We measured refractive indices and thicknesses of SiO$_2$ thin films that have been plated on LCD glass substrate for the purpose of preventing the out-diffusion of sodium ions. The best experimental condition to determine refractive index and thickness of SiO$_2$ thin film by using ellipsometry is searched for, where ⅰ) the film thickness is increased uniformly by 20 $AA$ from 0 $AA$ to the period thickness while the angle of incidence is fixed and ⅱ) the angle of incidence is increased uniformly by 1$^{circ}$ from 45$^{circ}$ to 70$^{circ}$ while the film thickness is fixed. We estimated the errors in determining the refractive index and thickness by comparing the measurement error of $Delta$ and Ψ with the calculated one. The ellipsometric constants of SiO$_2$ thin film on LCD glass substrate are measured at several angle of incidence around the Brewster angle, which is the best angle if the experimental error of ellipsometer is not sensitive to the incident angle. Also the best fit refractive index and thickness of SiO$_2$ thin film to these ellipsometric constants measured at several angle of incidenc eas well as the best fit ones to the SE data are obtained using regressional analysis.