  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 $\tilde{d}$ and show that it
satisfies the optical scalar equation. The distance provides relations between
quantities used in the gravitational lensing theory (the convergence-, the
shear- and the twist-term) and those used in the scalar optics theory (the
rates of expansion, shear and rotation).
