Polonius and Gertrude wait for Hamlet in Gertrude's chamber. Polonius advises her to be tough with Hamlet. Just then they hear Hamlet coming. Polonius hides behind a tapestry.
Polonius has no idea that his spying is now pointless since Claudius already knows Hamlet has found him out.
Hamlet enters. Gertrude says he has offended his father (i.e. Claudius). Hamlet says that she's offended his father (i.e. Old Hamlet). Hamlet then furiously says he'll show her the "inmost part" of herself. Gertrude thinks he means he's going to kill her and cries out.
Hamlet suggests his mother is hiding from the truth she knows in her heart.
From his hiding place behind the tapestry Polonius hears Gertrude's cry and calls for help. Hamlet, mistaking Polonius for Claudius, stabs Polonius through the tapestry.
By stabbing Polonius (whom he thinks is Claudius) Hamlet proves it wasn't fear of killing that caused him to delay.
Gertrude shouts, "What a rash and bloody deed!" (3.4.27). Hamlet responds, "As bad… as kill a king, and marry with his brother" (3.4.29). Gertrude is shocked. Hamlet pulls back the tapestry and sees Polonius. He dismisses him as a "rash, intruding fool" (3.4.32).
Hamlet links Claudius's crime of murder with Gertrude's "crime" of marrying Claudius! Is he testing to see if Gertrude was in on the plot?
Hamlet forces Gertrude to look at a picture of his father and compare it to one of Claudius, whom he describes as a "mildewed ear" (3.4.64). Gertrude begs him to stop, but Hamlet can't: "but to live in the rank sweat of an enseamed bed, stew'd in corruption…honeying and making love over the nasty sty" (3.4.82-84). She again begs him to stop.
Hamlet's graphic description of Gertrude's lovemaking with Claudius makes it sound dirty and corrupt. Once more his anger at his mother's betrayal takes precedence over his goal of revenge.
The Ghost appears in order, it says, to refocus Hamlet on his duty—revenge against Claudius. Hamlet speaks to it. Gertrude can't see the ghost and thinks Hamlet's mad. The Ghost tells Hamlet to calm her.
The Ghost's visit is ambiguous. Why can't Gertrude see it? Why would it risk making Hamlet look insane? Many directors cut this scene.
Hamlet tries to convince Gertrude that he's sane, and begs her to confess her sins, to be pure and avoid sleeping with Claudius, and to keep secret that he, Hamlet, is not actually mad. Gertrude promises.
Does Gertrude agree to keep silent because Hamlet has convinced her he's right, or because he frightens her?
Hamlet exits, dragging Polonius's body after him.
Quests for vengeance often result in more than the intended death.