The main purpose of this paper is to construct and analyze the Michelson interferometer with rotating sample in order to measure refractive index of solid plate. The theoretical equation and experimental method was proposed in this work. The measured refractive indexes by this system are $n_{6328}$=1.5159 in BK7 and $n_{6328}$=1.4528 in fused silica. These values make a differences by 0.001 in BK7 and 0.003 in fused silica from those of reference. As a result, Michelson interferometer with rotating sample is very advantageous method to find refractive index of plate sample.