what ia the dramatic importance of the passage ACT 1 SCENE 3 WHEN POLONIUS ENTERS?

That is not a passage. It is a stage command or "cue".

It is the scene in which Polonius' oft-quoted "advice to Laertes" speech occurs. They both play an important part in the story line.

I think it set the social conflict for the rest of the play: that which is rotten in Denmark. The choice is what the brother says, and the father says: truth vs nonsense maxims. The truth is that Hamlet will love just as much as Denmark allows, no more, and that is what is rotten in Denmark.

It's also setting up the parallel plot -- Hamlet avenging his dad's death = main plot; Laertes avenging his dad's death = secondary (parallel) plot.

Parallel plots are included to set up "foils" for the main plot -- here, to contrast how Laertes reacts (immediately and violently) to how Hamlet reacts (hem-hawing around, avoiding making a decision and acting on it...).

The dramatic importance of the passage in Act 1 Scene 3 when Polonius enters in Shakespeare's play Hamlet lies in several factors. This scene is crucial for character development, plot advancement, and the exploration of themes within the play.

To determine the dramatic importance of this passage, follow these steps:

1. Read the passage: Begin by reading Act 1 Scene 3 of Hamlet, paying close attention to the dialogue and actions of the characters involved, especially Polonius.

2. Analyze Polonius' character: Polonius is a minor character in the play but holds significant dramatic importance. Consider his role as a father to Ophelia and Laertes, as well as his position as an advisor to King Claudius. Pay attention to his traits, motivations, and how they affect the story.

3. Consider the plot advancement: This scene helps advance the plot in several ways. Polonius, being a trusted advisor to King Claudius, provides insight into the political climate of the court. He also conveys important information, such as the instructions he gives to Ophelia about her relationship with Hamlet. This sets the stage for subsequent events.

4. Examine the exploration of themes: Shakespeare often incorporates various themes into his plays. In this scene, themes such as appearance vs. reality, manipulation, and the complexities of familial relationships can be observed through Polonius' actions and dialogue. Consider how Polonius embodies these themes and how they contribute to the overall dramatic impact of the passage.

5. Connect with the larger narrative: Finally, consider how this scene fits into the larger narrative of the play. Does Polonius' entrance contribute to the overall themes and conflicts of the story? Does it foreshadow events or create tension? Draw connections between this passage and other significant moments in the play to fully understand its dramatic importance.

By following these steps and analyzing the passage, you can elucidate the dramatic importance of Act 1 Scene 3 when Polonius enters in Hamlet.