Refractive indices of Zamzam, bottled drinking and distilled waters have been measured by computer simulation phase shifting digital interferometry at six discrete wavelengths across the visible spectrum. Some  optical parameters related to the refractive index were deduced,  such as: specific refraction; polarization; group refractive index;  permittivity; transmittance  and  reflectance. The dispersion of the deduced  optical parameters across the visible spectrum was calculated. The computer simulation phase shifting digital interferometer have been used  to design an experimental setup to investigate the   intensity distribution of the correlation fringes  obtained for Zamzam, bottled drinking and distilled waters. The present  computer simulation phase shifting digital interferometer  and the new theoretical formulae   have been confirmed with  a previous  experimental results. Error value of the measured and the calculated optical parameters have been given. A detailed study between the new equations and the Cauchy dispersion equation is presented. The present study proved that Zamzam water has special and distinct optical properties  that are different than those of  bottled drinking and distilled waters.