Determination of the speed of light from the longitudinal modes beat frequencies of an open-cavity helium-neon laser

We empirically determined the speed of light by measuring the variation in longitudinal mode frequencies, or the beat frequencies, of an adjustable-length, open-cavity helium-neon laser as a function of its cavity length. The TEM$_{00}$ mode lasing output of the laser was analyzed using a fast frequency photodiode detector and a radio frequency spectrum analyzer. A Fabry-Perot interferometer was used to monitor the intensity of the longitudinal modes and we found that the phenomena of frequency pushing and pulling had little effects on the beat frequency measurements. Plotting the reciprocal of the beat frequency as a function of the change in cavity length, the speed of light was found, by using linear weighted least squares regression, to be $(2.997 \pm 0.003) \times 10^{8}$ ms$^{-1}$. This value is $0.3 \sigma$ away from the defined value of speed of light and is accurate to 1 part in 3200.