I learned in psychology that as long as you go through at least 1 cycle of REM sleep than you have benefitted. It generally takes 1.5 - 2 hours to complete one cycle. Power naps aren't very good for you because you go into beta sleep and come out so your brainwaves have slowed and you feel groggy still, and also your brain hasn't repaired itself. It only repairs itself in the deeper stages of sleep.