Who are Prospero and Miranda? Where are they at this moment?

This is in act 1 sc 2. Miranda is appealing to her father Prospero to spare the men who have survived the storm. Prospero is the rightful Duke of Milan, though his kingdom and title were usurped by his brother Antonio. Prospero was able to survive a plot on his life, and he and his daughter Miranda were set aboard a wrecked craft, but managed to land safely on the island. Miranda is Prospero's only daughter, and so young that she cannot remember anyone she knew before she came to the island. She is intelligent and headstrong, having learned a lot from her father; but, when under Ariel's enchantment, she follows her father's plan, and falls in love with Ferdinand willingly. She and Ferdinand end up together, bound by their mutual infatuation.