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Is it possible to use a clever combination of lenses and mirrors placed between your eye and a screen 1m away from you to make the eye react to the screen as if it were 20m away from you?
What I'm asking is whether it's possible to, using lenses, modify the light emanating from a screen physically placed 1 m away from the eyes so that the eyes behave as if the screen were 20m away. This isn't a pure physics/engineering question, nor is it a claim that video games cause myopia.
Yes, but you would have to modify the optic array in 2 ways:
(1) Accommodation: if your eye accommodates for 20m (top row), an object at 1m will be out of focus (middle row). Thus for accommodation to be identical to that of an object at 20m, you need to add a lens in front of the eye (bottom row).
(2) Vergence: if you look at the object binocularly, your eyes will cross (vergence angle) at 20m. If the object is at 1m that angle will be different. Therefore you need to place prisms such that the resulting vergence angle will match that of an object at 20m. This is essentially a stereoscope.
So in order to correctly simulate an object at 20m, you need to add both a spherical lens to change the accomodation, and prisms to change vergence. Of course if the observer sees the object monocularly you do not need the prisms. Finally if your observer moves then the parallax of the object also needs to match that of an object at 20m, so you'll need to physically move the object accordingly.