  This paper extends the de-Sitter/anti-de Sitter (dS/AdS) background method
based on the optical metric for gravitational lens [Phys. Rev. D 105, 084022
(2022)] to a static optical constant-curvature (SOCC) background. It is shown
that the exact lens equation on the SOCC background can be written in the same
form as that for either Minkowski, dS or AdS background in terms of flat,
spherical or hyperbolic trigonometry, depending on the Gaussian curvature of
the equatorial plane in the SOCC background. To exemplify the SOCC method, we
consider the gravitational lens in Mannheim-Kazanas (MK) solution of Weyl
gravity, which includes Rindler and de Sitter terms. In the zero mass limit,
the deflection angle of light for the MK solution in the literature diverges to
infinity. This is because there is a self-contradiction in their perturbative
approximations of the MK metric and the orbit equation. The SOCC method
incorporates the long-distance curvature effect into the background. Thereby
the SOCC expression for the deflection angle of light in the MK solution is
finite also in the zero mass limit.
