Well it's a bit more complicated than that. But easier in a way.
From the minute you fall asleep you go through a series of sleep cycles through the night. You start in N-REM, going down through stages 1, 2, 3, 4 (each successive stage is characterised by deeper sleep and a lower frequency of brainwaves). When you finish stage 4 you start to climb up again, through 3, 2, 1, and finally, REM. Then the whole cycle repeats.
Exiting REM can also be accompanied by brief awakenings (what you have at 4 o'clock).
As the night goes on you start to skip the deeper stages of sleep, 4 and then 3, altogether. By about 4hrs in you're ping-ponging between stage 2 and REM, going up and down through the 90 minute cycles. Perhaps during those dozy weekend lie-ins we drift in and out of pure REM.
So in answer to your question, by 4hrs of sleep you're spending 30mins+ of each 90min cycle in REM, dreaming. And that doesn't even account for dreams in NREM or other confounding variables like REM rebound from sleep debt and caffiene/alcohol/drug consumption.
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