What is the paradox of blindness in Oedipus Rex and the connection to irony?
This is a great question. Oedipus is the leader of Thebes in the beginning of the play. He is great in the eyes of people, and he is deeply insightful. We know this because he was able to solve the riddle of the sphinx. This shows that Oedipus has insight.
So, when there is a plague that strikes the city, the people look to him to solve how they can find a cure. When Oedipus inquires, he realizes that a murder of the former king caused a plague from the gods. As he seeks to cure the problem, he does not see that he is murderer. He killed Laius. More importantly, he fails to see that Laius is his father, and he is married to his mother currently. So, he sees physically, but he is really blind.
Tiresias is a blind prophet, whom Oedipus calls to get answers. When Tiresias intimates that Oedipus is the murderer, Oedipus get angry. So, we can say that Tiresias, who is blind, sees perfectly; and Oedipus, who sees (at least physically), is blind. This is the irony of the play.
At the end, Oedipus gouges his eyes out; this is when he really see - another irony.
In this play, it is ironically the blind who actually "see" the truth and try to convince the others about the errors of their ways; likewise, the ones who have sight are misled by their own thoughts and lack of "vision".
Of course, the obvious example of this from the story is when Tieresias, the blind prophet, tries to convince Oedipus that he was the one who killed Laius; Oedipus, the king, refuses to believe this outrageous story. Tieresias, however, is speaking the truth about Oedipus's fate.
Similarly, when Oedipus finally understands the full complexity of his situation and his decisions, he becomes overwhelmed and (ironically?) blinds himself now that he knows the truth.