Planar graded index optical waveguides have been formed by Ag$^{+}$ ion exchange in the BK7 optical glass. The experimental results of diffusion and modal characteristics of Ag$^{+}$-Na$^{+}$ exchanged BK7 glass waveguides are presented. Measurements of the mode indices have been measured. We found the relations between the process and device parameters such as the diffusion depth and the square root of the diffusion time, diffusion coefficient and diffusion temperature, and diffusion ion concentration and surface index change. A theoretical gaussian function refractive index profile matched best with the measured data for all the guided modes. The empirical relations between the process and the device parameters are derived and subsequently used to formulate a systematic procedure for fabricating singlemode and multimode waveguides.uides.