  Recent wide-field surveys discovered new types of peculiar optical transients
that showed diverse behaviors of the evolution of photospheric properties. We
develop a general theory of homologous explosions with constant opacity, paying
special attention on the evolution of the photospheric radius $R_{\rm ph}$. We
find that regardless of the density distribution profile, $R_{\rm ph}$ always
increases early on and decreases at late times. This result does not depend on
the radiation and cooling processes inside the ejecta.The general
rising/falling behavior of $R_{\rm ph}$ can be used to quickly diagnose whether
the source originates from a supernova-like explosion. The shape of the $R_{\rm
ph}$ evolution curve depends on the density profile, so the observations may be
used to directly diagnose the density profile as well as the temperature
profile of the ejecta. All the well-monitored supernovae show such a $R_{\rm
ph}$ rising/falling behavior, which is consistent with our theory. The recently
discovered peculiar transient AT2018cow showed a continuous decay of $R_{\rm
ph}$, which is disfavored to be of a supernova-like explosion origin. Our
result therefore supports the interpretation of this transient as a tidal
disruption event.
