Actually, REM cycles are close to 1.5 hours. If you are going to sleep, you should sleep: 1.5, 3.0, 4.5, 6.0, 7.5, etc. hours to avoid being groggy. Had you slept for less time or about 30 minutes more, you would have probably felt even worse. Personally, I believe that naps should be only 20 minutes or so. If you need to sleep longer than that, it shouldn't be called a nap.