This moment has to be at the end of the drama. Act IV is the point where Oedipus learns of his true heritage in that he is Laius' son. The fact that the Chorus speaks at this moment is quite telling:
Alas, o child of Laius,
if only, if only we had never
set eyes on you!(1250)
My grief is like a libation poured from my mouth.
But to speak the truth, because of you I could breath again
and because of you I sink my eyes into sleep.
This is the reality that Oedipus grasps at the end of Act IV. This "sleep" is something that ends up continuing into Act V, where the disastrous end of the play is where eyes need to be closed in "sleep." Oedipus' search for truth that lived outside of the palace walls was an internal one. This reversal is initiated at this point and then continued on into the drama's final act when he recognizes the full extent of the wrong committed and the consequences it brings onto both his kingdom and his name. The full catastrophic moment is seen when his wife/ mother hangs herself and he blinds himself. This is the moment in Act V where the reversal of fortune is complete. The intial discovery is one that is seen in Act IV's end and the implications of it come to fruition in Act V.