The scene between Oedipus and Teiresias in Oedipus the King is crucial in terms of characterization and themes. First, the interaction reveals Oedipus's obstinacy and arrogance, tragic flaws that contribute to his downfall. Second, the scene heavily relies on the contrast of blindness and insight, which is central to the play's themes, is a great example of irony, and also provides some foreshadowing for the play's ending.
At the point in the play Oedipus summons Teiresias to help him solve the decades-old murder of former King Laius, Oedipus has not yet realized that he, himself, is the killer of Laius, who is his biological father. He admirably announces that he will find the killer and end the plague to protect his citizens; however, the dramatic irony here is that the audience knows from the start (due to the myth of Oedipus, with which viewers would have been familiar) that Oedipus is actually the killer he seeks. At first, Oedipus is mostly respectful of the blind prophet Teiresias, but once the seer starts to suggest Oedipus may be at fault, Oedipus turns on him. He refuses to believe he could be responsible, and he begins to insult the prophet, namely the fact that he is blind. Teiresias fires back that Oedipus is the one who is truly blind, not physically, but due to his ignorance of his origins and his past actions. In his arrogance, Oedipus believes he is above criticism, even from someone who he purposely called in for advice because Teiresias is supposed to be able to provide key insight into the case.
The theme of blindness is central to Oedipus the King, and that is what is primarily developed in this scene between Oedipus and Teiresias. Oedipus's lack of insight into his own past, his very slow realization of what he has actually done, and his refusal to see that he could be the one responsible for the king's death, all contribute to his downfall. He is contrasted with Teiresias who, while physically blind, has immense insight into what has occurred in the past and what its future results will be. Although Oedipus insults the blind prophet, it is Teiresias who is proven to "see" the truth in the end. Ultimately, Oedipus learns that he has fulfilled the prophecy of his birth: that he would murder his father and marry his mother. As a result, he gouges his own eyes out to physically blind himself. While he now has the insight into who he is and what he has done, he now does not have physical vision. The play suggests that physical blindness and insight cannot or do not coexist in the characters.
Oedipus's weaknesses are also reinforced by his choice to blind himself because he admits that he cannot, or does not, want to look upon the destruction he has caused, and he does not want to have to physically see his parents in the Underworld after his death; he feels that he cannot face them. Some readers might see this as a way for Oedipus to avoid some of the consequences of his actions.