That sounds like an interesting optics problem! Itís going to be very difficult to get this exactly right. The problem is that the red, green, and blue LEDís are in different places. If the optical system bends and reflects the red, green, and blue rays the same, you cannot do it, as the rays from each of the LEDís can be traced back through an optical system to identify where the came from. If they started out in different places, then they must end up either in different places or at the same place with different angles. You can focus light from each one down to the same spot, but move the screen or whatever it is youíre focusing the light on a little bit, and youíll get your separate colors back again. If youíre only interested in white light at a particular spot, you can get away with doing this, but you may need collimators (that is, sheets of paper or something with holes cut in them to let light through to places where you want it and which block light where you donít want it) -- that can get rid of the rings.
But I see you may want a "beam" of white light, which means the three LEDís light should be put along the same direction in the same place. You can do this with dispersive optics. A prism will split white light into its colored components. Prisms also work in reverse -- you can put the colored light back through a prism to make white light. You can find out exactly where to put your prism and three LEDís by splitting parallel white light (say a collimated beam of sunlight) with a prism, seeing where the red, green and blue bands lie on some screen, and then put your LEDís where the red, green and blue bands are. You will have to collimate the resulting beam, because a lot of stray light will go where you donít want it to, and so your white beam will probably be a lot weaker than the sum of the LEDís, but at least itíll be a white beam.
People make LED displays for sports stadiums and hopefully someday television sets. Here the idea is just to put a lot of these LEDís close together and your eyes wonít be able to tell them apart (get a telescope and youíll be able to see each one), and the result will look white if all three colors are turned on. The same trick works in ordinary phosphor television screens -- look real close and youíll see little red, green, and blue dots or stripes.
(republished on 07/27/06)