Measurements of the Speed of Light Since light travels at a very high speed, early attempts to measure its speed were unsuccessful. Remember c = 3.00 x 10 8 m/s Galileo tried by using two observers separated by about 10 km. The reaction time of the observers was more than the transit time of the light.
Measurement of the Speed of Light – Roemers Method In 1675 Ole Roemer used astronomical observations to estimate the speed of light. He used the period of revolution of Io, a moon of Jupiter, as Jupiter revolved around the sun. The angle through which Jupiter moves during a 90° movement of the Earth was calculated.
Roemers Method, cont. The periods of revolution were longer when the Earth was receding from Jupiter. Shorter when the Earth was approaching Using Roemers data, Huygens estimated the lower limit of the speed of light to be 2.3 x 10 8 m/s. This was important because it demonstrated that light has a finite speed as well as giving an estimate of that speed.
Ole Roemers Investigation J1, E1 and J2,E2 are the positions of Jupiter and Earth approximately six months apart in their respective orbits around the sun S. Romer realized that the time difference between the maximum and minimum period times signified the finite speed of light. Light had to travel further to reach the earth when the two planets are on opposite sides of the sun. The Speed of light could be found by dividing the diameter of the Earths orbit by the time difference.
Christian Huygens calculation Using Ole Roemers data, Christian Huygens first did the arithmetic and obtained 211,000,000m/s for the speed of light. The correct value is 299,000,000 m/s. Despite Christian Huygens calculation being correct, the data that he got from Ole Roemers calculation was wrong. Roemer estimated that the time difference due to light crossing the earths orbit required 22 minutes. It has been since shown to require 16.7minutes only.
Measurements of the Speed of Light – Fizeaus Method This was the first successful method for measuring the speed of light by means of a purely terrestrial technique. It was developed in 1849 by Armand Fizeau. He used a rotating toothed wheel. The distance between the wheel (considered to be the source) and a mirror was known. By rotating the wheel at a certain speed, he allowed light from the source to pass through one gap on the toothed wheel on its way to the distant mirror and the reflected light through the next gap on its way back. Since he knew the angular frequency of the wheel, he could calculate the time interval between the two gaps and use it with the distance between the wheel and the distant mirror to calculate the speed of light.
Fizeaus Method, cont. d is the distance between the wheel and the mirror. Δ t is the time for one round trip. Then c = 2d / Δ t Fizeau found a value of c = 3.1 x 10 8 m/s. t = time between the two teeth
Michelson used a mirror rotating at about 520 revolutions per second. Speed of light = 2*35km/time. Time = time required for 1/8 rotation. This can be worked out from the known speed of rotation. Michelson obtained a value of about 299,775,000m/s.
How the Michelson Calculation works.