WHAT TELESCOPE FOCAL RATIO OFFERS THE HIGHEST MAGNIFICATION?

[refractordude]

I know there is a mathematical reason, but please explain. Thanks for your responses.

[Demonperformer]

The magnification is given by the focal length of the telescope divided by the focal length of the eyepiece. So, a telescope with a focal length of 1000mm (whether it be a 500mm f/2 scope or a 50mm f/20 scope) using a 25mm eyepiece will give you 40x magnification. Focal ratio does not alter the magnification. But at that magnification you would get very different views through the 2 scopes mentioned!

I may be "jumping at shadows", but don't fall into the 'high-magnification-good, low-magnification-bad' trap. The greater the magnification the fainter the image (2x magnification = 1/4 as bright). You will always be able to see more on a small bright image than a big faint image (using 'image' as 'what you see in the eyepiece', rather than 'photo'). There are far more important considerations than simple 'magnification' when deciding on your equipment (both 'buying' decision and 'using' decision).

HTH

 

[Tim]

Also remember that even on very large instruments, which are technically capable of giving very high magnification, in practice, on the majority of nights we get to observe, atmospheric conditions limit the useful magnification to a fraction of what the telescope, on paper, can provide.

It would be fantastic for example to be able to observe the  moon at, say 1000X, but all you would see is a jumping, unstable, blurry mess, the effects of looking through miles of moving air.

You can usually take the maximum magnification figures banded around with telescopes with a large pinch of salt.

Is there anything in particular you are hoping to achieve?

Tim

[cloudsweeper]

Mag depends on the 'scope's FL as already pointed out, and not on aperture.  (Slower 'scopes with higher f-numbers often have larger FLs anyway, but always look to the FL as your indicator for mag, and not f-number.)

And yes, mag is not everything.  Low power views are generally sharper, more steady, better framed, and less prone to vibration.  I seldom go much above x120 or x150.  It depends on the target and the conditions.  (I got to x339 on the Moon the other day, but that was exceptional!)

Doug.

[drjolo]

The maximum usable magnification is somehow related to telescope aperture. Even assuming the optics is perfect, there are still diffraction limits. For visual range this limit is about 130 / D in arc sec (where D is in mm). So for 80mm refractor this limit is somewhere about 1.8", and since human eye can resolve details at level of 150 arc secs, then for 80mm telescope getting mag over 120/1.8 = 83x will not get more details. Although it is very subjective, and some observers stil find values over 2D (over 160x for this example) still useful, while other keep it rather close to 1D (about 80x for 80mm telescope). 

[Knighty2112]

Generally the longer the focal length of any scope, the higher the magnification is for any given EP. For example three scopes with focul lengths of 500mm, 1,000mm and 1,500mm focul lengths (nice and easy numbers for the maths) give the following magnification for a 5mm EP;

500/5= 100x

1,000/5 = 200x

1,500/5 = 300x

If we change the EP to a 2.5mm EP we get the following magnifications higher magnifications achievable (theoretically) for these these same three focal lengths as 200x, 400x and 600x respectively.However, as others have said the higher the magnification does reduce the image brightness, and also normal UK seeeing rarely allows much over 200x magnification on a normal light, so all objects apart from the moon will be too dim to make much out. On some good nights you may be able to push to 300+ but these are less rare. As the higher magnification starts to dim any images, to counteract this you need a larger lens/mirror to scoop up more light. 

[Demonperformer]

One area where I believe higher magnification can be used and is actually useful is for splitting double stars. You are still restricted by the diffraction limits of the scope, as per drjolo's comment, but you are no longer looking for "details", but are trying to get as much "black space" between the components as possible. Higher magnification in this case not only increases the distance between the stars, but also helps "darken" the sky so making them easier to split.

[Stu]

The craziest scope I had was an 8" f20 Mak, with a 4000m focal length. Even a 31mm Nagler gave x129 and only a 0.63 degree field of view! The 5mm in the example above would have given x800!

Longer focal ratios do mean a smaller secondary on compound scopes which should give better contrast, plus the ability to use longer eye relief eyepieces at high power.

[Ricochet]

2 hours ago, drjolo said:

The maximum usable magnification is somehow related to telescope aperture. Even assuming the optics is perfect, there are still diffraction limits. For visual range this limit is about 130 / D in arc sec (where D is in mm). So for 80mm refractor this limit is somewhere about 1.8", and since human eye can resolve details at level of 150 arc secs, then for 80mm telescope getting mag over 120/1.8 = 83x will not get more details. Although it is very subjective, and some observers stil find values over 2D (over 160x for this example) still useful, while other keep it rather close to 1D (about 80x for 80mm telescope). 

@drjolo is correct. Whilst you use the focal length of the telescope to calculate the magnification that a specific eyepiece will give you, the maximum useful or optimal magnification is proportional to the aperture of the telescope. Note that, as @Tim pointed out, the atmospheric conditions will often be the limiting factor for large telescopes.

[Stu]

I wonder if @refractordude can give a bit more info on the background to the question. I feel we are all scrabbling around in the dark a little ...  

[Demonperformer]

5 minutes ago, Stu said:

I feel we are all scrabbling around in the dark a little

Isn't that astronomy in a nutshell? 

[Tim]

18 minutes ago, Stu said:

 we are all scrabbling around in the dark a little

That should definitely be our catchphrase!

[Ruud]

Anyway, the answer has been given: the diameter of the front lens (or largest mirror) determines the highest usable magnification. When this diameter is D mm, the highest magnification is about 2xD. A 70 mm lens will have a maximum magnification of 140x.

If you go further two things go wrong: the image becomes too dim and noticeably blurry. Any more magnification will be "empty" magnification.

[Stu]

4 minutes ago, Ruud said:

If you go further two things go wrong: the image becomes too dim and noticeably blurry. Any more magnification will be "empty" magnification.

Theoretically perhaps, although I do go beyond x200 with my 4" and the additional image scale proves useful, either on say Mars when small or the moon where there is so much light and contrast available.

[Stu]

44 minutes ago, Tim said:

That should definitely be our catchphrase!

Think I will add that to my signature  

[25585]

High magnification & narrow field compress perspective of everything between your field lens and your viewing target. 

If you have an optical zoom lens on a camera, zooming from min to max, especially on a less than clear day will demonstrate that. Not only are you magnifying your target, but the space - as a 2D compressed mish-mash - of everything in between. 

[vlaiv]

Btw, magnification per aperture figure is based on simple premise that human eye on average is able do see detail down to 1 arc minute.

This value is on average! So there are people that have sharper vision than this, and there are people that have lower ability to resolve detail. Also this figure is based on high contrast target. But actual ability to resolve detail is dependent both on amount of light and also on contrast.

[Stu]

17 minutes ago, 25585 said:

High magnification & narrow field compress perspective of everything between your field lens and your viewing target. 

If you have an optical zoom lens on a camera, zooming from min to max, especially on a less than clear day will demonstrate that. Not only are you magnifying your target, but the space - as a 2D compressed mish-mash - of everything in between. 

Not relevant for astro though....

[ollypenrice]

F ratio is the most abused term in astronomy...

lly

[Peter Drew]

The often quoted 2xD in mm as being the upper limit of useful magnification usually runs out at 200x in the UK due to seeing conditions. I'm unlikely to use 2xD in mm on my 750mm Dobsonian. 

[refractordude]

12 hours ago, Knighty2112 said:

Generally the longer the focal length of any scope, the higher the magnification is for any given EP. For example three scopes with focul lengths of 500mm, 1,000mm and 1,500mm focul lengths (nice and easy numbers for the maths) give the following magnification for a 5mm EP;

500/5= 100x

1,000/5 = 200x

1,500/5 = 300x

If we change the EP to a 2.5mm EP we get the following magnifications higher magnifications achievable (theoretically) for these these same three focal lengths as 200x, 400x and 600x respectively.However, as others have said the higher the magnification does reduce the image brightness, and also normal UK seeeing rarely allows much over 200x magnification on a normal light, so all objects apart from the moon will be too dim to make much out. On some good nights you may be able to push to 300+ but these are less rare. As the higher magnification starts to dim any images, to counteract this you need a larger lens/mirror to scoop up more light. 

This is what I was looking for. Thanks.