What: Hamlet conjures a play mirroring his father's murder
May be the devil, and the devil hath power t' assume a pleasing shape. Yea, and perhaps out of my weakness and my melancholy, as he is very potent with such spirits, abuses me to damn me. I’ll have grounds more relative than this. The play’s the thing wherein I’ll catch the conscience of the king.
Act 2, scene 2
Why: Hamlet is unsure if the apparation he encountered was really his father, and wants to prove Claudius's guilt by staging a play just like his father's murder.
What: Polonius believes that Hamlet is acting strangely because of his love for Ophelia.
[Is he} Mad for thy love?
My lord, I do not know. But truely, I do fear it.
Act 2, scene 1
Why: Ophelia explains her strange encounter with Hamlet, and how he was acting very strangely. This causes Polonius to believe he has found the source of Hamlet's behavior.