This scene leaves no doubt that Prospero is the absolute ruler of his small island. Ferdinand is set to the same task as Caliban, carrying logs. Although he is a prince, Ferdinand must bow to the same authority that Caliban, a slave, observes. Even Miranda is not exempt from Prospero's rule. She is not supposed to speak to Ferdinand. Moreover, she is not permitted to even give him her name, although she does. As part of Prospero's power, he must pretend to oppose the romance between Miranda and Ferdinand; however, the audience knows that Prospero is not opposed to such a union, and in fact, he had hoped that they would love one another. But Prospero must maintain the illusion that he is in absolute control, and so, he imposes rules to guarantee his authority.
In part, Prospero is playing the role that any father must play when his daughter has a suitor. Protecting Miranda's worth is tied to protecting her virginity; thus, he watches the courtship, unseen. Miranda is an obedient daughter, as proved by her dismay when she forgets herself and reveals her name to Ferdinand. But she is also a young woman in love, and when her father is occupied, she immediately looks to release Ferdinand from his labors.
Miranda has no experience with people. She has never seen another woman and does not know that she is beautiful. She has no experience with men, other than her father and Caliban. Because of her isolation, she has developed no artful skills at flirting, and when Ferdinand tells her that he loves her, Miranda weeps. Their love scene is sweet and tender, and without artifice. Prospero watches this exchange, not just to control its outcome, but to protect his only child. Miranda is more vulnerable than most young women, and she needs a strong father to protect her. As such a strong authority figure, Prospero is well suited to protect Miranda from any dangers that this new experience might present. But his watchful observances also recall the godlike control that he has exercised over every other individual being and every action that has occurred on the island.
