In chapter 16, Rahim Khan becomes the first person narrator. He's going to tell Amir about how he found Hassan again, and in the next chapter, we understand that it's not Amir who's speaking to us anymore.
The first thing I notice is that Rahim clearly seems more adult. He explains and talks in a much more grown-up way. But this may be because we've been prepared for Rahim to talk to us. Rahim does not talk about childhood and childish things, like Amir has up to this part of the book. There are two other things I've noticed about the way Rahim talks. First, he doesn't sidestep. He sticks to the point, and doesn't interrupt himself with relevant stories. The other thing is that Rahim is religious. This is actually pretty clear if you're aware of it. When you read the chapter for the second time, you notice he says things like “Allah forgive me”, or “with the grace of God”. Amir doesn't narrate this way.
But is the narrator technique successful? It's nice to have someone else to narrate, for a change. It seems very logical to change narrator. The change comes very natural. The last thing we read before “the Rahim chapter” is “..Then Rahim Khan rested his head against the wall and spoke”. It's a very interesting technique. It's often used in crime fiction I've read. In crime fiction, it's used to create suspense and tension. We get a look into the murderer or the victim's life and thoughts, not only the protagonist. The narrator change is very successful.
Another thought strike us: where is Amir? We don't get any clear signs of him, but still we know he's there. Rahim sometimes “refers” to him, for instance describing a place and then asking Amir “do you remember?” One of the reasons the change of narrator seems natural, may be because we're kind of in Amir's position. The things Rahim know and uses chapter 16 to tell us about, are something Amir doesn't know either. Maybe that's why he is so quiet. We, the readers, and Amir, is for the first time at the same “level of understanding”, as Amir has had the narrator role the whole time up to now
Could the author used another technique? If he didn't want to switch narrator, and keep the same all the time, what could he have done? One possibility is to let Amir read a letter, although this kind of changes the narrator from Amir to the one who wrote the letter. Other than that, I cannot find a good way to do it. I think Khaled Hosseini did well, I liked the changing narrator.