Finally getting to the point...
We're finally getting to the part of the scene that was actually requested. As is often the case, after looking at it frame-by-frame, I think it's more complex than I did earlier.
The camera goes back to Frodo. I'd pick #3 as his first glimpse of Sam. It's more difficult to pin down than his other moments of recognition. Maybe he's so used to seeing Sam that it doesn't register right away that he's, well, seeing Sam. So I've started posting a couple of frames earlier, just in case. Definitely by #7, although the recognition still seems subconscious. In #12 we get an almost half-blink.
In #16, we're back with a Sam who still doesn't seem quite sure of himself. But that changes in #17 when he starts to smile. He spends the rest of the shot taking a deep breath - and a little raise of the eyebrows starting in #29.
(The light inconsistencies in these are my fault - not part of the scene.)
The background on these pages is made from the shutters behind Frodo's bed.