The three strange phenomena in measuring the refractive index of transparent medium with Michelson interferometer were analyzed. By considering the light dispersion and simplifying the visual function,the visibility of interference fringe,the range for moving mirror and the expression of refractive index were obtained. Meanwhile,the results were examined by experiments. Experimental results show that the refractive index measured with the above method is not the traditional phase refractive index but is the group index. Further more,the spectral dispersion at the central wavelength can be obtained by the measured group index and the known phase index.