Yes, that's how belaying glasses for rock climbing work.
(They let you see the climber in the wall above you without looking up all the time)

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Thanks for reading all of this, even if you didn't read all of this, and your eye started somewhere else, have a watermelon slice ๐.
Didnโt know this was a thing, Iโve only seen the gimmicky ones for reading that are angled down
yes, in fact modern projectors use a 'short throw' technique like this so that the projector lens part only needs to be inches from the screen above to lay out a very large, flat display below... kinda of the opposite of your image
"snorkel lenses" look ridiculous on large projectors.
https://epson.com/Accessories/Projector-Accessories/ELPLX02-Ultra-Short-throw-Lens/p/V12H004X02
Goes in the front like a normal lens, shoots backwards like a cursed lens.
The problem with short-throw lenses is that they will exacerbate any geometry issues. So aligning them is hard. And ANY tiny little non-planer issue with the screen surface gets massively multiplied.
You can get away with a lot of issues using long lenses. Short lenses are a pain.
ETA:
Linked is a 0.35 ratio lense.
So for every 0.35m from the screen, it will project a 1m wide screen.
0.7m away? 2m screen.
1.25m away? 5m wide screen.
3.5m away? 10m wide screen.
they work fine for their purpose in all of the places ive used them... schools/offices.
if ya wanna nitpick for the gaming/entertainment crowd go nuts. i just need shit to work well enough for people to work
There are prism glasses for reading etc while lying flat in bed, whether you're lazy (they're sometimes called lazy glasses) or in traction. The prisms point the opposite way from climbing prism glasses.