  We study the weak-field deflection of light by mass distributions described
by two-power-law densities $\rho(R)=\rho_0 R^{-\alpha}(R+1)^{\beta-\alpha}$,
where $\alpha$ and $\beta$ are non-negative integers. New analytic expressions
of deflection angles are obtained via the application of the Gauss-Bonnet
theorem to a chosen surface on the optical manifold. Some of the well-known
models of this two-power law form are the Navarro-Frenk-White (NFW) model
$(\alpha,\beta)=(1,3)$, Hernquist $(1,4)$, Jaffe $(2,4)$, and the singular
isothermal sphere $(2,2)$. The calculated deflection angles for Hernquist and
NFW agrees with that of Keeton and Bartelmann, respectively. The limiting
values of these deflection angles (at zero or infinite impact parameter) are
either vanishing or similar to the deflection due to a singular isothermal
sphere. We show that these behaviors can be attributed to the topological
properties of the optical manifold, thus extending the pioneering insight of
Werner and Gibbons to a broader class of mass densities.
