Dr. Zhang certainly knew that Liu Yi handed over the mirror for him to try and use it to see the writing on the paper... if that sheet of paper was face up.
Not to mention whether this idea was feasible, just from this action alone, it was clear that this mental patient's reaction speed was extremely fast. Almost immediately after shouting, when no one responded, he began looking for a tool to smash the mirror.
That is to say, in that instant, he deduced that there must be some important information on that piece of paper, and guessed that Dr. Zhang would definitely go for it. He also realized from the way the paper fell that Dr. Zhang surely couldn't reach it, and even came up with the idea of using the mirror's reflection to solve the problem!
All the above truly verified the saying, "Insane people have wide-ranging thoughts!"
Dr. Zhang snapped back to reality, took the mirror shard... stretched it out of the window and adjusted the angle.