In the experiment of observing white light interference with a Michelson interferometer to measure refractive index of a transparent medium, a key step is to move a the moving mirror of the interferometeron the basis of observing white light interference without the introduction of the medium to be measured,so that the interference fringes appear again after the introduction of the medium. In actual experiments, interference patterns can be observed just when the moving mirror moves halfstandard distance.In this paper, the reasons for this phenomenon are theoretically analyzed, and comparative experiments are designed for experimental analysis. The theoretical and experimental results show that this phenomenon originates from the single passage of the beam through the medium which is small in size and occupies only a small part of viewfield.In addition, the interference fringes for this case appear outside the medium region, while the interference fringes for the standard case appear inside the medium region.