A prism-pair interferometer comprising two homodyne interferometers with a common light source was developed for high-precision measurements of the refractive index of optical glasses with an uncertainty of the order of ${10}^{-6}$ . The two interferometers measure changes in the optical path length in the glass sample and in air, respectively. Uncertainties in the absolute wavelength of the common light source are cancelled out by calculating a ratio between the results from the interferometers. Uncertainties in phase measurement are suppressed by a quadrature detection system. The combined standard uncertainty of the developed system is evaluated as $1.1\times {10}^{-6}$ .