When the light source is with Gaussian shape spectrum, a dispersion media is inserted in the optical path to deduce the light intensity of double-beam interferences, and the analytic expression of the light intensity is obtained. The dependence of interference fringe visibility and visible range on media thickness, media dispersion and spectral line width are analysed. Meanwhile, the relations between phase and light intensity are also investigated. It′s concluded that the white light interference can also be used to measure both the media dispersion and the group refraction index; the formulation of spectral line width with high measurement accuracy can be deduced; the maximal interference fringe visibility does not appear exactly at the maximal light intensity point; an error of a quater of center wavelength is introduced when one objects the 3rd conclusion above. Some of this conclusions are certified with light sources of different spectral line width experimentally.