An extraordinary tabletop speed of light apparatus

Abstract

A compact, low-cost, pre-aligned apparatus of the modulation type is described. The apparatus allows accurate determination of the speed of light in free propagation with an accuracy on the order of one part in 104. Due to the 433.92 MHz radio frequency (rf) modulation of its laser diode, determination of the speed of light is possible within a sub-meter measuring base and in small volumes (some cm3) of transparent solids or liquids. No oscilloscope is necessary, while the required function generators, power supplies, and optical components are incorporated into the design of the apparatus and its receiver can slide along the optical bench while maintaining alignment with the laser beam. Measurement of the velocity factor of coaxial cables is also easily performed. The apparatus detects the phase difference between the rf modulation of the laser diode by further modulating the rf signal with an audio frequency signal; the phase difference between these signals is then observed as the loudness of the audio signal. In this way, the positions at which the minima of the audio signal are found determine where the rf signals are completely out of phase. This phase detection method yields a much increased sensitivity with respect to the display of coincidence of two signals of questionable arrival time and somewhat distorted shape on an oscilloscope. The displaying technique is also particularly suitable for large audiences as well as in unattended exhibits in museums and science centers. In addition, the apparatus can be set up in less than one minute.