Do you think Claudius and Polonius have the same reason for spying on Hamlet and Ophelia?
Absolutely not. Claudius, as the King who killed Hamlet’s father and is fearful of his nephew’s desire for revenge, spies on Hamlet to see if he suspects foul play. Polonius spies on Hamlet because he believes Hamlet has `gone mad’ over unrequited love of his daughter and, also (more importantly, to him) to prove himself right in his estimation of Hamlet’s `madness’ (as he says himself, “I will find where truth is hid though it were hid in the very center” in other words, `I know what I’m talking about, as I always do’). I don’t believe Polonius AT ALL suspects Claudius of having murdered King Hamlet and is only trying to do his duty as King’s Counselor and, also, as said, because of his ego-stake in the whole situation of needing to be seen as competent. The text of the play, I believe, bears this interpretation out.