Inside the palace, Claudius finds out that Hamlet is alive and coming home. Surprise!
Claudius just can't stop with the flattery and praise for Laertes, which is a super way to get the young man to be the fall guy for killing Hamlet.
He brings up some noble Norman who allegedly (emphasis on the "allegedly") said that Laertes was a fantastic fencer. Claudius claims this really infuriated Hamlet, who wanted to challenge Laertes to a duel.
Question: what would Laertes be willing to do to prove that he loves his father?
Laertes announces he'd cut Hamlet's throat in a church, if need be.
Great. Here's the plan: Once Hamlet gets home, Laertes will keep to himself, and everyone else around will be full of praise for his fine sword skills. Claudius figures they can get Hamlet to agree to have a duel. He's even willing to put a little bet down on the fight, which might help to convince the Prince to join in.
Because Hamlet is trusting, he's unlikely to really examine the different swords available to the men in the fencing match. That means Laertes can choose a sword that isn't blunted (dull swords were used for these friendly duels), and then plunge it into Hamlet.
The guys then go into planning overkill. Just in case Laertes can't kill Hamlet with a sharp sword, they have a Plan B: a handy-dandy ointment of death obtained from the local mountebank (a traveling quack doctor). If Laertes dips the tip of his sword in the ointment and then stabs Hamlet, Hamlet's sure to die.
Claudius's final contribution to this scheme is a Plan C: He'll poison his own drink and offer it to Hamlet, who's sure to get hot and thirsty with all the fencing.
But first, some bad news: Gertrude comes in to inform Laertes that Ophelia has drowned in a brook.
She went to the brook with garlands of flowers, intending to hang them on the boughs of a far out tree as though they were crowns. A branch broke beneath her, and she tumbled into the brook.
At first, Ophelia's clothes made her float, so she sang old songs and generally appeared like a singing mermaid, without even thinking to cry for help. But her clothes became soaked and pulled her down into the brook, still singing.
Gertrude presents Ophelia's death as a kind of accident, but it may also have been a suicide. It's also not entirely clear how Gertrude knows all of this. Was she there when it happened?
Laertes, hearing of Ophelia's death, calls himself a "woman" for crying over his sister and leaves to be alone.
Claudius comments to Gertrude that he worked very hard to calm Laertes (uh-huh), and he's afraid this will make the kid flare up again.