Click to enlarge:
OK, so that is the lightsaber then, falling away? I can't say that's the best shot of it falling away below the city that there is in the film. Still hard to make out there. Granting that it is, that's kinda bizarre, actually,
since his hand had gotten chopped off and it and the saber had already fallen away a minute or more (give or take) before Luke was dropped out at the bottom. That whole part of the film, from Luke diving away and then getting sucked (or is it telekinetically guided? or a combination of both?) into the air tube has always seemed pretty dodgy to me.
That's easy enough to explain if you're so inclined. It would be inefficient for the external hatch to open up every time some minor piece of garbage was dropped in the shaft, so it has a weight sensor that tells it to open after a certain amount of trash has accumulated, and Luke's weight set off the sensor.
So his hand and lightsaber fell down the shaft earlier, got sucked into an air tube for smaller debris, and was awaiting dumping. Then Luke fell in to another air tube and triggered the external hatch to open, and both were dumped at the same time.
I think we need a better screen grab.
The problem isn't the screengrab. The object is blurry and seen from a distance for a reason: to cover for the special effects compositing, because a detailed closeup of the hand would look fake, and probably because no one anticipated that 33 years later nerds would be arguing over what it was, so they didn't feel the need to have a close-up beauty shot of it as it fell.
To me, the simplest reason for believing that's it's his hand and lightsaber is a story-driven one. What purpose does showing some random piece of garbage falling serve the story? It's not as if it's necessary to convey the desperation of Luke's situation since he's hanging from the bottom of a floating city and pole dancing with his only remaining hand like a daytime stripper.
But to imply to the audience that it's his hand and lightsaber floating away beneath him reinforces the dark themes of the film and is of greater import to Luke. The hand symbolizes his defeat and his arrogance in thinking he could take on Vader so easily. Losing his father's lightsaber symbolizes the loss of the innocent and pure image of his father that existed until just a few moments before when Vader revealed the truth to him. He's literally losing the last connection he had to his father, or at least to the idealized version of how he had always thought of him.
To a lesser extent it's also a loss of his more innocent connection to Obi-Wan, who gave him the saber, which Luke now realizes was all part of a huge deception and manipulation about his father, hence the half-angry, half-sad "Obi-Wan, why didn't you tell me?" a short while later.
Thematically having it be his hand and lightsaber rather than just some random piece of junk is a lot more powerful and befitting of the dark tone that
Empire ends on. It's not like it's definitive in any way, but that's just my two cents.
Also, to me that pic does seem to have a pretty distinct hand shape with a long, thin silver tube next to it, which fits with the prop hand and saber falling together in the first shot right after Vader cuts it off. I don't have infinite CSI image enhancement, but here it is resized, sharpened, and with some contrast and brightness adjustments: