What is more strenuous on eyes, reading on a computer screen or text?

You can get eyestrain either way. Older monitors were worse than newer ones, but reading for long periods of time is also bad for causing eyestrain. The solution to the problem isn't switching from one to the other, but instead to give your eyes breaks to rest and change focal distances. There are muscles that help focus your eyes, so if you're holding them in one place for a long time, they get tired (think about how your arm gets tired if you hold it out a long time...it's not a hard thing to hold out your arm, but holding it there a long time is). Close your eyes, focus on a distant wall, or some other things in the room at different distances, and then return to reading. You'll notice quickly that your eyes don't get tired so fast if you do that.

If you have especially weak eye muscles for some reason, an optometrist can help teach you further eye exercises.

 

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(Quadrophenia reference)