Answer:
Hamlet compares two portraits of King Hamlet and his brother, the present king and new husband of Gertrude, Claudius.
The conversation led to greater enmity or discord between the mother and son and also led to the death of Polonius who was eavesdropping on the two. Moreover, the encounter also led Gertrude to believe that her son is adamantly against his new step-father and also insane.
Step-by-step explanation:
William Shakespeare's "Hamlet" revolves around the young prince Hamlet and his desire to avenge the death of his father, the King at the hands of his uncle, who at present is the husband of his mother. The tragic play deals with themes of betrayal, greed, power, love, marriage, etc.
In Act III scene iv, Hamlet and his mother Gertrude are seen arguing about how he has behaved rudely to his new step-father, his uncle Claudius. Queen Gertrude reprimands her son and tells him to not act so against the new king. But Hamlet refuses, instead he points out the 'flaws' of his mother, telling her that she'd 'polluted' the marriage bed of her first husband, that of King Hamlet. During the conversation, Hamlet strikes Polonius who was hiding behind a curtain to spy on Hamlet. He was killed, which Hamlet had wished was the new king Claudius instead.
Hamlet uses a comparison between the two portraits to show the 'outrageous action' that Gertrude had done. He praises his father, the dead king's picture, stating "Hyperion’s curls, the front of Jove himself,
An eye like Mars to threaten and command,
A station like the herald Mercury
New-lighted on a heaven-kissing hill—
A combination and a form indeed
Where every god did seem to set his seal".
Whereas, for the current king, he is not too appealing in the eyes of the young prince
"a mildewed ear
Blasting his wholesome brother
Have you eyes?
Could you on this fair mountain leave to feed
And batten on this moor?"
The conversation between the mother-son duo led to the death of Polonius and also showed Gertrude to believe that Hamlet has gone insane. The ghost of King Hamlet appears but only Hamlet saw him while the queen cannot, leading her to believe that her son is indeed insane.