This scene involves Claudius, Gertrude, Rosencrantz, Guildenstern, Polonius, Hamlet, and Ophelia
This is the famous scene where Hamlet gives his "to be or not to be" soliloquy, and is a turning point in the play for Claudius, who reveals some guilt before Hamlet's soliloquy, and also comes up with a plan to eliminate the threat that is his nephew, as soon as he senses danger
Unfortunately for Polonius, who continues to believe that Hamlet is merely mad for Ophelia's love, this scene is the exact opposite of a turning point
This belief (or deception) will be Polonius' ultimate undoing, as we will see in the scenes to come
Plot Summary
Rosencrantz and Guildenstern report back to Claudius, but they can't give any reasons to explain Hamlet's madness (other than the fact that Hamlet said himself he is mad sometimes, sane other times), so they don't get any reward like Gertrude mentioned earlier
They only reveal that Hamlet seemed interested in the travelling actors who recently arrived, and that Hamlet invited the King and Queen as well - just then Polonius butts in to say, ever redundantly, that the King and Queen have been invited to the play as well
Rosencrantz and Guildenstern exit the scene, leaving Claudius and Polonius to lie in wait for Hamlet's interaction with Ophelia. Polonius hands her a prayer book to make it seem like she just happened to be wandering around, looking virtuous - his exact words were:
POLONIUS
...(To Ophelia) Read on this
book,
That show of such an exercise may color
Your loneliness.—We are oft to blame in this,
'Tis too much proved, that with devotion’s visage
And pious action we do sugar o'er
The devil himself.
(3.1.49-55)
He's making an observation that people often cover up their shameful secrets and lies with the presentation of behaviors that are the direct opposite to lying and deceit - "with devotion's visage...do we sugar o'er The devil himself."
These words strike Claudius as he, for the first time, reveals some guilt, and we, as an audience, are relieved to discover that the ghost is more realistic than we may have imagined
Hamlet enters the scene, Claudius and Polonius take their positions, and Hamlet begins his famous soliloquy, stopping only when he notices Ophelia
It seems that not only has Polonius instructed Ophelia to break his rule of not speaking to Hamlet, but he may have even instructed her to return the gifts she received to Hamlet, so as to trigger his apparent love sickness
Hamlet does deny that he ever gave Ophelia gifts, and he berates both her (for being stupid, for believing that Hamlet had ever loved her), and he berates the entire female gender as well
As Hamlet storms off, Claudius and Polonius enter the spotlight again, only to reveal that Claudius has somehow found some way to see through Hamlet's words of apparent madness
Claudius suspects that Hamlet is actually sane, and that he's actually a threat to Claudius, so he reveals that he'll immediately send Hamlet off to England to try to shake off any dangerous plans that Hamlet may have had
It's pretty impressive that Claudius has caught on to Hamlet's intentions so quickly - After all, this is Claudius' first observation of Hamlet since he has gone mad, and in contrast to all the other characters who have witnessed Hamlet's act of madness, Claudius has seen right through it
Polonius is still stuck on the idea of Hamlet being love sick, so he asks Claudius to have Gertrude have a private chat with Hamlet, where Polonius can once again spy on them and try to learn something
After Hamlet's beautiful and most famous soliloquy (To be or not to be), Ophelia comes to "redeliver" the gifts that Hamlet had once given her. How does Hamlet respond to this?
He accepts them and spits at them and stomps on them until they are unrecognizably destroyed
He rejects even the slightest idea that he had ever given gifts in the first place
He accepts them and simply leaves
He rejects them and says that it would hurt him too much to actually have them with him