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focal length vs eye piece magnification

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#1 Serial

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Posted 27 February 2021 - 11:32 PM

For a given aperture, whats the difference between a long focal length with a low power eye peice and a shorter focal length with a high power eye peice? Pros/cons? Thanks!

#2 Ken Sturrock

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Posted 27 February 2021 - 11:45 PM

A longer focal length with longer eyepieces is usually more forgiving on eyepieces. In other words, you can get away with simpler and less expensive eyepiece designs. These designs may also be more comfortable to use. What you're really giving up with the slower OTA, though, is the option to view wider fields and (depending on the design, of course) the instrument will also be bigger, heavier and perhaps harder to mount.


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#3 SeattleScott

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Posted 27 February 2021 - 11:50 PM

You can get to the same place either way.

The advantage of the short focal length eyepiece with the short focal length scope is that you can also put a longer focal length eyepiece in the scope. So at low power you can go wider than what is possible with a long focal length scope. This can be helpful for finding things if not using GoTo, or for framing really large targets.

The disadvantage is low F ratio scopes are harder on eyepieces, so you have to spend more on eyepieces to get the same performance as cheaper eyepieces in a higher F ratio scope. Also the manufacturing process needs to be more precise at low F ratios, so either your odds of getting a really good optic goes down considerably, or the cost goes up considerably. Also, with achromatic refractors, low F ratio scopes will have more chromatic abberation. With reflectors, a lower F ratio means a larger central obstruction, which will rob a little contrast, but this is generally a minor impact.

Scott
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#4 Dave Mitsky

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Posted 28 February 2021 - 12:49 AM

A fast (i.e., low focal ratio) telescope can have a fairly long focal length, if the aperture is large enough, a 24" f/3.3 for example.  In that case, a low-power (i.e., long focal length) eyepiece will produce an overly large exit pupil.  



#5 macdonjh

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Posted 28 February 2021 - 09:33 AM

Serial, there are dozens of "eye piece calculators" on the internet, but here is some basic math.  You could write a spreadsheet with these equations and see the effects of changing things for yourself.

 

focal ratio = (telescope focal length) / ( telescope aperture)

magnification = (telescope focal length) / (eye piece focal length)

true field of view (approximate) = (eye piece apparent field of view) / (magnification)

exit pupil = (telescope aperture) / (magnification)

 

Since humans' pupils can only naturally dilate to 8mm diameter or so, having a telescope/ eye piece combination which provides an exit pupil larger than 8mm is not particularly useful.  This is really where "minimum magnification" limits come from.

 

As SeattleScott said, you can get high magnifications from both fast and slow telescopes.  What is difficult sometimes is getting low magnification with slow scopes.  For example, the scope I use most often is an f/15 classical Cassegrain.  Even with a 50mm eye piece it's lowest magnification is 105x.  You'll also notice, since true field of view is related to magnification, the TFOV through my scope is limited (about 1/2 degree).  Compare that to the same scope if it was f/4: 28x minimum magnification, 2o or so TFOV. 

 

As Ken Sturrock said, it is more difficult to create an aberration-free image if your objective is fast (like f/4) than if it's slow (like f/15).  With a fast objective the light is being severely "bent" as it's reflected or refracted and that puts greater demands on the eye piece than the more "gentle" bending with a slow objective.  In my f/15 scope, I can use Erfles and Konigs and get nice, sharp images.  Those same eye pieces produce awful images in my friends' f/5 and f/4 Newtonians.  That's really what you pay extra for when you buy wide field eye pieces from Tele Vue and Explore Scientific, etc.

 

One other difference between fast and slow objectives: depth of focus.  My slow scope is pretty forgiving of not quite finding that perfect focus spot.  I have a two-speed focuser, but never use the fine focus knob on that scope.  I am glad of the two-speed feature, though: the gear reducer allows my focuser to "carry" heavy eye pieces without slipping.  Contrast that with my f/5 Newtonian.  Since I bought that scope I have learned why people like their two-speed focusers.  The proper focus point is very small with this scope and having that fine focus makes it much easier to find.

 

One last point for me: fast mirrors require more precise collimation.  Like depth of focus, the tolerance between properly collimated and "not quite right" gets smaller as the mirror gets faster.  The procedure is the same, and the tools have gotten much better, so it's not necessarily harder to collimate a fast scope than a slow scope.


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#6 TheUser

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Posted 28 February 2021 - 09:58 AM

long focal length with a low power eye piece

has less aberrations



#7 Serial

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Posted 28 February 2021 - 02:50 PM

Everyone...you guys are great.  Thank you all for the patient lessons.  Macdon, great advice...I'm a big spreadsheet guy.  For me, if math isn't in a spreadsheet, it isn't real.  I just made a sheet and started playing with the numbers.  It's all still pretty confusing as there is so much to consider, but I'm well ahead of where I was before this post.  I understand the relationships between Focal ratio, aperture, and Objective focal length but am still trying to wrap my brain around the other variables.  

 

 

At a very basic level, it sounds like you can work around focal length and magnification with careful eyepiece selection (with some compromise) but aperture is a hard constraint.  

 

One more question, how can you call a scope slow or fast solely based on the focal ratio?  Isn't an F/15 with a 20" aperture much "faster" than a F/4 with a 4" aperture?   Hubble is F/24, does that mean it's slow?  

 

Thanks again, I can't believe all this expert advice is free! 



#8 SeattleScott

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Posted 28 February 2021 - 03:12 PM

F24 is very slow. A 20” F15 is much slower than an 8” F4. Fast or slow is specific to F ratio and has nothing to do with aperture.

Scott

#9 macdonjh

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Posted 28 February 2021 - 04:27 PM

F24 is very slow. A 20” F15 is much slower than an 8” F4. Fast or slow is specific to F ratio and has nothing to do with aperture.

Scott

+1

 

Somebody besides me is going to have to give you a "real" explanation because I still don't really understand it myself.  "Fast" or "slow" is entirely dependent on the focal ratio of the optical system.  Here's the part I don't understand: 

 

In a fast system, the light is focused into a smaller airy disc than it would be in a slow system.  Because of that, I believe, photographic exposures reach their desired intensity/ brightness/ saturation faster in fast (low focal ratio) systems than in slow (high focal ratio systems).  The part I don't understand, despite numerous attempts to explain it, is why is the airy disc in a fast system smaller than the airy disc in a slow system?  Focused is focused, isn't it?

 

One thing to take away from this discussion is "fast" and "slow" are actually photography terms appropriated to astronomy discussions.  Fast or slow optical systems have no effect on what you see in an eye piece (exit pupil being equal).  But it sure effects how  long a photographic image takes to form.



#10 Ken Sturrock

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Posted 28 February 2021 - 04:47 PM

Sorry, a bit of a divergence (and an AP one in Beginners, no less! That's a double foul...).

 

This is a vast and vague simplification in plain English, but: Fast and Slow are terms principally related to photography. A "fast" telescope can create a good quality image faster than a "slow" telescope. What makes it fast or slow is the proportion between the aperture and the focal length. In other words, the focal ratio makes an instrument fast or slow.

 

The idea is that more magnification (focal length) will create a bigger image which will spread the light coming through the aperture across a larger area which means that each photo site (pixel) or square unit of film will receive less light and, therefore, record less signal. On the other hand, less magnification, with the same amount of aperture, will spread the same amount of light across a smaller surface area which concentrates it and those photo sites (or square unit of film) will receive more signal in the same time.

 

As a hypothetical example, imagine that you had a 100mm aperture telescope that was 1000mm long (an f/10). Imagine that you are taking a picture of a perfectly square and evenly illuminated object that conveniently illuminated an 8x8 pixel grid (64 pixels). The light from the object coming through that 100mm aperture would be divided such that each pixel received 1/64th of the object's light. Now, imagine the same aperture and the same object but the focal length is only 500mm (f/5). The image size produced will be only half of the f/10 telescope's image and would only cover a 4x4 pixel area (16 pixels). Since the object and the aperture are the same, the light coming from that object through the instrument is the same. Because that light is now being spread across 16 pixels instead of 64 pixels, each pixel receives four times the light as in the f/10 OTA. This leads to a brighter (but smaller) image faster when using the f/5.

 

Astrophotographers tend to fetishise the speed of their optics because not only do fast optics make collecting a quantity of light for a pixel more efficient, it means that, in that shorter time required to collect that light, fewer things can go wrong: There is less chance for an airplane to fly through the frame, less chance for the seeing to go turbulent, less chance for the mount to track badly. Less chance for your neighbor to turn on their security lights.

 

Of course, you still have the issue of image resolution. In order to get fast optics at longer focal lengths (to get more magnification to make higher resolution images) then you need a much bigger aperture and that tends to drive cost up. It's always a compromise.

 

When you are looking with eyepieces, you have more flexibility because you can swap them out.



#11 macdonjh

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Posted 28 February 2021 - 05:02 PM

 

Sorry, a bit of a divergence (and an AP one in Beginners, no less! That's a double foul...).

 

...

 

As a hypothetical example, imagine that you had a 100mm aperture telescope that was 1000mm long (an f/10). Imagine that you are taking a picture of a perfectly square and evenly illuminated object that conveniently illuminated an 8x8 pixel grid (64 pixels). The light from the object coming through that 100mm aperture would be divided such that each pixel received 1/64th of the object's light. Now, imagine the same aperture and the same object but the focal length is only 500mm (f/5). The image size produced will be only half of the f/10 telescope's image and would only cover a 4x4 pixel area (16 pixels). Since the object and the aperture are the same, the light coming from that object through the instrument is the same. Because that light is now being spread across 16 pixels instead of 64 pixels, each pixel receives four times the light as in the f/10 OTA. This leads to a brighter (but smaller) image faster when using the f/5.

Ken Sturrock, I won't tell on you, thank you for explaining...

 

I guess this is the part I have a hard time with.  I do understand that when talking about photographic systems magnification is determined solely by focal length.  So I understand a longer focal length system will produce more magnification than a short focal length system (angular as opposed to linear magnification, correct?).  I am fixated on the airy disc, which may not be applicable since you are describing photographing an extended object, but...  can you explain why the airy disc is smaller in a fast optical system than in a slow optical system?  And, isn't an extended object made up of a large number of airy discs?  



#12 Ken Sturrock

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Posted 28 February 2021 - 05:17 PM

can you explain why the airy disc is smaller in a fast optical system than in a slow optical system? 

Um. No. Regrettably, I'll have to leave that to my betters. flowerred.gif



#13 Dave Mitsky

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Posted 28 February 2021 - 07:56 PM

As SeattleScott said, you can get high magnifications from both fast and slow telescopes.  What is difficult sometimes is getting low magnification with slow scopes.  For example, the scope I use most often is an f/15 classical Cassegrain.  Even with a 50mm eye piece it's lowest magnification is 105x.  You'll also notice, since true field of view is related to magnification, the TFOV through my scope is limited (about 1/2 degree).

One of the telescopes that I frequently use is the 17" f/15 classical Cassegrain at the Naylor Observatory.  It has a focal length of 6477mm.  The lowest possible magnification with this scope is 116x (2" 56mm Meade Series 4000 "Super" Plössl).  The maximum true field of view is just under 26 arc minutes.

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#14 Dave Mitsky

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Posted 28 February 2021 - 08:12 PM

can you explain why the airy disc is smaller in a fast optical system than in a slow optical system?

Two telescopes with the same aperture but different focal ratios working at the same magnification produce the same angular-size Airy disk. The Airy disk of the faster telescope is smaller at prime focus since the image scale is smaller. 



#15 topomountain

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Posted 28 February 2021 - 11:00 PM

i dont know all of the technical lingo, but in my 8" f/3.9 reflector vs the 8"f/6 reflector...

 

the f/3.9 is way brighter, the moon is blinding, i suspect it has a better mirror, they are both colimated the same.

 

it is said the faster scopes bring in more light, idk but my faster scope is much brighter, even factoring the same eye piece  will produce different magnifications in each scope.  i have read that in both of these scopes if you calculate for matching the same magnification with the proper eye piece, the view would be the same.... not my experience, my fast scope is much brighter and wider fov.  i also note that the f/3.9  has a much larger secondary proportionally, in fact the same size as my 12" f/5



#16 macdonjh

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Posted 01 March 2021 - 08:14 AM

i dont know all of the technical lingo, but in my 8" f/3.9 reflector vs the 8"f/6 reflector...

<...snip...>

I can't explain your experience.  Both of your 8" scopes will capture the same amount of light (I doubt you'd notice higher amount of light blocked by the large secondary in your f/3.9 scope).  If you use eye pieces which provide the same exit pupil (e.g. 16mm in your f/6 for 75x and 2.67mm exit pupil and 10.4mm in your f/3.9 for 75x and 2.67mm exit pupil) the image through each scope should look the same.  


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#17 SeattleScott

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Posted 01 March 2021 - 02:25 PM

i dont know all of the technical lingo, but in my 8" f/3.9 reflector vs the 8"f/6 reflector...
<...snip...>

In general the F ratio shouldn’t change the brightness outside of magnification. Let’s say a 24mm eyepiece to keep the math simple. That will provide a 6mm exit pupil in the F4 and a 4mm exit pupil on the F6. So the view in the F4 should be over twice as bright as the F6 using a 24mm eyepiece. You would need to compare to something like a 24mm in the F4 versus a 36mm in the F6.

That being said there can be other factors. One mirror could be cleaner or have higher reflectivity coatings. The F4 is designed for imaging so it might have a proportionately larger secondary in order to fully illuminate a large sensor.

Scott



#18 spaceoddity

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Posted 01 March 2021 - 05:34 PM

i dont know all of the technical lingo, but in my 8" f/3.9 reflector vs the 8"f/6 reflector...

<...snip...>

The f/3.9 should have a much wider FOV but the brightness should be the same if the magnification is the same. I would be surprised if the f/3.9 has a better mirror as a f/6 is much easier to get a good figure than a f/6. I suppose it is possible though. A good test would be to look at Jupiter at the same magnification(not the same eyepiece) at the same time and see which one shows more detail.



#19 topomountain

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Posted 02 March 2021 - 01:21 PM

of my f/3.9 and f/6 8" scopes, both are cleaned and colimated the the same by me.  just the subjective view of the primaries while cleaning, the f3.9 "looks" more impressive, shinier and all.  neither mirror shows dull ge etc of some older mirrors i have.  when i view the sky, the f3.9does always bring a better focus than any other telescope i own, except the 12" which i have yet to have side by side.  

 

i only have a 9mmt1 naggler, a 18mm criterion are and es 24mm 68 for good eyepieces so i cannot get exact comparisons on magnifications etc.  i also know the f3.9 has  large secondary and the primary is very close 21" and the focusser must be fully out to focus and i know that these things effect views, exit pupil and fov in some way.

 

i also have 2 similar vintage c8 xlt both clean and colimated by me, and one is clearly sharper with any ep... i have read tht there is some notiable variation in optical quality by figure variation.

 

i am currently trying to determine how to maximise my f/3.9 in any way due to its already impressive visuals.

 

it is great to share and learn from this group, compare theoretical and observed effects of modifications and upgrades etc.  sometimes when i get a really good view of the sky it is so wonderful, kind of like the free flow of knowledge and information here.... thank you all




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