In article , Mike B
someone@noplace.? writes
This is for a searchlight application where the light source shines backwards
into the reflector which then reflects the light forwards producing a narrow
beam.
The reflector needs to be about 2 to 3 inches in diameter with a focal point
about 2 to 3 inches in front.

Presumably this was possible in the days before CNC machinery, so how did they
do it?
Snip
For a searchlight you probably don't need anything like the
precision that you would need for a telescope.
If you use a spherical surface then the focus will be 1/2 the radius of
curvature for rays near the axis. The figures you quote would mean that
some of the rays are well away from the axis so the approximation is not
very good. If you could use a mirror with a longer focal length then a
spherical surface would probably be good enough for your application.
I wonder if you could use a spherical glass laboratory flask, or
even a large light bulb to act as a mould for casting resin and then
silver the surface?

--
Chris Holford