the same body when stationary, v is the velocity of the body, and c is the velocity of light. The expression (1-(v/c)2)-1/2 is known as the Lorentz factor and is often written as the Greek symbol '(' (gamma). The ratio v/c is often expressed as '\$' (beta). One of the first few people to have attempted to calculate the velocity of light was Galileo, who used two lanterns placed on two different mountains, both of which had shutters that were to be closed and opened by two people standing on each hill after oberving the light coming from each other's lanterns. However, his method was not very successful, because even if the distance between the two hills would be as large as 15km, light between them would cover the distance in only about ten-thousandth of a second, which was too less a time for a human to react to. Some years later, a Danish astronomer, Ole Roemer calculated the value of the speed of light as 2.2 x 108 ms-1, which was later shown to be too low a value. The method used by Roemer was to record the time Jupiter's moons took to circle the planet, by observing that at certain times of the year the moons seemed to be a liitle ahead or behind their time-table. He relalised that this must be due to the different distances that the light has to travel. An English astronomer, Bradly, in 1728, proposed another method to calulate the speed of light, which gave results that were quite close to the exact value. The first measurement of the speed of light from purely land-based experiments was made by a French physicist, Armand Fizeau in 1849. Another method was proposed a year later by another French scientist, Leon Foucault. American scientist Michelson came up with another method some years later. Fizeau's method This method proposed by Frech scientist, Fizeau in 1849, used light rays emerging from a source, S placed at a certain distance from a convex lens, LA. The light beam refracted by the convex lens is made to fall on a semi-transparent material plate, G, which reflects a part of the incident light onto a toothed wheel that sends out the light rays in regular bursts. These light beams covers a large distance of upto hundreds of kilometers before being converged back onto the rim of the wheel. As this toothed wheel is rotated, it makes only those light rays form an image that pass through a gap in the rim. Those rays that hit a tooth do not form an image. As the angular velocity of rotation of the wheel is increased, the image flickers due to interception of light by the teeth. However, at a particular angular velocity, no image is seen at all. This is because this angular velocity is such that by the time light passes through a gap, goes to the mirror and comes back, a tooth comes in its way, and intercepts it. The angular velocity of the wheel T, distance between the mirror and the wheel, d and number of teeth in the wheel, n are then measured and the velocity of light can then be calculated using the formula c = 2dnT/B If the wheel makes v revolutions per unit time, the expression can be written as c = 4dnv However, this method has two drawbacks. First, the distance between the wheel and the mirror being so large, the image formed is very dim. Secondly, since the distance is so large, the experiment cannot be done inside a laboratory and needed a large open space. Foucault's method This method, proposed in the middle of the 19th century, was just an improvement over Fizeau's method, and tried to remove its drawbacks. Light from a source, S is made to pass through a convex lens, L after being partially transmitted by a glass plate, G. the convergent beam emerging from the lens is intercepted by a plane mirror, M1 that is capable of rotation along an axis perpendicular to the plane of the screen. The light reflected by the plane mirror is converged onto a concave mirror, M2, which is at a distance equal to its radius of curvature, R, away from the plane mirror's axis. Theis arrangement is made to ensure that the central ray reflected by the plane mirror retraces its path. Now, if M1 is still, the beam being emited by S retraces its path, and forms an image on being reflected by the partial reflecting glass plate, G. But when the plane mirror is rotating with an angular velocity of T, the image formed by the beam that retraces its path will be slightly displaced from the original one. Everytime the mirror rotates by an angle of )2, the light reflected by it the second time forms an angle of 2)2 with the one reflected earlier. Hence, from the diagram, it is clear that OO' = R(2)2) where, O' is the point from where the reflected rays seems to come from, due to the rotation of the plane mirror. It can also be seen that SS' = II' = s where, S' is the point where the part of the light rays that completely retrace their path converge finally. Thus, magnification produced by L is given by SS' / OO' = a / (R+b) where, a is the distance of doure from the convex lens and b is the distnce of the mirror from the convex lens. Hence, s / (2)2) = a / (R+b) Since light travels at a speed of c, it takes time t = 2R /c to go from M1 and come back to it again after reflection from M2. Now, )2 in the above equation can be written as T)t. Replacing T)t in the above equation by 2RT/c, s / (2R(2RT/c) = a / (R+b) Hence the expression for the speed of light can be written as: c = (4R2Ta) / s(R+b) Since all the quantitiies on the right hand side are known, Foucault could calculate the speed of light. This method does not require a very large space as in Fizeau's method and can easily be performed inside a laboratory. Another advantage of this method was that it could be used to measure the speed of light in media other than air. The whole experiment could be performed in water, or any denser material like glass could be placed in the light's pathway to determine the speed of light in that media. Michelson's method This method given by Albert Michelson, came few years after the two above. Light from a source S is mde to fall on one face, pq, of a polygon-shaped mirror, whose centre lies on the prinicipal axes of two concave mirrors placed facing each other at a large distance of several kilometers apart, one on each side of the polygon. The light reflected from the mirror, is made to fall on the lower region of one of the concave mirrors after reflection from two plane mirrors, M1 and M2 in such a way that reflected light travels parallel to the principal axis. This light falls on the lower portion of the other concave mirror, and is reflected by a plane mirror placed at its focal point onto the upper region from where it is again reflected parallel to the principal axis. This light then reaches back to the first concave mirror, from where it is reflected onto another face, tu, of the polygon after reflection from another two plane mirrors, M3 and M4. When the polygon-shaped mirror is stationary, an image of S is seen in the telescope by this light. But, when the mirror rotates, the light reflected by the face of the polygon does not reach the telescope and no image is formed. However, an image is again formed when the next face, uv comes into place of tu and the image is again seen. When one looks through the telescope, it is seen that as the angular velocity of the polygon is increased, the image flickers at first, but at a particular velocity the image does not flicker at all. Let this angular speed be T. But if the polygon moves )2 in time )t, T can also be expressed as )2/)t, which can then be written as (2B/N) / (d/c) = 2Bc / dN where, N is the number of faces in the polygon-shaped mirror, and d is the distance traveled by light between the reflection from the two faces of the polygon-shaped mirror. Therefore the expression for the speed of light becomes: c = dTN / 2B = dvN where v is the frequency of rotation. The speed of light is different in different media of different densities, the maximum being in pure vacuum. As the refractive-index of a medium increases, the speed of light in that medium decreases. This led to another difinition for the refractive index of a material, besides the Snell's law: : = speed of light in the medium / speed of light in the air As shown earlier, according to Special Relativity, no body can travel faster than the speed of light. But this barrier is only in vacuum. In other media, where the velocity of light less than 3.0x108 ms-1, certain particles can actually be accelarated to speed higher than that. In such a condition, the glowing of these 'faster than speed' particles can emit a blue glow known as 'Cerenkov radiation'. Some scientists believe that there are certain particles, known as tachyons, that can actually travel at speeds faster than light. However, any such particles have not been detected till date. In the recent times, some scientists have made claims that they have sent electromagnetic waves at speeds faster than light. In June, 2000, a team of Italian scientists reported that they have suceeded in sending a faster-than-light microwave pulse over a distance of about 1m with the help of a simple apparatus. However, the analysis of the wave-form of the microwave being very complex, the interpretation of results is still very debatable. (adapted from http://tier.net/spacetime/readpage.asp?page=060500.htm) Another group of scientists, one month later claimed to have used lasers and specially prepared atoms to make pulses of light zoom through a tube at speeds much greater than that of light. They claim that the peak of the light pulse had left the tube 63 billionths of a second bore it had even entered! (adapted from http://biz.yahoo.com/rf/00720/n2064618.htm) But these experiments are yet to be confirmed to edit the firmly set views about light, and what the final results will be, only time can tell. Colours  |  Speed of Light  |  Wave-Particle Duality  |