  In this work, we investigate the relationship between the photon sphere
radius and the first-order phase transition for the charged EPYM AdS black
hole. Through the analysis, we find with a certain condition there exist the
non-monotonic behaviors between the photon sphere radius, the impact parameter,
the non-linear YM charge parameter, temperature, and pressure. And both the
changes of photon sphere radius and impact parameter before and after phase
transition can be regarded as the order parameter, their critical exponents
near the critical point are equal to the same value $1/2$, just like the
ordinary thermal systems. These indicate that there maybe exists a universal
relationship of gravity nearby the critical point for a black hole
thermodynamical system. Furthermore, the effect of impact parameter on the
deflect angle is also investigated.
