One thing not being mentioned is you go through cycles when you sleep. Being woken in the middle of a cycle will make you feel more tired, groggy, etc than if you woke up at the end of a cycle OR BEFORE you hit the deep sleep part
So a 15 minute nap will be more refreshing than a 60 minute nap because you havent interrupted your deep sleep stage.
The other answers are also correct just wanted to give an answer from a different perspective
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