only almost completely wrong.Woo a topic about sleep, my expertise
The body sleeps in 90 minute cycles, with the last 30 minutes being the most effecient and restorative. The first 30 minutes are the next most effecient (so if you're randomly tired at the library, take a 20-30 minute nap!). The 30 minutes in between is 'deep' sleep and can actually 'cause you to be more tired than you originally were if you wake up during this period.
It's best to wake up near the end of the last 30 minutes or 5 minutes after the last 30 minutes (which is a middle-stage, where you're not actually 'sleeping' but your body is just switched off, 'cause sleeping is when your body is restoring itself), as it allows you to make maximum use of your sleep.
tl;dr Don't wake up in the 30 minutes in between of a sleep cycle, sleep in 90 minute multiples (1.5 hours, 3 hours, 4.5 hours, 6 hours etc.) and a quick 20-30 minute nap is more effective than a 30-60 minute nap!
the body sleeps in 90 minutes, but it is the last 30 minutes of this cycle that is the beneficial sleep.
you can train your body to immediately enter the beneficial phase of sleep, but that's quite the bit of effort and only worth it if you keep with a polyphase sleep cycle.