Highest Useful Magnification

[beka]

Hi All,

It has been suggested that the maximum useful magnification of a telescope is about 50X for every inch of aperture. So for a 4 inch for example it would be 200X.  I was wondering what the basis for this is? On Celestron's site, the magnifications they give for their scopes seem to be higher. For the NexStar 130 SLT it is 307X but it should be about 250X (5" X 50) from the rule above. I tried some calculation based on the image scale of the telescope and the resolution of the human eye but did not really get numbers close to these. Does anyone know how these numbers are arrived at?

Best

[johninderby]

The maximum useabe magnification varies from night to night and deends on  what you are  looking at. What is suitable for the  moon or double stars isn’t the same for other things. Often lower mag will show more. 

Many scope manufactures will give wildly inflated max magnification and I just ignore them. The old rule of thumb of 50x per inch is a starting point for general observimg.

The Televue calculator gives useful info when you input your scopes specs and select magnification.

https://www.televue.com/engine/TV3b_page.asp?id=212&plain=TRUE

 

Edited October 24, 2021 by johninderby

[Tiny Clanger]

Plenty of information available on this, here are the first few results of a quick search :

:https://www.astronomics.com/info-library/how-to-pick-an-eyepiece/highest-useful-magnification/

https://learnastronomyhq.com/articles/how-much-magnification-can-i-get-with-my-telescope.html

https://telescopeschool.com/telescope-magnification-guide-where-does-it-get-blurry/

https://www.optics-trade.eu/blog/lowest-and-highest-useful-magnification/

[rl]

The idea of maximum magnification is to extract all the detail in the image without over-magnifying which makes it dimmer and fuzzy. 

The image at the prime focus contains a finite amount of detail. the bigger the aperture, the more detail. It's like a mosaic...the bigger the aperture, the smaller the pieces in the mosaic. The resolution (mosaic piece size) depends on the wavelength of the light and the scope aperture. Resolution in arcseconds = 138mm divided by the scope aperture in millimetres, so a 60mm scope will resolve just over 2 arcseconds of angle. A 6" will resolve to about 0.9 arcseconds which is finer detail

The maximum magnification will match the scope's resolution to that of the eye. Now, people's eyes are all a bit different so there is no cast-in-stone rule for this, but on average most people's eyes can resolve between 1 and 4 arcminutes of angle depending on the brightness of the object and its contrast. This is between 60 and 240 arcseconds. Thus, for your 60mm scope resolving 2 arcseconds, you need to multiply by 60/2 to 240/2 or 30 to 120 times.  For a 6" scope, you get 60/0.9 to 240/0.9 or 66 to 267 times. The 50 times per inch figure is just a generalisation of this principle assumimg your eye resolves just over 4 arcminutes. 

A lot of caveats apply. Astigmatism in your eye favours higher magnification. Floaters favour dropping the magnification down a bit since the very narrow exit pupil is more easily scattered.

Edited October 24, 2021 by rl

[beka]

1 hour ago, rl said:

The idea of maximum magnification is to extract all the detail in the image without over-magnifying which makes it dimmer and fuzzy. 

The image at the prime focus contains a finite amount of detail. the bigger the aperture, the more detail. It's like a mosaic...the bigger the aperture, the smaller the pieces in the mosaic. The resolution (mosaic piece size) depends on the wavelength of the light and the scope aperture. Resolution in arcseconds = 138mm divided by the scope aperture in millimetres, so a 60mm scope will resolve just over 2 arcseconds of angle. A 6" will resolve to about 0.9 arcseconds which is finer detail

The maximum magnification will match the scope's resolution to that of the eye. Now, people's eyes are all a bit different so there is no cast-in-stone rule for this, but on average most people's eyes can resolve between 1 and 4 arcminutes of angle depending on the brightness of the object and its contrast. This is between 60 and 240 arcseconds. Thus, for your 60mm scope resolving 2 arcseconds, you need to multiply by 60/2 to 240/2 or 30 to 120 times.  For a 6" scope, you get 60/0.9 to 240/0.9 or 66 to 267 times. The 50 times per inch figure is just a generalisation of this principle assumimg your eye resolves just over 4 arcminutes. 

A lot of caveats apply. Astigmatism in your eye favours higher magnification. Floaters favour dropping the magnification down a bit since the very narrow exit pupil is more easily scattered.

This is the kind of calculation I attempted - I assumed the eye to have a resolution of about 0.2mm for near objects and came up with numbers closer to the lower end of the ranges you mentioned.

Thanks

[Sunshine]

Those manufacturers numbers assume absolute ideal conditions which chances are you’ll never encounter, there are so many variables involved it can be dizzying. Accessories, temperature, collimation, seeing conditions, stray light, optical quality (not all scopes of a given aperture and design are equals) etc. Sometimes I can use 70x per inch while the very next night I struggle with 30 on the same object.

Edited October 24, 2021 by Sunshine

[vlaiv]

2 hours ago, beka said:

This is the kind of calculation I attempted - I assumed the eye to have a resolution of about 0.2mm for near objects and came up with numbers closer to the lower end of the ranges you mentioned.

Thanks

I think that most discrepancy in "useful" magnification comes from differences in visual acuity of observer in question.

https://en.wikipedia.org/wiki/Visual_acuity

On that page you have comparative scale. 20/20 vision - often quoted as perfect vision corresponds to minimum resolving of 1 arc minute. If you have two white lines separated by black line - you'll be able to tell it is two white lines if they are separated by 1 arc minute with 20/20 vision. You'll be able to resolve them.

In any case - it is better to talk about minimum useful magnification rather than maximum useful magnification. How much do you need to magnify image to be able to see all there is to be seen - rather than how much you can magnify image in general.

You can magnify as much as you like - and not sure if useful is something that I would put next to max magnification.

 

[Franklin]

50x per inch of aperture gives and exit pupil of 0.5mm, anything smaller than this and eye defects such as floaters become a major problem. I've found that backing off from the higher magnifications allows me to see more detail, all be it on a smaller scale. It also helps train the eye to see finer detail. Ultimately it all depends on the sky conditions. I'm lucky to be able to use 40x per inch under my bortle 6 skies and only then when the seeing allows.