How would you compare Telescopes ?
Since the focal lengths and F/ratios are different it is impossible to have both the magnifications and exit pupils be identical in both scopes.
What would be the best options for a comparison? magnication, exit pupil or both?
That is true.
Stating magnification typically lets people know: did you have a tiny view of Saturn at 40x or did you have a humongo view at 300x? This is useful particularly when referring to seeing conditions.
Exit pupil is the much more useful and much less understood metric. For one thing, realize that exit pupil in mm at the eyeball is just one way of stating magnification, it's just that we customarily look at magnification as the total sum, rather than the function of the parts.
On any telescope 0.5x per mm of aperture = 2 mm exit pupil
On any telescope 1x per mm of aperture = 1mm exit pupil.
On any telescope 2x per mm of aperture =0.5 mm exit pupil.
If you know the scope's focal ratio you know the oculars needed to get both. And by using ratios you can interpolate everything else (magnification, approximate ocular size required). There is an enormous amount of information packed into this way of thinking.
If you have an 80mm f/7 and are at 0.5x per mm of aperture we know you are at 40x and a 2mm exit pupil and using a 14 mm ocular. If you have 2x per mm of aperture you are at 160x and using a 3.5 mm ocular. And if you are at 80x you are using a 7 mm ocular. The ocular at the focal length of the telescope always yields the magnification of the objective (or primary mirror) in mm. In an 8" (200 mm) f/10 SCT a 10 mm ocular yields 200x.
This is why we are so stupid to keep using imperial measurement and talking about things like "50x per inch". Inches are not useful in this game.
ANYHOW, we also know
That the zone of optimal viewing, relative to the organic structure of the eye, is 1mm to 2 mm.
That high powers, relative to what the eye will accommodate, basically start at 1mm exit pupil and below.
That there is seldom any utility (in terms of information in the view) to pushing magnification below 0.5 mm exit pupil, though all of us do it.
That as a rule color saturation starts to fade at 0.5 mm and below (as in 0.3 mm exit pupil etc.) This is also called "dimming out".
=> How dim do you like it? That is one of the determinants of how far to push magnification. (along with floaters, see below)
That if you want to convert exit pupil to magnification per mm (and from there to the total magnification of the scope) you just take the reciprocal of the exit pupil. 0.5mm exit pupil = 1/0.5 = 2x per mm. 0.3 mm exit pupil = 1/0.3 = 3.3x per mm. Because that is substantially more than 2x per mm, we know the magnification is in all likelihood being pushed past what yields a meaningful improvement in the view--"empty magnification."
A lesser known feature of exit pupil is the "astigmatism boundary." About 30 to 60% of the population has astigmatism. Astigmatism creates viewing defects as magnification decreases. Where the exact boundary is depends on the individual, but let us say that people with astigmatism who don't use corrective lenses will probably begin to have problems as exit pupil increases beyond 4 to 5 mm.
Another organic eyeball structural feature is on the opposite end. Everyone has what are called "floaters" which are junk that comes between you and what you want to see. It is illuminated very well at exit pupils of 0.5 mm and below. And I have heard people say they prefer to stay 0.8 mm.
=>The general rule for floaters is, the better the telescope you can afford, the older you are, and as a result, less able to appreciate your precision optic with your decrepit eyes. This also applies to astigmatism.
If you have certain magnification goals in mind as a regular basis then you should pay attention to magnification per mm. If you're going over 2x per mm then you should probably be thinking about a bigger telescope.
There is also what may be called the general magnification ceiling prevailing over most places most times, 200x to 300x being where magnification caps except in extraordinarily stead places like on top of Hawaii, in the Andes, or in Florida. You find out what it is for your area by trying it out or talking to other amateur astronomers.
Once you know how tight an exit pupil you can tolerate, what the local seeing cap is, and whether you are bothered by low powered astigmatism, you are in a position to consider your optimal focal ratio and aperture.
so in the case of these scopes:
a 120mm f/5 achromat with focal length of 600mm versus
102mm f/7 ED with focal length of 714mm
I say well do I want to use the refractor for low power viewing or high power viewing. Because to get to 2x per mm in the 120mm f/5 I will need a 2.5 mm ocular. Those tend not to be pleasant to look through for long times. In addition, it is an achromat, and that would bother me, so I would automatically cut in half the magnification I expect to get from it: 1x per mm or less. On the other end, in the low magnification zone, I would consider my personal low exit pupil comfort zone to be about 5 to 6 mm. That would suggest a 25 to 30 mm eyepiece. Beyond that it is likely to be unusable to me without either a dioptrx or wearing contacts, etc.
I like my 40 mm XW. This scope could not use it.
Because it is a large fast achromat this scope will also be losing about half the useful high power magnification on planets.
With such limitations at the bottom and top of the exit pupil scales, I would not buy this scope. The 102 mm f/7 is the obvious choice.
A more interesting case is:
130 mm f/7 ED vs 102 mm f/7 ED.
I like magnifications in the mid 200s. That's a big plus for the 130 mm. To get into the mid 200s with the 102 mm I would either have to use eyepieces below 3.5 mm or take say a barlow and put it on a 5 mm. Those combinations do not appeal.
On the other end it is pretty clear that the 102 mm is in a good place at the 5 mm exit pupil for wide fields. That would be one fifth the 1mm exit pupil that gives 1x magnification per mm, we can see from the relationship that 0.2x per mm will give a 5 mm exit pupil and 102*0.2=20x magnification. That is by definition a wide field view, if we need a 7mm ocular for 1x per mm then we will need a 35mm ocular or, for some of us, a 40mm such as the Pan 41 or XW40.
On the 130 mm f/7 telescope the 7 mm gives us 130x at 1mm exit pupil and we can work from that to get the 5 mm exit pupil ratios 130/5=~25x magnification, and 5*7 = 35 mm ocular zone again (hence the famous Pan 35).
The catch is the *lowest* magnification is now 25x instead of 20x, so the field of view MUST decrease. Hence one critical element of having a wide field is not to push the aperture too big...in the usual focal ratios.
On the other hand our "sacrifice" of a 20x wide field view has "purchased" for us easier access to high magnifications. A 1mm exit pupil "buys" us 130x, not 100x.
The quest for magnification at one end of the viewing experience and wide fields at the other is what pushes some people to buy different aperture refractors, or to buy a small refractor and some other aperture telescope (not necessarily a refractor) to use with it.
Well it's all just arithmetic folks no fancy calculus here. But I fear the MEGO factor in this answer is too great (My Eyes Glaze Over).
Edited by gnowellsct, 02 September 2020 - 01:11 PM.