How to diffuse narrow viewing angle LED?

i have some nice 5mm LED's from all electonics: UV, blue and green are 15 degree. these are nice and bright, but i need to diffuse them to be used close to my lighthouse project.
i want to place the LED's at ground level about 3 feet away, pointed up at the lighthouse to gently illuminate it--but the beams are too tight.

any ideas on how to do this?

i was thinking of using a frosted lens or something similar (not even sure where to get a frosted lens. maybe a chunk of milk jug will work)
i think there is a way of sanding the LED to diffuse it--but i dont want to try unless someone has specific directions.

thanks,
Bob

I wanted to do the same in order to get an area light for HO passenger cars. I only did one LED, but by first grinding away most of the package up to nearly the die, and then rounding and polishing it (putting the LED in a drill press for this works well), I made a 15° ChiWing white LED into a wide angle area light. Of course, the light appears less intense because it is spread over a wider angle. As a bonus, it seems less light is lost due to total internal reflection in the package, so there might be a bit more lumens coming out (maybe 25%?). Just sanding the package with 600 grit emery cloth without grinding it down might work as well, but I haven't tried it. As a general rule, the wider the angle, the shorter the package is, and the less rounded the end is. Perhaps just grinding the end flat and close to the die may have worked just as well. Just be careful not to grind away too much and end up destroying the LED. Best to experiment first on cheap LEDs before touching anything expensive.