Wavelength and Refractive Indices from Interferometry

Abstract: PASCO scientific 012-05187C Precision Interferometer is used in Michelson mode to investigate wavelengths and refractive indices. From varying the distance of the movable mirror in the Michelson setup the wavelength of the HeNe laser beam is found to be $630.6\pm7.9~\mathrm{nm}$; $0.28$ sigmas away from the accepted $632.8~\mathrm{nm}$ and agreeing with it. Then after considering the fact that the index of refraction for low pressure gasses varies linearly with pressure we place a vacuum cell in front of the movable mirror and pump out the air within it to find the individual slopes. By extrapolating the average slope we calculate the index of refraction for air to be $n=1.000226\pm0.000026$. This is $1.44$ sigmas away from the manufacturer's measured $1.000263$ and barely agreeing with it as we underestimated our error in the fringe count (which is caused by the change in pressure). Furthermore, the vacuum cell is replaced by a crown glass plate which is rotated to vary the length at which the EM wave travels in the Michelson interferometer. The angle of rotation is measured and utilized to find the refractive index of glass to be $1.514\pm0.006$; agreeing with the accepted value of $1.515$ as it is $0.125$ sigmas away from it. Thus, along with the wavelength observation this experiment is conducted successfully. Although the experiment to find the refractive index of air is conducted less successfully, it is also prosperous as the measured value is close to the accepted.