## Terrestrial measurement

In 1849, the French physicist Hyppolyte Fizeau (1819-1896) made the first terrestrial measurement of the speed of light, in a simple but ingenious way. A beam of light was passed through one of 720 notches around the edge of a rotating wheel, was reflected by a mirror and retraced its path, as shown in Figure 1.3. When the returning light passed through a notch, an observer could detect it; if it hit the disc between notches, the light was eclipsed. The 'round-trip' distance from the open

Hyppolyte Fizeau

rotating toothed wheel (720 cogs) A

source rotating toothed wheel (720 cogs) A

source observer

Figure 1.3 Fizeau's experiment to measure the speed of light.

observer

Figure 1.3 Fizeau's experiment to measure the speed of light.

notch to the mirror and back to the edge of the disc was measured. Fizeau timed the eclipses and measured the rotational speeds of the disc at the time of the eclipses. With this information he calculated the speed of light in air and obtained a value only about 4% different from the currently accepted value of 299,792,458 ms-1.

Fizeau demonstrated considerable craftsmanship when he constructed the 720-cog wheel with the light focused accurately to pass through the gaps!

We can estimate the speed at which Fizeau needed to rotate his wheel as follows:

Suppose that the distance d = 5 km. How fast must the wheel rotate so that a tooth has replaced a neighbouring gap by the time light which has passed through the gap has returned from its 10 km back-and-forth journey? (Assume that the speed of light c = 3 x 108 ms-1.)

Remembering that there are 720 teeth and 720 gaps, light must cover the back-and-forth journey 1440 times during each revolution of the wheel. This has to be repeated n times every second.

3 x 108

= 20.2 revs per second

Jesse Owens in Berlin 1986 Olympic Games.

1.3.3 The speed of light in context

The speed of light c is 3 x 108 ms-1 and the speed of sound in air is 330 ms-1. Light travels about 1 million times faster than sound!

The reaction time of an athlete to the start signal is about 0.3 seconds. In that time sound will travel a distance of about 100 metres, which means that it will have just about reached the finishing line of the 100 m sprint.

By comparison, light will have gone 100,000 km, or 2.5 times around the world!

In the everyday world the speed of light can be considered almost infinite. As we look at a landscape, light reaches us from different objects practically instantaneously. There is no appreciable delay between the light reaching us from a tree in the garden, and from the top of a mountain on the horizon. Radio waves and telephone messages reach us within a fraction of a second from the most distant places in the world. Light from stars and distant galaxies, however, may take billions of years to reach us.

The constant c is one of the fundamental constants of our universe, and nobody can tell why it has the value it has. It is interesting to speculate how different the laws of physics would be if the constant c had another value, particularly if it were much smaller — say, of the order of the speed of sound. Obviously the speed of communication would be reduced; it would take hours for news to reach us from other parts of the world. Travel by jet plane would not be safe, because we would not know what was ahead of us! These changes, however, are insignificant compared to the fundamental differences in space and time which would exist in such a 'slow light' universe. The features of Einstein's theory of relativity would now be part of the everyday world.

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