Measuring the speed of light
Relative Theory Relative Theory


1.    Time-of-flight method
In general the amount of an object (e.g. a moving car, sound propagation, expansion of a light pulse) moving with constant velocity v is defined as the difference in distance s divided by the passed time intervall t:


As an example: If one is driving a car a distance s = 100 km from A to B in one hour, the avarage velocity of this car is 100 km/h = 28 m/s. For comparison sound is dispersing in air with a velocity of 340 m/s, whereas in water with 1500 m/s, light in vacuum approx. 300 000 000 m/s. The velocity of light c can be determined by this time of flight method measuring the interval Δs and the interval in time Δt.

From technical point of view it is not so easy to measure such high velocities. Historically several famous known methods are reported in literature: the astronomical method by Rømer in 1676, the terrestrial methods by Fizeau in 1849 and by Foucault in 1850. Common to all these historical experiments is the fact, that the small time intervall Δt (part of a second), which was not accurately measureable in those days, was compensated by very large distances. But nowaday light sources are available, by which one can produce a sufficiently short light pulse. With such short pulses one may use relatively small distances, e.g. few meters.

2.    Principle of measurement

In case of the driven car it is simple: one starts a stopwatch (at time t1 = 0) and is driving from A to B. At position B one stops the watch (t2 - t1 = Δt). The distance Δs one can read from the mileage of the car.

In case of sound propagation we follow the same principle: the answer is known to the following question, how far away is an thunderstorm. If one observes the lightning, then one starts counting the seconds till one can also hear the respective thunder. If we count till Δt, then we have to devide by 3 to get the distance in km. The estimation is Δs = v·Δt, with the velocity of sound v ~ 1/3 km/s. (image 1).

Fig. 1: Schematic representation of experimental setup.

We repeat in Fig. 1 the experimental setup with some more details: A light source (LED) emits a short light pulse (width of pulse about 20 ns), which hits a beamsplitter S and a fixed mirror T2 via an diaphragm F2 of the electro-optic unit and is reflected back on the same way; by transmitting the beamsplitter S this light pulse hits the detector D. This signal is displayed at the oscilloscope and acts as a reference signal, defining the starting point of "our clock" t1 = 0. A certain amount of the light pulse, produced by the LED and split up by the beamsplitter S, passes the diaphragm F1 of the unit; the fixed lense L transforms the light pulse into parallel light, which then hits a mirror T1 positioned at a certain distance Δs, this part of the light pulse is also reflected backward on the same way, is again reflected by the beamsplitter S and then it is detected by the same detector D. The oscilloscope displays this light pulse as a second signal. The time interval Δt between both signals belongs to the distance 2s between position diaphragm F1 and mirror T1 (two times because the light pulse travels back and forth).

Eminently important here is that both light pulses should be kept at the same height (Fig. 2). Therefore, the user of this experiment has to adjust the heights of the signals by means of two separateley operating diaphragms for mirrors T2 and T1.

Fig. 2: Measurement of time.

The animation of signals at the oscilloscope screen during movement of distant mirror T1 (Fig. 3) should give an impression of what is to be expected. Notice that the signals are adjusted to have the same height (voltage). The rectangular signal above the signals of light pulses has to be used for calibration of the time axis (frequency f = 10 MHz, i.e. period T = 100 ns).
3.    Importance of speed of light

The speed of light is one of the most fundamental constants in physics; this value is relevant in electrodynamics, in atomic physics, in astrophysics and special theory of relativity. In addition, this velocity plays an important role in technical applications, such as determination of distance on earth or in space as well as in the global positioning system (GPS). The value of speed of light is closely connected with the SI unit system; since 1983 the length unit meter is defined as:

The meter is the length of path traveled by light in vacuum
in 1/299 792 458 of a second.

4.    History of measurement of c
The first methods to determine the velocity of light c were astronomical observations (Rømer 1676, Bradley 1726). On the contrary to terrestrial methods these technics did not use a reflected light pulse. The first terrestrial methods were performed by Fizeau (1849) and by Foucault (1862). The chief attraction of the cogwheel method by Fizeau was to apply a frequency measurement (of the rotating cogwheel) instead of measurement of a time interval. The improvement of Foucault was to replace the cogwheel by a rotating mirror. The following generations of this kind of experiments were more or less variations and/or improvements of these first terrestrial methods. Experiments (Bergstand 1951) using the modulation of a light wave are quasi time of flight measurements.

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