How does Iago continue to provoke Othello's jealousy in Act IV?
I agree mostly with the first response given by another eNotes educator, but I would like to add a few important points from the beginning of the first scene in Act IV. In the first scene, Iago simply uses cryptic speech and hypothetical question to incite Othello’s further jealousy.
First, Iago is suggestive at asking a hypothetical question which is if someone could be naked and in bed with someone while not meaning any harm. Othello’s response is rife with jealousy:
Naked in bed, Iago, and not mean harm! / It is hypocrisy against the devil!
Iago, then puts this image in to Othello’s mind when this has most certainly not happened with his wife Desdemona and anyone else other than her husband. Iago then incites Othello even further by reminding Othello about the handkerchief. Iago mentions that any gift, like a handkerchief, that is a present from a husband, could be given away to any other man. Othello then suddenly “remembers” that he saw Cassio with the handkerchief that Othello had given to Desdemona.
It is at this point that Iago uses some very cryptic speech when he says that “what he did” was “lie.” When Othello questions further about how that is so, Iago replies “with her, on her, what you will.” This, combined with the first two incriminating ideas, makes Othello fall down into “a trance.”
In conclusion, we can’t leave out Iago’s use of Cassio. A later scene in act four is what the former educator is speaking about: Iago asks Othello to hide in order to observe Cassio speaking. It is important to note, however, that Cassio is speaking about Bianca and not about Desdemona. Othello has no idea, and this indicates an example of dramatic irony: a time when the reader/watcher knows something that the character doesn’t.
Iago continues to build Othello's jealousy through use of Cassio. For example, when Iago and Cassio speak about Bianca, Iago leads Othello to believe they were speaking about Desdemona, so Othello is further angered by hearing Cassio speak negatively about "Desdemona" (really Bianca). Another example is when Iago tells Othello that he should believe that Desdemona has slept with Cassio when he says that Cassio has lain "...with her, on her; what you will.” Othello has become so enraged that he strikes Desdemona for no apparent reason. His complete fall has nearly taken place when Iago tells him that he should strangle her in her bed.