Alan French wrote:
[Frank Bov wrote:]
[SNIP]
Now, at low power, the eyepiece does not magnifying the image enough for the
resolution at the focal plane to matter; the eye's the limiting factor. So
at very low power, once the exit pupil exceeds the dilated eye, the
resolution in the perceived image stays the same as if the exit pupil just
filled it. [SNIP]

Frank,

Yes, that's one reason the debate I'm in elsewhere is so strange. Folks
want to believe they are utilizing the full resolution of a pair of 8x42
binoculars on a bright sunny day, yet 8 power is not enough magnification to
use the resolution of even a much smaller lens.

In the full light of day, visual acuity allows resolution of angular
separations as small as about 1 arc minute, on average. If we apply Dawes
limit, we can predict a resolution limit for a single 42-mm aperture objective.
(Is there a Dawes limit for binocular optics?)

Dawes limit is often stated as R (resolution in arc seconds) = 4.56/D, where D
is the aperture of the optic in inches. Converting to millimeters
(1-inch=25.4-mm), R = 115.8/D. Applying this to a 42-mm objective, we get a
theoretical resolution (angular separation) limit of 115.8/42 = 2.75, or about
3 arc seconds. The magnification needed to make that 3" angle appear 1' in size
to the eye would be 20X. Theoretically, we can say this is the magnification
needed to allow the eye to make full use of the resolution potential of that
aperture.

Under low light conditions, even more magnification is needed. Visual acuity
degrades to about 4 arc minutes, on average, if the observer is viewing objects
against a sufficiently dark background. Theoretically, we would need to magnify
the image by 80X to take full advantage of the resolution potential of that
same 42-mm objective.

Of course, visual acuity varies with the individual. So, to state the above as
hard and fast rules applying to all observers would be inaccurate. But the
above analysis does illustrate a foundation for the commonly quoted guideline
that a 0.5-mm exit pupil is the highest useful magnification for an
astronomical telescope. This may, perhaps, be better stated as the highest
"needed" magnification for a given aperture. It is not uncommon for observers
to use magnifications producing exit pupils smaller than 0.5-mm. But assuming
at least average visual acuity, magnification producing a 0.5-mm exit pupil is
enough to allow an observer to resolve to the full potential of the aperture
being used.

Getting back to Alan's original question I think it's fair to say in a general
sense that, under daylight conditions, an observer isn't taking full advantage
of the resolution potential of that aperture unless the exit pupil is ~2-mm or
smaller.

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
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