Telescope Formulas, Common Telescope Myths
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|Magnification =||Objective focal length / Eyepiece focal length|
|=||Objective diameter / Exit pupil|
|f/# =||Objective focal length / objective diameter|
|Field Size (°) =||eyepiece field stop diameter / telescope focal length) x 57.3°|
|Exit pupil =||Objective diameter / Magnification|
|=||Eyepiece focal length / (Objective f/#)|
|Dawes limit =||4.56 arc seconds / Objective diameter in inches|
|Aperture gain =||(Objective diameter / Eye pupil diameter)2|
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.
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.
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.
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.
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.
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.
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.
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.