  In a recent work PRD 106, L021501 (2022), a new geometric approach is
proposed to obtain the photon sphere (circular photon orbit) and the black hole
shadow radius. In this approach, photon spheres and the black hole shadow
radius are determined using geodesic curvature and Gaussian curvature in the
optical geometry of black hole spacetimes. However, the calculations in PRD
106, L021501 (2022) only restricted to a subclass of static and spherically
symmetric black holes with spacetime metric $g_{tt} \cdot g_{rr}=-1$,
$g_{\theta\theta}=r^{2}$ and $g_{\phi\phi}=r^{2}\sin^{2}\theta$. In this work,
we extend this approach to more general spherically symmetric black holes (with
spacetime metric
$ds^{2}=g_{tt}dt^{2}+g_{rr}dr^{2}+g_{\theta\theta}d\theta^{2}+g_{\phi\phi}d\phi^{2}$).
Furthermore, it can be proved that our results from the geometric approach are
completely equivalent to those from conventional approach based on effective
potentials of test particles.
