Continuous Limit of Multiple Lens Effect and the Optical Scalar Equation

We study the continuous limit of the multiple gravitational lensing theory based on the thin lens approximation. Under the approximation, we define a new, light-path dependent angular diameter distance d̃ and show that it satisfies the optical scalar equation. The distance provides relations between quantities used in the gravitational lensing theory (the convergence-, the shearand the twist-term) and those used in the scalar optics theory (the rates of expansion, shear and rotation). Subject headings: cosmology:theory — distance scale — gravitational lensing