Telescope Formulas
Magnification = Objective focal length /
Eyepiece focal length = Objective diameter / Exit pupil
f/number =
Objective focal length / objective diameter
Field Size (degrees) =
(eyepiece field stop diameter divided by telescope focal length) x 57.3 degrees.
Exit pupil = Objective diameter / Magnification = Eyepiece focal
length / Objective f/number
Dawes limit = 4.56 arc seconds /
Objective diameter (inches)
Aperture gain = (Objective diameter /
Eye pupil diameter) squared
As explained in the text, there is
no practical limit to the low magnification that can be used with a refractor.
But the secondary obstruction found on most reflectors does set limits, because
the shadow spot it forms in the exit pupil grows as the magnification is
reduced. Consider this extreme example of an exit pupil formed by an 8-inch
Schmidt-Cassegrain with a central obstruction equal to 43 percent of the
aperture's diameter. A telecompressor lens and long-focal-length eyepiece give
14x magnification. While the central shadow remains 43 percent of the exit
pupil's diameter, it is now 6.2 millimeters in diameter and would nearly fill
the 7-mm pupil diameter of the dark-adapted eye.
Common Telescope Myths
Through the years, many myths (or, if you prefer,
misconceptions) have become woven into the fabric of amateur astronomy. The
following is a selection that involves telescope magnification. A number of the
answers described here are further explained in the accompanying
text.
Myth #1: A 7-mm exit pupil gives the lowest useful
magnification.
Not so! With a refractor there is no limit on the size
of the useful exit pupil. Use whatever is necessary to get the field you need to
frame the subject. A reflector's low-power limit is reached when the black spot
in the exit pupil (caused by the secondary obstruction) becomes obtrusive.
While a 7-mm exit pupil, by matching that of the eye, does give the
brightest views of deep-sky objects, it does not necessarily give the best ones.
Higher magnifications, despite their smaller exit pupils, will reveal more
details, maintain contrast, show fainter stars, and help bypass defects in the
eye itself.
Myth #2: Exit pupils larger than 7 mm waste light and
resolution.
With refractors larger pupils do waste aperture. But the
magnification is so low that the wasted aperture is of little concern: both
image brightness and resolution are as great as possible at that magnification.
With reflectors, however, larger pupils do waste light, but primarily because
the black spot in the pupil caused by the secondary obstruction becomes larger.
Both light loss and field shadowing occur with reflectors, but as with
refractors there is no resolution loss because of the low power.
Myth
#3: Faster telescopes show brighter images.
This is a misconception
carried over from photographic use, where the fast f/ratios do mean brighter
images and shorter exposures for extended objects. Telescopes with equal
apertures and equal magnifications have the same visual image brightness,
regardless of the objective's f/number.
Myth #4: Long-focal-ratio
telescopes give higher-contrast images.
In general, refractors offer
the potential for higher contrast because mirror coatings, by their nature, tend
to scatter more light. But when comparing well-made, highly corrected
refractors, there is no gain in contrast with instruments of long focal ratio.
Reflectors too, if well made and having the same size of secondary
obstruction, will have the same contrast at the same magnification regardless of
the f/ratio.
Myth #5: The highest useful magnification is 50x per
inch of aperture.
What is "useful"? Although small telescopes little
affected by the atmosphere may give pleasing images even up to 100x per inch of
aperture, no more detail is seen than at 50x per inch. On the other hand, large
instruments, more affected by atmospheric seeing, may top out at 20x or 30x per
inch. In practice, a 3- or 4-inch refractor may work well at 200x, but it is
rare indeed that any size instrument benefits from more than two or three times
that magnification.
Myth #6: Barlow lenses degrade image quality.
There may have been some truth to this when Barlows were made with
low-index glasses and not specifically designed for use with modern eyepieces.
Modern, high-index Barlows actually improve eyepiece performance by reducing
astigmatism at the edge of the field. Furthermore, using a Barlow increases the
effective f/number of the objective and permits using longer-focal-length
eyepieces (with their longer eye relief) for high-magnification viewing.
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