How long should one nap for it to increase mental agility in the long run

There have been some large epidemiology studies that have suggested both benefits and harms with napping on a population level. That makes it difficult to recommend for or against napping. If you do plan to take a nap during the day, here are some guidelines you can follow to help ensure that it won’t interfere with your nighttime slumber.
•    Time it right. The best time to sleep is the early afternoon, when your body experiences a natural circadian dip.
•    Keep it short. Abbreviated sleeps, around 20 minutes, may be best to avoid grogginess when you wake up. Shorter naps can also help to prevent you from having trouble falling asleep that evening. 
•    Get comfortable. For a high-quality rest, be sure to find a quiet, cozy spot where you won’t be distracted.