spherical mirrors matching the curve of parabolic

The stuff I read says they match well enough for small mirrors that it
doesn't matter which you use - but this is for a comparison of two mirrors
each centred on the optical axis.

What I'm wondering is if you could use a small pair of spherical mirrors
tipped a bit towards a single flat one and two eyepieces to make light cheap
binoculars...lighter at the far end anyway...

jtaylor wrote:

The stuff I read says they match well enough for small mirrors that it
doesn't matter which you use - but this is for a comparison of two mirrors
each centred on the optical axis.

Provided that the radius of curvature R is long compared to the diameter
of the mirror D then the spherical mirror is a close enough
approximation to a parabola. Faster mirrors need to be parabolised.

What I'm wondering is if you could use a small pair of spherical mirrors
tipped a bit towards a single flat one and two eyepieces to make light cheap
binoculars...lighter at the far end anyway...

You can do it, but you won't get what you expect. Try it out instead
with an aperture mask placed in front of a larger telescope.

Regards,
Martin Brown

Why tie yourself to one secondary flat?
I'll note that if you do run an offset mirrror, the aberrateions of hte
telescope will be that of a mirror that would be the full diameter of the
parabola that your mirror would have been cut out of. In other words, if
the optical axis is 1" outside the 4" mirror edge, the aberrations would be
that of a 10" parabolic mirror.

--
Why isn't there an Ozone Hole at the NORTH Pole?

At f/10 a sphere is about the same as a parabola with 1/4 wave error.
Works for most scopes, but they are small because at f/10 the tubes can
get pretty long!

Gonna be one hell of a big pair of binoculars when you get done!

"Bob May" wrote in message
...
Why tie yourself to one secondary flat?

I thought it might make things simpler.

I'll note that if you do run an offset mirrror, the aberrateions of hte
telescope will be that of a mirror that would be the full diameter of the
parabola that your mirror would have been cut out of. In other words, if
the optical axis is 1" outside the 4" mirror edge, the aberrations would
be
that of a 10" parabolic mirror.

If the two mirrors were touching and tilted slightly towards each other, a
flat could be mounted above the tubes, and eyepieces above the mirrors. The
optical axes would then be what, 1/2, 2/3of the way to the edge? For a pair
of 3" mirrors how much difference could it make?

Gil wrote:
At f/10 a sphere is about the same as a parabola with 1/4 wave error.
Works for most scopes, but they are small because at f/10 the tubes can
get pretty long!

Actually it depends on the aperature of the mirror. In a 4" mirror you can
go even faster than f/10. Larger than 8" and there is just too much
difference from a sphere for f/10 to handle it.

--
Bill

"jtaylor" wrote in
:

The stuff I read says they match well enough for small mirrors that it
doesn't matter which you use - but this is for a comparison of two
mirrors each centred on the optical axis.

It actually has nothing to do with the size of the mirror. The key thing
is the focal ratio. An f100 spherical mirror would be indistinguishable
from a parabola. When you get to f10 the error is about 1/4 wave so would
probably still be acceptable. For mirrors faster than f10 you would
definitely want to parabolise. Note that with small mirrors it is
possible to parabolise them via mechanical distortion (via a bolt glued
to the back of the mirror - there was an article in S & T about this a
few years back).

If you are interested in binoscopes in general, a guy in our local club
has a superb 16"er. See he

http://www.binoscope.co.nz/index.html

Klazmon.






What I'm wondering is if you could use a small pair of spherical
mirrors tipped a bit towards a single flat one and two eyepieces to
make light cheap binoculars...lighter at the far end anyway...

jtaylor wrote:
The stuff I read says they match well enough for small mirrors that
it
doesn't matter which you use - but this is for a comparison of two
mirrors
each centred on the optical axis.

What I'm wondering is if you could use a small pair of spherical
mirrors
tipped a bit towards a single flat one and two eyepieces to make
light cheap
binoculars...lighter at the far end anyway...

Hi
The only issue with tilting mirror is that you increase
the error from a parabola as you move off the optical axis
of a parabola. A tilted mirror is most correct when it
fits into the location on the surface of a parabola that
has the same relative focus point and source. Imagine going
up the side of the parabolic surface and drawing a circle
to cut out that piece. Now use that piece at the same
offset and angle from the original parabolas axis.
Dwight

wrote in message
ups.com...

jtaylor wrote:
The stuff I read says they match well enough for small mirrors that
it
doesn't matter which you use - but this is for a comparison of two
mirrors
each centred on the optical axis.

What I'm wondering is if you could use a small pair of spherical
mirrors
tipped a bit towards a single flat one and two eyepieces to make
light cheap
binoculars...lighter at the far end anyway...

Hi
The only issue with tilting mirror is that you increase
the error from a parabola as you move off the optical axis
of a parabola. A tilted mirror is most correct when it
fits into the location on the surface of a parabola that
has the same relative focus point and source. Imagine going
up the side of the parabolic surface and drawing a circle
to cut out that piece. Now use that piece at the same
offset and angle from the original parabolas axis.
Dwight

I knew that.

What I don't know is how far from the centre you could put a spherical
mirror of some specified dimension before the error would be above
acceptable limits.

And as a practical matter, how closely matched, in terms of focal length, am
I likely to get two, say, 3" mirrors (buying, not making, me making them
would make the answer "not at all close").

Lkazlan Klazmon wrote:

It actually has nothing to do with the size of the mirror. The key thing
is the focal ratio. An f100 spherical mirror would be indistinguishable
from a parabola. When you get to f10 the error is about 1/4 wave so would
probably still be acceptable. For mirrors faster than f10 you would
definitely want to parabolise.

Actually, it involves *both* the f/ratio *and* the diameter of the
primary mirror. Long focal lengths can make the spherical mirror
approach the curve of a paraboloidal one to at least a point which will
satisfy the Rayleigh limit (1/4 wave wavefront error or 1/8th wave
surface error). However, as the mirror size gets larger, the physical
deviation between a spherical mirror and a paraboloidal one of
approximately the same focal length can go beyond the often-quoted 1/8th
wave criteria. You then have to increase the f/ratio of the mirror to
compensate (see HOW TO MAKE A TELESCOPE by J. Texereau, p. 18-19):
The formula for this is 88.6D**4 = f**3 (** means to the power of: i.e.:
2**3 = "two cubed" = 8), where f is the focal length and D is the
aperture (in inches). Substituting F=f/D to get the f/ratio, we get:
F = cube-root (88.6*D). The following minimums can just achieve the
1/8th wave surface rule of thumb:

APERTURE TEXEREAU MINIMUM F/RATIO
3 inch f/6.4
4 inch f/7.1
6 inch f/8.1
8 inch f/8.9
10 inch f/9.6
12 inch f/10.2

A better somewhat more "diffraction limited" performance can be
achieved by making the circle of least confusion of the light from the
spherical mirror smaller than the radius of the diffraction disk. This
results in the following relation: D = .00854(F**3) (for D in
centimeters and F is the f/ratio), and for English units: D =
..00336(F**3). Thus, the minimum f/ratio goes as the cube root of the
mirror diameter, or the DIFFRACTION-LIMITED F/RATIO: F =
0.675(D)**(1/3). For example, the typical "department store" 3 inch
Newtonian frequently uses a spherical f/10 mirror, and should give
reasonably good images as long as the figure is smooth and the secondary
mirror isn't terribly big. For common apertures, the following
approximate minimum f/ratios for Diffraction-Limited Newtonians using
spherical primary mirrors can be found below:

APERTURE F/RATIO FOR DIFFRACTION-LIMITED SPHERICAL MIRRORS
-----------------------------------------------------------------------
3 inches f/9.6 (28.8 inch focal length)
4 inches f/10.6 (42.4 inch focal length)
6 inches f/12.1 (72.6 inch focal length)
8 inches f/13.4 (107.2 inch focal length)
10 inches f/14.4 (144 inch focal length)
12 inches f/15.3 (183.6 inch focal length)

Clear skies to you.

--
David W. Knisely
Prairie Astronomy Club: http://www.prairieastronomyclub.org
Hyde Memorial Observatory: http://www.hydeobservatory.info/

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