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).
Categories: astro-ph gr-qc