Speed of light demonstration using Doppler beat

Abstract

From an apparatus previously designed for measuring the Doppler shift using a rotating mirror, an improved, versatile version was developed for speed-of-light demonstrations in a classroom or a teaching laboratory. By adding a second detector and adequate beam-splitter and mirrors three different configurations are easily assembled. One configuration is used for time-of-flight measurements between a near and a far detector, allowing to measure the speed of light provided that the path length between detectors is known. Another variation is the interferometric method obtained by superposing the far and near signals, in such a way that a minimum of the combined signal is obtained when the time delay makes the signals arrive out of phase by π radians. Finally, the standard Doppler configuration allows the measurement of the frequency beat as a function of the rotation frequency. The main advantages of the apparatus are: a) the experimental setup is simple and completely accessible to undergraduate students, b) the light is visible, students can see the rays, which, with the use of appropriate screens, can be blocked at any point along their paths, c) the experiment can take place entirely within the teaching laboratory or demonstration room (using the interferometric method, the shortest distance to the far mirror was as small as 0.5 m), d) different configurations can be built, including some economical setups within the budget of teaching laboratories.

An undergraduate laboratory experiment to accurately measure the speed of light

“…They then have to carefully measure (or deduce) d 3 to d n (n = 20 in the example in figure 4) to calculate (L tot − d 1 ) = (d 2 − d 1 ) given + n i=3 d i . The uncertainty in their path-length measurements can then be propagated through equation (8) to determine the uncertainty in their calculation of the speed of light.…”

“…This can be carried out in undergraduate laboratories with an accuracy of a few percent, by pulsing a laser beam and by using a fast photo-detector. Alternatively a continuous wave laser beam directed onto a mirror rotating at high speed can be used so the returning beam translates a small distance due to the flight time (Foucault's method, see [7,8] for modern versions of this experiment which can now produce accuracies of ∼1%). In both cases the speed can be measured, however the experiments tend to require a large footprint in the laboratory.…”