What is a detailed account of Miranda and Ferdinand's meetings? Why does Prospero treat his guest so badly?
Because Miranda has been on the island for as long as she can remember, Prospero is her only knowledge of humans. Caliban and Ariel reflect perhaps the dual nature of humanity: spiritual and earthy. When she sees Ferdinand, a gracious and gentle young man, she must rightly think him a spirit, having just chided Caliban for not making use of the instruction she has labored to bestow on him:
Why speaks my father so ungently? This
Is the third man that e'er I saw, the first
That e'er I sigh'd for: pity move my father
To be inclined my way!
Ferdinand, for his part, falls in love with Miranda and promises to make her Queen of Naples. Believing all his party has drowned, he is grateful not only to find humans on the island but one like Miranda, who appears more wondrous than he could imagine in a young woman:
Most sure, the goddess
On whom these airs attend! Vouchsafe my prayer
May know if you remain upon this island;
And that you will some good instruction give
How I may bear me here: my prime request,
Which I do last pronounce, is, O you wonder!
If you be maid or no?
Both Miranda's innocence and Ferdinand's grief add to their "love at first sight" moment, and they immediately commit themselves to each other, at least in words and intent. Their open generosity and simple affection stand in contrast to all other relationships in the play.
Prospero, having orchestrated the shipwreck as a revenge, is more cynical and embittered in his attitude toward humans. He considers Ferdinand something of a threat to himself and Miranda and orders a kind of enslavement so that Ferdinand can prove himself worthy of Miranda. Prospero accuses Ferdinand of being a spy and takes his title from him.
Carrying logs for Prospero, obeying Prospero, promising to be respectful and chaste in his dealings with Miranda, Ferdinand eventually proves to Prospero that he is worthy to marry Miranda, offering hope that this younger generation can amend the errors of their parents.
At the end of the play, when the full assembly is revealed, Miranda exclaims
How many goodly creatures are there here!
How beauteous mankind is! O brave new world,
That has such people in't. (5.1)
To this Prosper merely responses "Tis new to thee." However, the play offers hope that the young couple will return to Naples, able to make use of the time on Prospero's island and to bring its lessons about love and power to the old world.
Prospero created a wicked tempest to shipwreck his brother Antonio's ship. Also aboard the ship is the King of Naples and his son, Ferdinand. No one on the ship dies in the tempest, but they are separated from one another--this is all part of Prospero's plan. Ferdinand is left to wander the island alone. Ariel, Prospero's personal spirit, tells Ferdinand that the King has died in the tempest.
Prospero and Miranda are watching from the side. Miranda has never seen another man before, so, at first, she thinks Ferdinand is a spirit of some kind. Ferdinand sees Miranda and introduces himself as the King of Naples, considering he believes his father to be dead, and offers to make Miranda queen.
Prospero sees that Miranda and Ferdinand have exchanged loving glances and becomes protective of his daughter. Prospero thinks Ferdinand is weak, and knows that he and Miranda have complete control over Ferdinand. Prospero also does not want to give himself away, so he accuses Ferdinand of being a spy and threatens to kill him.