Is it possible to enlarge the output angle of a projector with outside lens? I have a very small projector, with a small output angle (30 degree). In my current demand I want a bigger output angle(90 degree), so that I can get a bigger image within a given distance. Is it possible to get it by outside lens?
The projector:

What I expect:

If it's possible, how to design the lens?
If not, why? What would I lose? (resolution,brightness,distortion etc)
 A: I am not sure how to design it, but the ray-diagram in your figures is not correct. After the first concave lens, the ray should diverge instead of converge.
There are few disadvantage of using lens to create such large angle. (1) The angular resolution decrease, assuming the projector are of the same distance from the screen. (2) The brightness decrease by the same factor. (3) To obtaining such large angle using lens will cause severe dispersion, that is the color of each pixel now spreading out and might overlap with other pixel. (4) The image at the edges would be distorted by most lens.
The brightness is usually adjustable, but not the angular resolution. But your aim seems to be have a larger image in a screen so it is not a problem whatever scheme you are using. So the (3) and (4) are the problems caused by using lens.
If you want a large image, my suggestion is to simply move your projector further away from the screen. If you have size limit in your room, you might consider to use a mirror on the opposite side to reflect the projecting image. Though not very practical for large image.
A: Yes, you can use lenses to enlarge the output angle/size of the image formed.
However, you would lose the intensity of light (brightness) since the light would be distributed over a larger area.
