Editing Optical telescope (section)

===Magnification===
The magnification through a telescope makes an object appear larger while limiting the FOV. Magnification is often misleading as the optical power of the telescope, its characteristic is the most misunderstood term used to describe the observable world.{{clarify|date=April 2019}} At higher magnifications the image quality significantly reduces, usage of a [[Barlow lens]] increases the effective focal length of an optical system—multiplies image quality reduction.

Similar minor effects may be present when using [[star diagonal]]s, as light travels through a multitude of lenses that increase or decrease effective focal length. The quality of the image generally depends on the quality of the optics (lenses) and viewing conditions—not on magnification.

Magnification itself is limited by optical characteristics. With any telescope or microscope, beyond a practical maximum magnification, the image looks bigger but shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the finest detail the eye can see. Magnification beyond this maximum is sometimes called ''empty magnification''.

To get the most detail out of a telescope, it is critical to choose the right magnification for the object being observed. Some objects appear best at low power, some at high power, and many at a moderate magnification. There are two values for magnification, a minimum and maximum. A wider field of view [[eyepiece]] may be used to keep the same eyepiece focal length whilst providing the same magnification through the telescope. For a good quality telescope operating in good atmospheric conditions, the maximum usable magnification is limited by diffraction.

====Visual====
The visual magnification <math>M</math> of the field of view through a telescope can be determined by the telescope's focal length <math>f</math> divided by the [[eyepiece]] focal length <math>f_{e}</math> (or diameter).<ref name="SaharaSkyObservatory"/><ref name="RyukyuAstronomyClub"/> The maximum is limited by the focal length of the [[eyepiece]].

An example of visual [[magnification]] using a telescope with a 1200&nbsp;mm focal length and 3&nbsp;mm [[eyepiece]] is given by: <math>M = \frac {f}{f_{e}} = \frac {1200}{3} = 400</math>

==== Minimum ====
There are two issues constraining the lowest useful [[magnification]] on a telescope:
* The light beam exiting the eyepiece needs to be small enough to enter the pupil of the observer's eye. If the cylinder of light emerging from they eyepiece is too wide to enter the observer's eye, some of the light gathered by the telescope will be wasted, and the image seen will be dimmer and less clear than it would be at a higher magnification.
* For telescope designs with obstructions in the light path (e.g. most [[catadioptric system|catadioptric telescopes]], but ''not'' spyglass-style [[refracting telescope]]s) the magnification must be high enough to keep the central obstruction out of focus, to prevent it from coming into view as a central "black spot". Both of these issues depend on the size of the pupil of the observer's eye, which will be narrower in daylight and wider in the dark.

Both constraints boil down to approximately the same rule: The magnification of the viewed image, <math>\ M\ ,</math> must be high enough to make the eyepiece exit pupil, <math>\ d_\mathsf{ep}\ ,</math> no larger than the pupil of the observer's own eye.<ref name=RASC-OH-2023/> The formula for the eypiece exit pupil is
:<math>\ d_\mathsf{ep} = \frac{\ D\ }{\ M\ } \ </math>
where <math>\ D\ </math> is the light-collecting diameter of the telescope's aperture.<ref name=RASC-OH-2023/>

Dark-adapted pupil sizes range from 8–9&nbsp;mm for young children, to a "normal" or standard value of 7&nbsp;mm for most adults aged&nbsp;30–40, to 5–6&nbsp;mm for retirees in their 60s and 70s. A lifetime spent exposed to chronically bright ambient light, such as sunlight reflected off of open fields of snow, or white-sand beaches, or cement, will tend to make individuals' pupils permanently smaller. Sunglasses greatly help, but once shrunk by long-time over-exposure to bright light, even the use of opthamalogic drugs cannot restore lost pupil size.<ref name=RASC-OH-2023>{{cite book |editor1-first = James S. |editor1-last = Edgar |display-editors = etal |year = 2023 |title = Observers' Handbook |publisher = Royal Canadian Astronomical Society |type = annual |edition = USA |isbn = 978-1-92-787930-6 |publication-date = October 2021 |url = https://secure.rasc.ca/store/product/observer-s-handbook-2023 |access-date = 2024-05-10 }}</ref> Most observers' eyes instantly respond to darkness by widening the pupil to almost its maximum, although complete adaption to [[night vision]] generally takes at least a half-hour. (There is usually a slight extra widening of the pupil the longer the pupil remains dilated / relaxed.)
 
The improvement in brightness with reduced magnification has a limit related to something called the [[exit pupil]]. The [[exit pupil]] is the cylinder of light exiting the eyepiece and entering the pupil of the eye; hence the lower the [[magnification]], the larger the [[exit pupil]]. It is the image of the shrunken sky-viewing aperture of the telescope, reduced by the magnification factor, <math>\ M\ ,</math> of the eyepiece-telescope combination:
:<math>\ M = \frac{\ L\ }{ \ell }\ ,</math>
where <math>\ L\ </math> is the [[focal length]] of the telescope and <math>\ \ell\ </math> is the focal length of the eyepiece.

Ideally, the exit pupil of the eyepiece, <math>\ d_\mathsf{ep}\ ,</math> matches the pupil of the observer's eye: If the exit pupil from the eyepiece is larger than the pupil of individual observer's eye, some of the light delivered from the telescope will be cut off. If the eyepiece exit pupil is the same or smaller than the pupil of the observer's eye, then all of the light collected by the telescope aperture will enter the eye, with lower magnification producing a brighter image, as long as all of the captured light gets into the eye.

The minimum <math>\ M_\mathsf{min}\ </math> can be calculated by dividing the telescope aperture <math>\ D\ </math> over the largest tolerated exit pupil diameter <math>\ d_\mathsf{ep} ~.</math><ref name=RocketMime>{{cite web |title=Telescope equations |date=17 November 2012 |department = Astronomy |website=Rocket Mime |url=http://www.rocketmime.com/astronomy/Telescope/telescope_eqn.html}}</ref><ref name=RASC-OH-2023/>
:<math>\ M_\mathsf{min} = \frac{\ D\ }{\ d_\mathsf{ep} } \ </math>
Decreasing the magnification past this limit will not increase brightness nor improve clarity: Beyond this limit there is no benefit from lower magnification. Likewise calculating the [[exit pupil]] <math>\ d_\mathsf{ep}\ </math> is a division of the aperture diameter <math>\ D\ </math> and the visual magnification <math>\ M\ </math> used. The minimum often may not be reachable with some telescopes, a telescope with a very long focal length may require a longer focal length eyepiece than is available.

An example of the lowest usable magnification using a fairly common 10″ (254&nbsp;mm) aperture and the standard adult 7&nbsp;mm maximum [[exit pupil]] is given by: <math>\ M_\mathsf{min} = \frac{ D }{\ d_\mathsf{ep} } = \frac{\ 254\ }{ 7 } \approx 36\!\times ~.</math> If the telescope happened to have a {{gaps|1|200|mm}} focal length (<math>\ L\ </math>), the longest recommended eyepiece focal length (<math>\ \ell\ </math>) would be <math>\ \ell = \frac{\ L\ }{ M } \approx \frac{\ 1\ 200\mathsf{\ mm\ } }{ 36 } \approx 33\mathsf{\ mm} ~.</math> An eyepiece of the same apparent field-of-view but longer focal-length will deliver a wider true field of view, but dimmer image. If the telescope has a central obstruction (e.g. a [[Newtonian telescope|Newtonian]], [[Maksutov telescope|Maksutov]], or [[Schmidt–Cassegrain telescope]]) it is also likely that the low magnification will make the obstruction come into focus enough to make a black spot in the middle of the image.

Calculating in the other direction, the [[exit pupil]] diameter of a 254&nbsp;mm telescope aperture at 60× [[magnification]] is given by: <math>\ d_\mathsf{ep} = \frac{\ D\ }{ M } = \frac{\ 254\ }{ 60 } \approx 4.2\mathsf{\ mm\ } ,</math> well within pupil size of dark-adapted eyes of observers of almost all ages. Assuming the same telescope focal length as above, the eyepiece focal length that would produce a 60× magnification is  <math>\ \ell = \frac{\ L\ }{ M } = \frac{\ 1\ 200\mathsf{\ mm\ } }{ 60 } \approx 20\mathsf{\ mm} ~.</math>

====Optimum====
The following are [[rule of thumb|rules-of-thumb]] for useful magnifications appropriate to different type objects:
* For small objects with low surface brightness (such as [[galaxies]]), use a moderate magnification.
* For small objects with moderate surface brightness (such as [[planetary nebulae]]), use a high magnification.
* For small objects with high surface brightness (such as [[planet]]s), use the highest magnification that the current night's "seeing" will allow, and consider adding in [[astronomical filter]]s to sharpen the image.
* For large objects (such as the [[Andromeda Galaxy]] or wide-field [[diffuse nebulae]]), regardless of surface brightness use low magnification, often in the range of minimum magnification.
* For very to extremely bright, large objects (the [[Moon]] and the [[Sun]]) narrow-down the aperture of the telescope by covering it with a piece of cardboard with a small hole in it, and insert filters as-needed to both cut down excess brightness and to enhance the contrast of surface features.

Only personal experience determines the best optimum magnifications for objects, relying on observational skills and seeing conditions, and the status of the pupil of observer's eye at the moment (e.g. a lower magnification may be required if there is enough moonlight to prevent complete dark adaption).