Magnification eyepiece
An eyepiece, in conjunction with the telescope, projects a magnified object image onto the retina. The size of these object images can be compared with the theoretical object size on the retina without using any aids.
The magnification of the telescope is influenced via an eyepiece. It applies:
But what magnifications are useful so that the human eye can still handle them? When asking this question, it must be taken into account that the human pupil is an aperture that can open to different degrees depending on age. A suitable calculation formula can be found in this document: (https://articles.adsabs.harvard.edu/pdf/1990PASP..102..212S, page 213, formula 5)
The eyepiece, in cooperation with the telescope, creates an exit pupil for which the following equation applies:
The exit pupil should not be larger than the pupil entrance. Image information would not reach the retina and are, so to speak, superfluous. If the pupil diameter corresponding to the age is used in the formula for the exit pupil, a minimum useful magnification can be determined.
R. H. Garstang published a document in 1999 (https://articles.adsabs.harvard.edu/pdf/1999JRASC..93...80G) in which he gives a formula for the maximum magnification depending on the seeing and the sky brightness (page 82, formula 8) in order to be able to see those stars that can just be recognized with the telescope eyepiece system used (limiting magnitude).
where:
D – Telescope aperture in [cm]
t – Transmission factor of the telescope (losses due to obstruction as well as lens and mirror surfaces)
b – sky brightness in [nL] (nano Lambert)
p – Pupil diameter
θ – Seeing value in arc minutes [‘]
The sky brightness can be determined approximately for the respective location at https://www.lightpollutionmap.info/. To convert this into the required unit nL (nano Lambert), the following formula can be used: (https://articles.adsabs.harvard.edu/pdf/1990PASP..102..212S, page 215, formula 17)
A more simple approach for the maximum magnification can be found using the following argument: The human eye cannot further resolve image information generated by an exit pupil smaller than 0.5 mm (https://www.teleskop-spezialisten.de/shop/Die-richtige-Vergroesserung:_:86.html). If magnification is increased beyond this, the object depicted is shown larger, but the person cannot recognize any further details. With this knowledge, the same formula can therefore be used to calculate a maximum useful magnification.
What would be the optimum magnification for a telescope eyepiece system? This arises when it is possible to be within the range of the resolving power of the telescope, taking into account the maximum resolving power of the human eye. The following formula has been established for this purpose.
A formula based on the practical experience of several observers with different telescopes was published by T. Lewis in 1913. (https://articles.adsabs.harvard.edu/pdf/1913Obs....36..423L, page 428)
A suitable combination of telescope and eyepiece can be determined via the 'Eyepiece' calculation tool in the ‘Tools’ menu point.
Magnification camera
In astrophotography it does not make sense to talk about magnification, but about a section of the image that is displayed on a chip. In simple words, a telescope is a telephoto lens on a camera. Telescopes with a large focal length represent a small section of the sky on the chip. If the same camera chip is used on a telescope with a small focal length, a much larger section of the image is displayed. When viewing the image on the computer at different distances, or when printing at different sizes, the magnification also changes. The more pixels a camera chip has, the more can be magnified on the screen. Therefore it makes sense to use the image scale (see menu item 'Basics' - 'Telescope-Camera-Combination' - 'Image scale') for astrophotography.