A phase refractive index is measured directly from an unwrapped spectral phase distribution whose 2π ambiguity is determined by fitting the spectral phase distribution with functions based on Cauchy's equation. The phase refractive index of a quartz glass with 20 µm thickness is measured exactly from three spectral phase distributions detected in two different configurations of a spectrally resolved interferometer. Since there is a high possibility that the 2π ambiguity cannot be correctly determined when there is a large difference between a function of the real refractive index and Cauchy's equation, characteristics of the fitting are examined.