RE: ATM ROC 101

["Andersen, Clark R." <clanders@utmb.edu>]

Fundamentally, for a parabola the focal length is the distance from the
vertex to the point where previously parallel rays of light reflected from
the parabola converge (of course a circle can approximate a parabola up to a
point...).  The radius of curvature is a very different thing, simply the
radius of a circle which fits the region about a point (the vertex) on a
curve (the parabola).

If you draw a nice graph of a parabola or semicircle on a sheet of paper,
then draw parallel lines approaching it, followed by their reflections (the
angle of incidence is equal to the angle of reflection), this relationship
can be seen intuitively.

Exactly why they are exactly a factor of two different from each other is an
exercise in mathematics for the student with some expertise in calculus :)
One useful hint:  the key word as regards curvature is "differential
geometry".  This site may be helpful:  http://mathworld.wolfram.com/

Clark

>Can someone please explain to me why the ROC is twice the focal
>length, not equal to?