Curtis L. Olson wrote:
> My initial speculation is that the position of my eye is an important
> factor that isn't addressed by the simple theory, but from the simple
> theory, I don't see how that could be possible.

One nit is that the simple theory only works for small mirrors (large
curvature radius to diameter ratio) and for reflections that are close
to the axis of the mirror.  Large mirrors really need to be
paraboloids and not spheres, and off-axis images will experience
distortion (the focal "plane" is only flat in its middle).  But these
aren't issues here, and wouldn't explain what you saw.

> If I move my eye point away from the mirror and watch myself, I seem
> to hit the singularity at 40" which is the center of curvature, not
> the focal point.  Yes, I've verified that the radius is indeed 40"
> and is most definitely not 80".

This sounds right.  At 40", your eye is in the center of the mirror.
It is seeing its own reflection in every direction, which looks like a
singularity.  You should also see a singularity at 20", but that's a
little different: At the focal point, your eye's reflection should be
discernable, but everything else in the world will appear to be coming
from all directions.  If you didn't see one at 20" at all, then I'm
confused too. :)

Remember that your eye and the background are separate objects at
separate distances.  Objects at different distances have different
focal planes (especially when those distances are already on the order
of the focal length).  Only objects that are infinitely far away will
converge exactly at the focal point of the mirror.  The mirror is not
a pinhole camera.

Andy

-- 
Andrew J. Ross                NextBus Information Systems
Senior Software Engineer      Emeryville, CA
[EMAIL PROTECTED]              http://www.nextbus.com
"Men go crazy in conflagrations.  They only get better one by one."
 - Sting (misquoted)


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