The tempest act 1 scene 2 - Explore thedramatic significance of this episode within the play.

Prospero, who is the rightful Duke of Milan, stands outside a cave
with his daughter Miranda, watching the storm toss the ship
ashore. Miranda appeals to her father to use his magical powers to
calm the storm, not realising that it is his magic that has caused the
tempest. She says she has seen the ship break up on the rocks and
heard the shrieks of drowning seamen. Her tender heart is filled
with pity. Her father reassures her and tells her the shipwreck has
not injured anyone. He explains that he has caused the storm and
shipwreck for a reason takes place in one afternoon, on an
enchanted island in the middle of the open sea somewhere between
Africa and Italy.

Twelve years earlier, Prospero was the Duke of Milan, and
Miranda was his only heir. Prospero had a younger brother,
Antonio, to whom he had entrusted the business of ruling the
dukedom while he himself spent his time learning as much as he
could. Unfortunately, while Prospero was concentrating on his
studies, Antonio was busy making plans to seize the dukedom for
himself, with the help of Alonso, King of Naples. Since Antonio
could not kill his brother directly, he arranged to put Prospero and
young Miranda in a small boat and set them out on the sea without
tackle, sail, or mast. What Antonio did not know, however, was
that kind-hearted Gonzalo had secretly stored provisions, water,
clothing, and some books on magic in the boat. Prospero and his
daughter drifted ashore on the island, where they have lived
undisturbed until the present.

After listening to her father's account of their history, Miranda asks
Prospero why he has raised the terrible storm. He replies that the
storm has forced his enemies to land on the island. Prospero then
prevents his daughter from asking more questions by casting a
magic spell on her so that she immediately goes to sleep.

While Miranda is asleep, Prospero calls for Ariel, an airy spirit
whom he commands. Ariel reports to Prospero on the storm and
the fear he has caused in the stranded royal party. Ariel says he
appeared before the royal passengers in the form of a flame and
frightened them all into jumping off the ship and swimming to
shore on the other side of the island. The crewmen who remained
on board the ship are sleeping unharmed under a magical
enchantment. The young Prince Ferdinand is separated from the
other royal party and thinks they have all perished. After listening
to Ariel's account, Prospero tells him that during the next couple of
hours they have much work to do. Ariel, however, reminds
Prospero that he has been promised his liberty for the work he has
already done. At this Prospero flies into a rage. He scolds Ariel and
calls him an ungrateful wretch who has already forgotten the
torment from which he has been freed. He then proceeds to tell the
story of how the airy spirit first came under his command.

When Prospero first landed on the enchanted island, he found Ariel
imprisoned in a pine tree by an evil witch named Sycorax. When
Sycorax died, Ariel could not free himself and had been stuck in
the spell for twelve years. Prosperous heard Ariel's wailing and
released him. After recounting this story, Prospero promises Ariel
his freedom within a week if all of his orders are properly carried
out. He then sends Ariel to fetch Ferdinand, the young prince, and
bring him to his part of the island.