Do-it-yourself projector, need advice from an optician?

Question

Do it yourself

Hello Q&A. I come to you for more advice.
I inherited such a projection TV.

It is clear that he is already many years old, the lamps have dimmed, it is difficult to watch him during the day, but at night it is quite tolerable. The main thing is big. In general, I always had a dream at home to make a projector on the ceiling. I decided to try to somehow implement this using this old piece of iron and optics. The scheme there is quite simple.

From bottom to top, three lamps shine on the back surface with a mirror, each with its own color and at its own angle.
Reflected from the mirror, it hits the screen.
Remove the screen and shine on the wall, it will not work, it will interfere with the mirror to perceive the picture. It will not work to remove the mirror, because. each lamp at its own angle, the mirror has a non-rectangular shape and hitting the screen, the image turns back into a rectangle. You can try to align all three lamps in one line so that they shine in rectangles. And here the question arises, how to focus three beams of light into one place? Use prisms? Or just do not touch it and look at it as it is.

Answer 1

I think this community should help: diyprojector.info

Answer 2

Look here, a lot about electronics