Determination of the Refractive Index of a Solid using a Far Infra-red Maser

IF the mirrors of a Michelson interferometer, illuminated by monochromatic radiation of wave-length λ, are in the zero path-difference position, the insertion into one arm of a plane-parallel specimen of refractive index n and thickness t , placed so that the angle of incidence is θ, produces a path-difference x (θ) given by: If the specimen is rotated so that the angle of incidence changes from 0 to θ the path difference increases by the amount: and as a result m fringes pass the detector where: (2) and (3) may be combined and re-arranged to yield the linear relation: where: from which n is easily found either by direct calculation for each pair of y and x or from the slope of a straight line plot of ( y + 1) against x .