How does the handkerchief function in act 4? Keeping track of its movements from here to the end of the play.
The handkerchief, which belonged to Othello's mother and was given to Desdemona as a love token, becomes extremely important in the second half of the play when Iago decides to use it to serve his scheme. When Desdemona drops the handkerchief after trying to mop Othello's forehead with it, it is Emilia who picks it up. She gives it to Iago, knowing that he has often "woo'd" her to steal it. She does not know what he plans to do with it, but she wants to "please his fantasy." Iago will not explain what use he has for the handkerchief to Emilia, but he then explains to the audience that he "will in Cassio's lodging lose this napkin / And let him find it." He knows that he will be able to use Cassio's possession of the handkerchief to stoke Othello's jealousy.
Cassio gives the handkerchief to his lover, Bianca, to "take out the work," but she takes it to be "some minx's token" and is offended. Othello witnesses this argument between the two lovers and notes that it is his handkerchief over which they are arguing. He interprets this, as Iago thought he would, of proof that Cassio and Desdemona are sleeping together.
At the end of the play, Othello accuses Desdemona of having given the handkerchief "which I so loved and gave thee" to Cassio, which Desdemona denies, but Othello does not believe her. When he insists that he saw his handkerchief in Cassio's hands, Desdemona says, "He found it then"—an explanation which Othello rejects. He goes on to kill her. In the closing scene of the play, Emilia tells Othello that it was she who found the handkerchief "by fortune" and that she then gave it to Iago. Othello now knows that Iago has orchestrated his downfall and declares him a "villain." Emilia's explanation about the handkerchief is what leads to Iago's unmasking.
Othello's handkerchief that he had given to Desdemona before the play begins becomes the play's most important prop and an ironic symbol of their relationship. The handkerchief actually comes into play in Act 3 when Desdemona attempts to wipe the brow of her agonized husband with it. In his impatience, he brushes it away, and since Othello is distraught at the possibility of Desdemona's unfaithfulness and Desdemona is worried about the strange behavior of her husband, neither notices that the handkerchief is dropped. It is this "trifle" that Iago uses to frame Desdemona. Emilia picks up the handkerchief for her husband, and Iago plants it in Cassio's lodging.
In Act 4, the handkerchief reappears in the hands of Bianca, Cassio's mistress. Cassio had found the handkerchief in his room and given it to Bianca to copy the work. Bianca, thinking it the token of another mistress, gives it back to Cassio. This scene in enacted while Othello is eavesdropping. Othello incorrectely believes that the handkerchief is the "ocular" proof that Cassio is sleeping with Desdemona.
After this scene, the handkerchief is not mentioned again until Act 5 when after Desdemona's death, Othello defends his act by declaring that Desdemona was unfaithful, and that the handkerchief in Cassio's hands was proof. Emilia realizes now the truth. She explains that it was she who took the handkerchief and gave it to her husband. Iago, not Desdemona, gave the handkerchief to Cassio.
This revelation clears Desdemona's name, and Othello now is full of regret for the wrongful act he has committed.