How does Luke feel when he has to face his father in Star Wars?

Luke feels conflicted about facing his father because he has committed many atrocities, but Luke still feels that there is good in him. 

Growing up, Luke never knew his father or anything about his background.  He was raised by an aunt and uncle, and his uncle told him that Darth Vader killed his father.  Until he met Obi-Wan Kenobi, he had no idea that his father was a Jedi.  Even Obi-Wan did not tell him everything.  He never told him that Darth Vader was his father. 

Yoda warned Luke about confronting the emperor, but he did not tell Luke the truth about his father either.  Even though Yoda told him that he risked following the path of his father if he faced them too early, Luke felt that he had to go because his friends were in danger.

 When Luke first confronted Vader, he was shocked to learn that he was his father.  When Luke accused Vader of killing his father, Anakin Skywalker, Vader chose that moment to tell him that he was actually his father.  The knowledge stunned Luke.  He could not believe that his father had turned into such an evil figure. 

He didn’t want to believe Vader, tried to convince himself that it was Vader who lied to him—but somehow he could feel the truth in the Lark Lord’s words. … His mind screamed louder than any wind the Dark Lord could summon against him. (The Empire Strikes Back, Ch. 13) 

Luke is in pain from the loss of his hand, and also in shock from the news.  In his heart, he knows that Vader is not lying.  Luke really is his son.

Despite all of the evil that he has done, Luke tells Leia that he knows his father can be saved.  After knowing so little of his past, finding out he is a Jedi, and training with Yoda, Luke is starting to become more confident in his abilities.  Besides Leia, Vader is the only relative Luke has.  He feels a connection with him. 

For his part, Vader does try to turn Luke instead of killing him.  He sees in Luke the potential to finally get out from under the Emperor’s thumb.  He is too weak on his own, but if Luke joins with him they can overthrow Palpatine. 

During his fight with Vader, Luke severs his father’s hand.  Doing so makes him come to a realization about how much he is like his father. 

Luke stared at his father’s twitching, severed, mechanical hand—and then at his own black-gloved artificial part—and realized suddenly how much he’d become like his father.  Like the man he hated. (Return of the Jedi, Ch. 8) 

Luke renounces the Dark Side.  As Palpatine attacks him, Vader intervenes, throwing his master into the power core.  In doing so, he not only rescues Luke but proves him right.  There is still good in him.  He refused to let Palpatine destroy his son.  He tells Luke that he was right about him.  He wants Luke to tell Leia. 

Luke is saddened that his father is dead, but relieved that the Emperor is gone.  In the end, Vader was turned back to the light, and that means that Luke accomplished what he set out to do.  He still has Leia.