Your approach sounds perfectly reasonable -- use a converging
(convex) lens to focus light down to a spot. But of course you have
stumbled on the primary limitation already of making small spots of
light, and that is the size of the source (or lack of control over the
optics that comes with the source in this case).
There's a limit to how small a bright spot of light you can make
by focusing sunlight with a magnifying glass, and this limit comes from
the angular size of the sun in the sky -- light from the sun comes to
you from lots of different places and in lots of different directions.
An ideal lens can focus parallel light rays down to a point, but if the
light rays aren't parallel, then you won't get a point; you'll get an
image of the source.
The idea to get as small a spot of light as possible is to make
the light impinging on your lens as parallel as possible. You can do
this by making the source as small as possible and placing it far away
from your lens. (note: jewlery stores use very small, very bright
lights place on the cieling in order to make diamond rings sparkle more
-- the image of the light source is much more well defined and light
reflections come and go if the source and your eye are lined up just
right. A diamond ring just doesn't sparkle as much outside on a rainy
You could cover up the LED with a piece of paper with a pinhole in
it. Then you can focus the remaining light down to a small spot, I'll
bet. But this isn't a recipe for a bright spot, just a small one.
Bright LED's from Radio Shack and other places come with little plastic
lenses molded into their packaging, and some bright ones I have on my
bicycle rear-projecting flashing light have a red plastic diffuser all
over everything. The whole purpose of these is to spread the light out
as far as it will go in all directions. You may want to try removing
these obstructing, poorly-controlled, and hard to correct for, optics.
The actual light-emitting part of the LED is probably pretty small and
bright to begin with.
Unfortunately, as Tom says each light source has its own intrinsic
brightness, which depends both on the intensity of the light at the
brightest spot and how big an angle it's direction is spread out over.
The best your image can do is maintain that brightness. If you want to
get something really bright, use a laser, even a small cheap one. Its
light is spreading out over a narrow range of angles, so that it can be
focussed down to a tiny spot. You'll want a good lens with a small
ratio of focal length to diameter, and then you'll want the beam spread
out over most of the diameter of the lens, which you can do with
another good lens.
(published on 10/22/2007)