Luke continues to resist Vader's taunts, but they're growing harder and harder to ignore. Though he keeps silent at the mention of his friends, his thoughts are deafening. And though he's hiding his physical form, those thoughts are clear as day to Vader.
(Brief aside -- I have to register my thorough dislike of the "interrogation" used by the Darth Vader-wannabe in the Disney Space movies. If you could use the Force to pry through any old person's thoughts like that, why would Vader go through the trouble of the interrogation droid in Episode IV? It's Luke's connection to Vader that makes his thoughts so transparent. But anyway.)
So Leia's identity is revealed. What a spectacular moment of silent acting for Mark Hamill. The desperation, shifting to horrified realization and despair. Obi-Wan warned him this might happen. He tried to keep it buried, but he couldn't. Failure. Anguish. Desperation and despair. Vader is leading Luke down a very familiar path. Then he delivers the final crushing blow.
"If you will not turn to the Dark Side, then perhaps she will."
Losing his sister, not just to death, but to darkness. That is the fear that cuts the deepest, and Luke is drawn out of hiding at last. Driven by fear, anger, hatred. Filled with an awful power. Yes, the Dark Side empowers Luke, insofar as physical dominion is concerned. Vader lies defeated at his feet. His son towers over him in grim triumph.
This part is necessary, though it makes me cringe in anguish no matter how many times I see it. We have to see Luke teetering at the very edge, in true danger of being consumed by evil. Otherwise, the glorious reversal that's coming would not be nearly as joyful and miraculous.
Next, Luke reclaims his soul while affirming his belief in another....