Luke is a Jedi master. He can sense a force sensitive presence coming near him. If it was someone he didn't know, he wouldn't even have to turn around to acknowledge them let alone take off his hood and get misty eyed. When he sees her his face begins to quiver, once she pulls out the lightsaber he begins to look uneasy. The lightsaber I seriously doubt has that much sentimental value to him.
It's his daughter. The reaction he's giving her is from the fact that he hid his daughter to keep her from danger and she not only finds her, she's holding a lightsaber. She's ready to get into danger. Add to the fact that she found a long lost lightsaber which shows him that she's been getting into danger already....
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