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I previously came across an excellent thread which explained how to calculate the max magnification you could effectively use given i believe the focal length/aperture of the tube devisable by a specific number.

The problem is i cannot find it again! I know the author was a well known and long standing member of the group and countless people said it should be posted as a sticky!

Apologies for the vague post but being extremely new to astronomy i'm still struggling with some of the concepts.

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The focal length of the scope divided by the focal length of the eyepiece.  So a 650mm FL scope with a 10mm eyepiece will give you a 65x magnification.  The max theoretical magnification of the scope as a whole is 2x the aperture in mm - so a scope with a 105mm aperture will have a theoretical maximum magnification of 210.

In reality this figure may be lower or in some case much higher though.

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It's not always simple. I've found, through experience, an SCT gives its best at around x1 per mm. My 102mm apo easily exceeds x2 per mm, even x3 per mm on a good night. A Newtonian is somewhere in between. My 250 is good to around x300 but seeing conditions usually prevent going above that. It's all to do with how a scope delivers its MTF rather than outright resolution - and then there's those pesky seeing conditions.

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There is no maximum theoretical magnification for any given scope.

Don't agree? Stick in shorter FL eyepiece and you'll get higher mag - don't have shorter FL eyepiece - throw in a barlow lens

There is just a point after which there is in principle nothing to be gained from magnification, although people tend to use higher magnification than that as it is easier to view.

Check out visual acuity:

Especially this table and MAR column:

This says that someone having 20/20 vision is able to resolve down to 1 arc minute angle. They can't resolve smaller angle than that.

It also says that actual angle that you can resolve will depend on your visual acuity. If you have 20/30 - then you'll be only able to resolve 1.5' rather than 1', but if you have 20/10 - then you'll be able to resolve 0.5'

Now you can take any definition of resolving power of telescope - either Rayleigh criteria or Dawes limit or one related to Airy disk and spatial cutoff frequency - whatever you like and you'll get rather surprisingly small magnification number.

Say we take Rayleigh criteria.

Let's take 500nm and 100mm of aperture, so we have 1.22 * 0.5µm / 100000µm = ~1.26"

For 100mm aperture, Rayleigh criteria says that we should resolve 1.26 arc seconds separated features. Say we are 20/20 vision person - which means we can resolve 1'. That is 60".

It only takes 60" / 1.26" = ~ x47.6 or about x48 magnification for us to see all there is to see. Much smaller than what x50 per inch or similar "rule of thumb" criteria say.

If we have worse vision than that and can only resolve 1.5' then we might need to use 90" / 1.26" = ~ x72 magnification instead.

Thing is - no one really likes to look at detail that is at the edge of our ability to resolve. We like to view it at about x2-x3 times more magnified than bare minimum. It is easier to see and we don't have to strain as much.

So there you go.

20/20 vision person will enjoy x100-x150 magnification for 100mm aperture

20/30 vision person will enjoy x150-x200 magnification for 100mm aperture, but someone that has very sharp vision (20/10) will enjoy x50 - x75 for 100mm aperture and image will start looking softer.

So you see - no "maximum useful" magnification - only minimum magnification that resolves everything and that depends on our eyesight and then "comfortable" viewing magnification that is usually 2-3 times more - again personal preference.

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FLO have a very useful app called Astronomy Tools, you can find it on their site under info.

2 hours ago, Deepblue12 said:

I previously came across an excellent thread which explained how to calculate the max magnification you could effectively use given i believe the focal length/aperture of the tube devisable by a specific number.

The problem is i cannot find it again! I know the author was a well known and long standing member of the group and countless people said it should be posted as a sticky!

Apologies for the vague post but being extremely new to astronomy i'm still struggling with some of the concepts.

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3 hours ago, dannybgoode said:

The focal length of the scope divided by the focal length of the eyepiece.  So a 650mm FL scope with a 10mm eyepiece will give you a 65x magnification.  The max theoretical magnification of the scope as a whole is 2x the aperture in mm - so a scope with a 105mm aperture will have a theoretical maximum magnification of 210.

In reality this figure may be lower or in some case much higher though.

Thanks to everyone for their responses. I'm no maths whizz and whilst i understand the basics of vlaiv's explanation i think i'm after a more "rule of thumb" calculation.

So i have a Celestron 127slt (1500mm Focal length) and 25mm, 15mm, 8mm Eyepieces and a 2 x Barlow.

if i take dannybgoode's  calcs then i have a theoretical maximum magnification of 254 and the nearest i can get to this would be using my 15mm and the Barlow (1500/7.5=200)

That means my best option in optimal conditions would actually be to use a 6mm eyepiece giving me 250?

Fully understand that this isnt a hard and fast rule but are my maths about right.

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1 hour ago, banjaxed said:

FLO have a very useful app called Astronomy Tools, you can find it on their site under info.

ah thanks, i'll have a look

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5 minutes ago, Deepblue12 said:

Fully understand that this isnt a hard and fast rule but are my maths about right.

Yes, math is correct. I have only one suggestion - use barlow on focal length of telescope rather than on eyepiece.

Calculation would thus be 2x1500 / 15 = 3000 / 15 = 200

This is because barlow can also be used with camera and in some other situations and it extends focal length of telescope rather than shortens focal length of eyepiece (for example it changes F/ratio of telescope - which can be good for some eyepieces which may work good on F/10 while not being as good on F/5).

Another good rule of thumb - on most nights, atmosphere won't really allow for more than x150-200 regardless of what the scope is capable of.

I have 102/1300 mak and I purchased 6.7mm eyepiece to be my "high power" eyepiece for lunar. It turns out that I use 11mm most of the time and 6.7mm is just giving me too much magnification for my eyesight (image too soft).

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23 minutes ago, vlaiv said:

Yes, math is correct. I have only one suggestion - use barlow on focal length of telescope rather than on eyepiece.

Calculation would thus be 2x1500 / 15 = 3000 / 15 = 200

This is because barlow can also be used with camera and in some other situations and it extends focal length of telescope rather than shortens focal length of eyepiece (for example it changes F/ratio of telescope - which can be good for some eyepieces which may work good on F/10 while not being as good on F/5).

Another good rule of thumb - on most nights, atmosphere won't really allow for more than x150-200 regardless of what the scope is capable of.

I have 102/1300 mak and I purchased 6.7mm eyepiece to be my "high power" eyepiece for lunar. It turns out that I use 11mm most of the time and 6.7mm is just giving me too much magnification for my eyesight (image too soft).

excellent thanks...so much to learn

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What is the highest power usable on a given night in a given scope?

1) 350x.  This is the usual maximum the atmosphere allows with average seeing, no matter what the scope size is.  On average, which is when? LOL.

2) 50-60x/inch of aperture.  This is predicated on excellent optics, excellent seeing conditions, and excellent vision.  Is it usable?  Sometimes, but not often.

3) the point where the scope reaches maximum resolution because the Airy Disc becomes visible with a size, usually around a 1mm exit pupil (magnification = aperture in mm).

4) The magic "eutectic point, where dimming due to increased magnification is offset by the increased size.  Higher power makes the object less visible.  This will be different for nearly every object.

5) The limit allowed by whatever the seeing conditions allow.  Could be 200x, could be 2000x.

6) the maximum allowed by the optical quality of the scope.

7) the maximum allowed before floaters in the eye significantly interfere with the image.  It will be higher with double stars, lower with the Moon.  I simply cannot use 60x/inch any more except on a double star.

Otherwise, whatever I observe is filled with floaters.  I stop around 0.65mm in exit pupil (exit pupil = eyepiece focal length / telescope f/ratio).  But I can go a lot higher on double stars, ~0.4mm exit pupil.

I usually say to people, "Magnification range is from whatever eyepiece yields an exit pupil equal to the dark adapted pupil in your own eye at low power up to where floaters in your eye interfere with high power.

Another way to look at it is:

Low Power: 4-10x/inch of aperture.  You may have astigmatism in your eye at these low powers.  If so, use glasses or contacts to correct it and the images will be a lot sharper.

These magnifications are limited by light pollution in how low you can go, because lower powers make the eyepiece field background brighter and reduce contrast.

Medium Power: 10-20x/inch of aperture.  The range where your vision will have its greatest acuity, where seeing will interfere very little, if at all, and where most deep sky objects will be visible easily.

High Power: 20-30x/inch of aperture.  You may be running into seeing issues here.  Floaters in the eye may interfere with magnifications near the upper end.  Usable many, if not most, nights.  Best choice for planets and Moon IF seeing allows.

Ultra High power: 30 to 50-60x/inch of aperture.  Not typically usable every night, but can be used more often on double stars and small planetary nebulae than most other objects.  My recommendation--use a Barlow to get here, using a lower power eyepiece in the Barlow.

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15 hours ago, Deepblue12 said:

Thanks to everyone for their responses. I'm no maths whizz and whilst i understand the basics of vlaiv's explanation i think i'm after a more "rule of thumb" calculation.

So i have a Celestron 127slt (1500mm Focal length) and 25mm, 15mm, 8mm Eyepieces and a 2 x Barlow.

if i take dannybgoode's  calcs then i have a theoretical maximum magnification of 254 and the nearest i can get to this would be using my 15mm and the Barlow (1500/7.5=200)

That means my best option in optimal conditions would actually be to use a 6mm eyepiece giving me 250?

Fully understand that this isnt a hard and fast rule but are my maths about right.

The best way to go is to actually try each combination on the object in question to see which looks best to your eye.  Math can only tell you so much.  At some point, you need to experiment to verify the theory.

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1 hour ago, Louis D said:

The best way to go is to actually try each combination on the object in question to see which looks best to your eye.  Math can only tell you so much.  At some point, you need to experiment to verify the theory.

Louis

Came to that conclusion myself last night, i'm an inpatient [removed word] (not the best trait for Astronomy) and think i was just looking for a shortcut

Thanks

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1 hour ago, Deepblue12 said:

Louis

Came to that conclusion myself last night, i'm an inpatient [removed word] (not the best trait for Astronomy) and think i was just looking for a shortcut

Thanks

I'm at the point I enjoy comparing the views through different eyepiece/scope/Barlow/filter/CC/flattener combinations now.  It can make the same old showpiece objects look compellingly different.

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50X per inch of aperture is generally considered the maximum magnification as far as resolving two stellar points is concerned, and so a 5" scope would have a top resolving power of 250X. The great American observer E. E. Barnard found 180X to be his prefered magnification for observing the planet's while using a 40" refractor. On the other hand,  William Herschel would at times use 1000X and beyond while using his 7" reflector. Sometimes it's best to use whatever power suits the observer, the target, and the atmospheric conditions, and not to worry too much about technicalities.

Edited by mikeDnight

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