Interference phenomena are the cornerstone of establishing the wave nature of light and have significant applications in metrology and spectroscopy. The double-slit interference phenomenon, as an important part of wave optics, has been widely discussed in various fields. In this paper, we will theoretically analyze the double-slit interference phenomenon using the principle of wave superposition and scalar diffraction theory, separately. The analysis shows that the product of the refractive index of the medium and the width of the interference fringes remains unchanged when other variables are unchanged. It is verified by the double-slit interference experiments in both air and water. By comparing the experimental results, the refractive index can be measured, and the measurement results are highly robust to variables such as the angle of the slits.