My two cats have similar responses. When we got a freestanding mirror, both were interested in their reflection (they'd seen their own reflection before in other mirrors and have lost interest in those). They tried to smell and touch with their nose and both looked and walked behind the mirror. Shortly after that they lost interest and rarely seem interested again.

Whether or not they know it's their own reflection I can't tell. It certainly seems like they thought it might be another cat. Perhaps they either determined there was no cat, or determined that is was just their own reflection. Either way, they don't seem to care much.