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I planned a projecting system based on a electrode-tube screen and two convex lenses, considering that only one lens would rotate the image in 180º, so two lenses would solve the problem.
Unfortunately, I realized that the image we see on the screen is actually projected as a mirror image by the electrode tube, therefore the projected iamge on the wall was horizontally flipped.
Another flaw of the system is that the screen is a very weak source of light, so you need to avoid any light in the room, including the light from the screen of course, so I had to build a black box for the screen. Its dimensions depend of the focal distance of the lens that is closer to the screen, and it must be hard enough to resist the weight of the lens system (you don't want to see the movies while you hold the lenses, do you?).
There are some basic rules about convex lenses regarding its focal point (it can be determined experimentally) and the light particles trajectory when they go through the lens. It's easy, you should check some optics book.
To solve the mirror image problem you have many solutions:
1) If you have a room big enough, you can project the image on a semi-transparent curtain and sit behind the curtain (so that the curtain is placed between the projector and you).
2) Someone told me to use a single-axis concave lens, but I can't figure how to use it...
3) Consider the fact that the more lenses you use, the more light you lose. If you want to project a PC screen image the best system should be junt one standard convex lens and a program that could rotate the screen output in 180º and mirror-flip it at the same time. Since I'm not a programmer I'm looking for such a program (or couple of programs working at the same time to obtain the same effects) to finally make my projector work.
So if any of you can build such a program please contact me.
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