It's about getting 5 REM-NREM cycles of sleep. [1][2] The exact time varies from person to person and situation to situation, but roughly speaking the cycle takes 90 minutes and 5 * 90 min = 7.5 hours. Add some minutes lying in bed but not yet asleep, and you've got the 8 hours.

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[1] https://en.wikipedia.org/wiki/Sleep_cycle

[2] http://healthysleep.med.harvard.edu/healthy/science/what/sle...