Final answer:
Hamlet is convinced of Claudius's guilt when he abruptly calls for lights to end the performance of 'The Mousetrap', signaling his distress and suggesting his involvement in the murder of Hamlet's father.
Step-by-step explanation:
When Claudius shouts for "lights" before the play "The Mousetrap" is over in Shakespeare's Hamlet, it is a pivotal moment. The play within the play is staged by Hamlet to catch the conscience of the King and unveil Claudius's guilt for the murder of Hamlet's father. Hamlet is convinced of Claudius's guilt when Claudius reacts to the reenactment of the murder by calling for lights and abruptly ending the performance; this reaction signifies his distress and hints at his culpability. This is a clear example of the maxim: 'the play's the thing wherein I'll catch the conscience of the King' being put to the test, and Hamlet sees the King's reaction as a confirmation of the Ghost's accusations.