Before Prospero's cell — Ferdinand carrying logs

In front of Prospero's cell. Ferdinand enters carrying a log. He has been set to the same work Caliban was set to — hauling wood — and is finding it light only because his love for Miranda makes it so. "There be some sports are painful, and their labor / delight in them sets off." He had thought his father drowned and the world ended; instead he finds himself a prisoner doing slave's work, and is happier than he has ever been.

Miranda enters. She has slipped away, she thinks, without her father's knowledge — Prospero is in fact watching from behind a rock at the side of the stage, invisible to both of them. She offers to carry the logs for Ferdinand; he refuses. She insists. They argue tenderly about which of them gets to do the labor. Then, in one of Shakespeare's plainest love-scenes, they exchange vows. He asks her name; she tells him; he repeats it as a miracle. She tells him she has been forbidden to speak with him and is doing so anyway, against her father's command, because she would rather be his wife than free. He says he is a king's son — though, he adds bitterly, he wishes he were not, because then he would not be set to log-hauling. They kneel. They are formally engaged.

Prospero, behind his rock, says aside what the audience can see in his face: this is exactly what he has been engineering for the entire play. "Fair encounter of two most rare affections! Heavens rain grace on that which breeds between 'em!" The trial — Ferdinand's willingness to suffer manual labor for Miranda — has been passed. The marriage will go through. The strategic dimension of Prospero's plot, the one that secures Milan to Naples by way of his daughter's heart, is now in place. He returns to his book. Ferdinand and Miranda return to their work. The play has just produced, in the middle of a revenge plot, one of its few unguarded scenes of love.