Re: [ATM] Slit and source arrangment

["Bob May" <rmay@nethere.com>]

<<So the appropriate conic
would be K=-e^2=0.000011. No eye could tell the difference
between this conic and a perfect sphere.
>>
Y et we see the difference!  I think you're having  a problem
with the Conic Constant and Eccenctricty values, the Conic
Constant being the negative of the square of the Eccenctricty
value.
What I am looking for is the math that goes between all of the
different ways that the optical engineering nuts have developed
over the years so that it will be in one place.  I've gotten the
formula that gives a Conic Constant from an Eccentricity balue
and Vlad just told me what the probable formula is in text for
determining the value of e  which, to paraphrase so I understand
it, is the value obtained when you take the distance from one of
the focii to the major axis radius and put it under the distance
between the two focii.  In other words, if you have an elipse
with a distance between the two focii of 6" and the ROC of the
elipse from the focii to the long sharp end of the elipse is 6"
then the elipse has an eccencitry of 1.  This doesn't make sense
to me.  Nor does using the side distance from the line between
the two focii.
Bob May

rmay at nethere.com
http: slash /nav.to slash bobmay
http: slash /bobmay dot astronomy.net

----- Original Message -----
From: vladimir sacek <vla@toast.net>
To: <atm@atmlist.net>
Sent: Sunday, April 27, 2008 8:17 AM
Subject: Re: [ATM] Slit and source arrangment


> Bob May wrote:
>
> > How do you figure the Ecentricity, Schwartzchild Constant and
> > other such values and how do you express an oblate elipsoid
(the
> > long side of the elipse) with each of the numbers.
>
> If you imagine the light source and its image formed by a pair
> of zonal openings as the two foci of an oblate
> (elongated orthogonally to the mirror axis) ellipsoid, then
> its eccentricity is given by the ratio of the source offset vs.
> mirror r.o.c. So for, say, 10mm offset and 3,000mm r.o.c.
> the zones that will produce a perfect geometrical null
> would belong to an ellipsoid with eccentricity
e=10/3,000=0.0033.
>
> For oblate ellipsoid, the eccentricity is an imaginary value
that
> is negative when squared. So the appropriate conic
> would be K=-e^2=0.000011. No eye could tell the difference
> between this conic and a perfect sphere.
>
> It doesn't really matter if the mirror is a sphere, or some
> other rotational conic. If it is, say, a paraboloid, the only
> difference is that the "perfect" zonal conic would slightly
vary
> with the zonal height, in proportion to zonal radius
variations.
> Since r.o.c. is only for a fraction of percent longer for the
most
> outer zone vs. the innermost, it is also entirely negligible.
> You could not tell the difference if the zonal openings would
> belong to the segment of a sphere focusing at that same point.
>
> Vlad
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>

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