Where do we see illusions in Shakespeare's Tempest and how are they utilized in the play?

This is similar to your former question about illusion. Let me know if there is something more specific that you need.

I have to do a discussion on illusion and reality and that's why I'm looking for specific scenes that provide examples of illusions in the play. I am having hard time explaining how the illusions with reality. The tempest in act 1 is an illusion but how/why? Ferdinand lives under the illusion that his father is dead and same goes for his father who lived under the illusion of his son's death. Why? The banquet and the masque are illusions. So what's the purpose behind these illusions?