How does Shakespeare use dramatic irony to show that Romeo and Juliet's love is doomed or finished in Act II, Scene 2 and Act III, scene 4?

Dramatic irony occurs when the audience knows something that a character(s) doesn't know. There are several instances of dramatic irony in Shakespeare's Romeo and Juliet. For almost the entire play, the love between the two young people is known only by two other people. The majority of the characters are not aware of what is really going on, and this proves to be a problem.  

Act II, Scene 2 is the balcony scene, one of drama's...

Dramatic irony occurs when the audience knows something that a character(s) doesn't know. There are several instances of dramatic irony in Shakespeare's Romeo and Juliet. For almost the entire play, the love between the two young people is known only by two other people. The majority of the characters are not aware of what is really going on, and this proves to be a problem.  

Act II, Scene 2 is the balcony scene, one of drama's most famous scenes. Romeo steals into the Capulet orchard to catch another glimpse of Juliet. He fell madly in love with her at the party earlier in the evening. The audience knows that Romeo is below the balcony, but Juliet does not as she utters the famous lines,

O Romeo, Romeo, wherefore art thou Romeo?
Deny thy father and refuse thy name,
Or, if thou wilt not, be but sworn my love,
And I’ll no longer be a Capulet.

In these lines she sums up the main conflict in the play. The Montagues and Capulets are bitter enemies and the only way the love between the two will succeed is if they "deny" who they are. Since they cannot escape their identities their "forbidden" love is doomed.

Act III, Scene 4 is one of the best examples of dramatic irony in the play. After the death of Tybalt, Lord Capulet is looking for a "day of joy" so he goes back on his earlier ideas about Juliet marrying Paris and promises his daughter to the Count. It is particularly ironic because while he is arranging a wedding for Juliet, she is in her bedroom with Romeo. The two have been joined by Friar Lawrence earlier in the day and are consummating the marriage. Neither Lord Capulet, his wife, or Paris have any idea. The arranged marriage with Paris greatly contributes to the ultimate tragedy. After the Nurse advises Juliet to forget Romeo and marry Paris, she becomes desperate and agrees to the Friar's unfortunate plan for her to fake death.