I actually bought one of these things just for shits and giggles. First off, it works about as well as you would expect for a $13 projector. Which means, not at all. OK? Questions at this point? Alright, movin' on.
Ok, on to how this works. Basically you get a thin plastic fresnel lense sent to you in a manilla envelope with instructions on how to use foam board or cardboard to make an enclosure around your TV. Basically, you construct a rectangular tube around your TV screen. In the tube, you build a sled for the lense so that you can zoom in and out by pulling the sled in and out of the tube. Ingenious? After the enclosure is built, you are to turn the color saturation, brightness, and contrast of your TV all the way up. The resulting image looks like a dim grease spot at worse, and a washed out tie-dye shirt at best :).
Now to the science (pun intended). First the lens. It is has the thinkness of cereal box paper and the optical passthru qualities of corrugated plastic like the stuff they use for ceiling light panels. Now to the lumen power of your TV. Any direct view TV only outputs maybe 150 lumens at best. That is then further diluted by the lens and the housing for the lens. Also since we are projecting here, the image displayed on your wall is past its maximum focal point. Remember, the image is focused at maximum on your TV already. So you have a bad lense (plastic just doesn't have good optical quality), low lumen output, and you have moved the image out of focal range of your TV and projected it on your wall. What do you think the image is going to look like?
This thing is a novelty at best. A serious viewing experience, or even passable image quality, it does not produce. Weird thing was when I was playing with this, my nephew said, "man, that is cool! Upside down, but cool!" Kids, easly impressed :). But the lense is sort of worth the 13 bucks. I use it when I soldering tiny connections circuit boards. For this purpose, it is great!