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400 lumens - you better have good curtains.

Exactly. I installed projection systems in classrooms, theatres and lecture spaces for three years and the minimum classroom system would be 3500 lumens for a 'short throw' projector. Standards at universities were a minumum of 5000 lumens for a visible screen image.

Did you install your 3500 lumen projector 12 inches from the wall? Isn’t there an exponential drop off for power which may be exploited here?

the inverse square law problem isn't different for short-throw projectors (and it seems the person you are responding to was in fact installing short-throw projectors anyway).

short-throw projectors are just normal projectors optimized for very large beam angles, so at the end of the day the brightness out is exactly proportionnal to lumen amount between regular and short-throw projectors, modulo negligible airborne particles loss.

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