His reaction convinces Hamlet of Claudius's guilt.

Hamlet suspects that Claudius murdered him. : Hamlet's mother and widow of the murdered king.
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Hamlet then runs Claudius through, killing him.

In a soliloquy in the second scene of Act I, Hamlet condemns Claudius as a “satyr” (line 144) and agonizes over his mother’s hasty marriage to him, saying, “O!

One of the central questions of the play is why Hamlet delays in killing Claudius.
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— Hamlet finally kills Claudius.

That the marriage took place within two months after the late king's funeral deeply disturbs Hamlet.
: An apparition of old King Hamlet.
: Bootlicking lord chamberlain of King Claudius.

Claudius suspects there is something sane and threatening behind Hamlet's strange behavior.
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8. Some commentators argue that the force of Hamlet's hatred of Claudius stemmed not from the fact that Claudius killed Hamlet's father but because Claudius has acted out Hamlet's own long-repressed Oedipal fantasy, i.e., to eliminate the father and marry the mother.

The scene so unnerves King Claudius that he rises and ends the play abruptly.
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20. Why could Denmark order the English King to kill Hamlet?

(Hamlet’s father, old King Hamlet, was murdered by Claudius, who succeeds to the throne and marries the late king’s wife—Hamlet’s mother—Gertrude.) Like Hamlet, Electra seeks to avenge her father’s death.

Hamlet kills the old man in a rash act aimed at Claudius.

Hamlet is not justified in killing Claudius until it is clear that Claudius corrupts everyone around him and that he needs to be removed for the good of the state.

Introduction to Claudius in Hamlet ..

In the second scene of the first act, Hamlet, deeply disturbed that his mother (Gertrude) has married Claudius a short time after the death of old King Hamlet, says, “Frailty, thy name is woman!” (150).

Why isn’t Prince Hamlet King of Denmark? | Hamlet …

(Treat others with respect; follow the Golden Rule; Be tolerant of differences; Use good manners, not bad language; Be considerate of the feelings of others; Don't threaten, hit or hurt anyone; Deal peacefully with anger, insults and disagreements)

8. In the context of this play, when kings held absolute power and there was no independent justice system, can you think of any way to deal with Claudius other than to kill him?

Mar 08, 2013 · Why isn’t Prince Hamlet King of Denmark

Claudius, remember, had poured poison into the king’s ear as reported by the Ghost of the old king: While “sleeping in mine orchard,” the Ghost says, “A serpent stung me” (1.5.42-43).

An analysis of Claudius, Hamlet's Uncle - Shakespeare Online

Ophelia's presence in the play helps to reveal Hamlet's thinking, in particular his detestation of women as a result of his mother's hasty marriage to vile Claudius.
Imagery throughout the play dwells on Satan’s toxic influence on Elsinore and its inhabitants.