The refractive index of water is precisely determined in the visible light range as a function of the pressure until 250 MPa by means of a new measurement device that uses a special pipe tee included in an interferometer set. This technique allows revisiting the Bradley-Tait and Sellmeier equations to make them dependent on the wavelength and the pressure, respectively. The Bradley-Tait equation for the pressure dependence of the water refractive index is completed by a wavelength-dependent factor. Also, in the considered pressure and wavelength ranges, it is shown that the Sellmeier coefficients can be straightforwardly linked to the pressure, allowing the determination of the refractive index of water for either any wavelength or pressure. A new simple model allows the determination of the density of water as a function of the measured refractive index. Finally, the polarizability of water as function of pressure and wavelength is calculated by means of the Lorentz-Lorenz equation.