He was planning a way that would let Claudius know that he knows about the murder, in order to see his reaction, and he was able to do this without saying a single word, which is something a madman would not have the mind to do. By this point, Claudius knows that Hamlet is dangerous. He uses the excuse of Hamlet’s “insanity” to send him off to England, but really he just doesn’t want anyone finding out the truth about his murderous acts, which Hamlet was close to exposing.
In trying to expose the king, however, he sometimes appeared to get a little too caught up in his act of insanity. At times, though it may seem that Hamlet has gone truly mad, he is still aware of his actions. When he is talking to the Queen after the performance of The Mousetrap, he stabs and kills Polonius. Though he meant to do this, he wasn’t aware that it was Polonius behind the curtain - he thought it was the King listening in on their conversation, instead. As much as he disliked Polonius, he wasn’t aiming to kill an innocent man. So this action, one that could be seen as insane, was a misjudged, yet justified action, for he thought he was actually avenging the death of his father. When Hamlet tells the queen about his father’s murder, she simply thinks that he’s not in the right mind, but he tells