  Within the framework of the effective Lagrangian approach, we perform a
thorough analysis of the $J/\psi \to P\gamma(\gamma^*)$, $J/\psi \to VP$, $V\to
P\gamma(\gamma^*)$, $P\to V\gamma(\gamma^*)$ and $P\to\gamma\gamma(\gamma^*)$
processes, where $V$ stand for light vector resonances, $P$ stand for light
pseudoscalar mesons, and $\gamma^*$ subsequently decays into lepton pairs. The
processes with light pseudoscalar mesons $\eta$ and $\eta'$ are paid special
attention to and the two-mixing-angle scheme is employed to describe their
mixing. The four mixing parameters both in singlet-octet and quark-flavor bases
are updated in this work. We confirm that the $J/\psi \to
\eta(\eta^{\prime})\gamma^{(*)}$ processes are predominantly dominated by the
$J/\psi\to \eta_c \gamma^{*} \to \eta(\eta^{\prime})\gamma^{(*)}$ mechanism.
Predictions for the $J/\psi \to P \mu^+\mu^-$ are presented. A detailed
discussion on the interplay between electromagnetic and strong transitions in
the $J/\psi \to VP$ decays is given.
