Abstract: Two interdependent differentiation equations between the ray cluster equation and dielectric refractive index function, i.e., light\|ray equation and refractive index equation were derived via Fermat principle and ray cluster equation. The expression of refractive index equation was presented in polar coordinate. Furthermore, the refractive index equation was applied to solving radial pattern index of cylinder lens in plane rectangular coordinates and radial pattern dielectric index in polar coordinate. The theoretical results are in good agreement with the facts.

Key words: light-ray optics, refractive index equation, Fermat principle, ray cluster equation