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If I've got the above wrong it's due to my lack of knowledge of photographic issues. I'm more confident on the astronomical side of things but these are not simple concepts.

For refractors the limitation is the last baffle or the focuser draw tube, you need the focuser so not much you can do about that.

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I think how this must work in like this. The objective projects a nice circular image at the focal point. Your eyepiece photographs this circle. If your eyepiece has a wide apparent field of view you see all of the image circle including the fuzzy edges. If your eyepiece has a narrower field of view you see only the central region of the objective image circle. In fact (just a guess) I reckon that orthos and plossls and the like actually have a much wider apparent field of view that you see in a practical eyepiece. However the edges of that apparent field of view have embarrasingly terrible image quality so the manufacturers include a fixed aperture stop in the eyepiece to block off the fuzzy regions, That would explain why the edge of the visble circle is always a knife edge sharp line. Real optical circles just sort of blurrily fade to black at the edges, that sharp circle has to be artificial.

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The CA reduction is due to refractive indexes of the glasses used in lenses and is an entirely different matter to the field of view issues that we started out on.

And if I am, with my 1250mm long focus refractor, if I want a wide field view showing the sky from horizon to horizon, getting a Nagler won't help at all. The wider apparent field of view won't make my telescope show a bigger patch of sky, The only way to do that will be to use a longer focal length eyepiece to reduce the magnification and increase the true field of view or use one of those gadgets that reduces the focal length of the objective (thus increases true field of view)....

For visual observations, the focal ratio on a telescope means diddly, I dont even go there, except to decide on what focal length eyepiece I need to get the best practical high power magnification for that scope

With photography, as I understand it, when the F number gets smaller, the effective aperture has reduced as well because the aperture stop has reduced in diameter, so the amount of light being bought to focus is reduced too. With astro scopes of differing focal ratio but the same aperture (as per your example) the aperture remains the same so the amount of light bought to focus stays the same.

What you are referring to is the size of the illuminated field, this is very important to imagers as it determines the size of sensor they can use and whether they will experience vignetting.

You stand in front of a window looking at a build in distance, the size of the window corresponds the apparent of field of view of an eyepiece, with bigger window, you see more of the build and its surounding, the size of building is the same (same magnification) no matter how big or small the window is.

Field of viewhuman eye

Apparent field of view (AFoV): Look down an eyepiece (not in the scope) and you will see a circular area of light bordered by a dark frame or rim. This is the Apparent field of view of the eyepiece and these vary, depending on the eyepiece design from 30 to 120 degrees. The AFoV is defined (framed) by the field stop of the eyepiece which is usually a fixed aperture.

True field of view (TFoV): This is, put basically, how much sky a given eyepiece + scope combination will show. It's expressed in degrees again but the number is much smaller than the AFoV. To calculate it roughly you can divide the eyepiece AFoV by the magnification that the eyepiece + scope combination gives for example:

Scopes designed for imaging normally state the illuminated field size in the specs. They may even go so far as to state a fully illuminated and corrected field size, this will be the size sensor you can use without suffering CA.

25mm eyepiece with a 50 degree AFoV used in a 1000mm focal length scope produces 40x magnification. Divide 50 by 40 and you get 1.25 which is the TFoV in degrees - about 2.5x the diameter of the full moon.

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- The patch of sky that the telescope sees is the True field of view. A high magnification will show a very small patch of sky with the subject (say Jupiter) quite large. A low magnification will show a larger patch of sky with the subject smaller and lots of surrounding stars visible that were outside the frame with the higher magnification. This is consistent with what you see in a camera viewfinder when you swap from a tele lens to a wide angle. The more wide angle you go, the more stars you can squeeze into the frame but the smaller everthing is.

Field of viewcamera

That is always an issue to understand and to get to grips with, when in possession of a telescope, coming from a photographic background.

It's true that a telescope does not have a variable iris but it effectively still has an iris: its fixed aperture lens. Camera lenses used to work the same before the iris aperture was invented. The lenses were telescopes with a fixed aperture defined by the focal length/size of the front lens. Exactly like a telescope.

The CA reduction is due to refractive indexes of the glasses used in lenses and is an entirely different matter to the field of view issues that we started out on.

- keep the telescope and don't change the EP focal length but swap the EP for a different design that has a wider apparent FOV

Given my current theory of how this probably works, the third option of using a fancy EP comes at a (technical cost): the extra field of view is making use of the outer edge of the objective's image circle which is of poorer quality than the central region. This is analogous to what happens if you put a lens designed for APS-C sensors on a camera with a full frame sensor: you can get a wide angle view but chances are the sweet spot of the image circle is too small for the big sensor and the edges of the frame will be a lot fuzzier than the centre of the frame. And if you go too far, the lens circle won't even cover the full frame centre and you will end up with a circular image in the middle of blackness.

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As you state here, the telescopes ratio is simply the answer to the sum F/A=f/? The telescope in use has a fixed aperture by design, you can reduce it by creating a smaller opening /cover over the end of the scope, but cannot increase it?

Field of view ofatelescopeformula

- Within any sensor format, the angle of view and inversly the magnification of the lens depend on the focal length. A long focal length will see a narrower angle of view/greater magnification; a short focal length a wider angle of view/lower magnification. Thus wide angle lenses are shorter focal length than telephoto lenses.

And this is not what happens when I use my spotter scope with a zoom lens. That behaves exactly like a camera. At low power you get get a wide view and at high power a much narrower view.

The "Up to a point" is because there is a physical limit to the size of the apparent field of view that an eyepiece can have and that is set be the internal diameter of it's barrel. What this means in practice is that, in the 1.25" fitting, a 40mm focal length eyepiece can't have a field stop any larger than a 32mm one so the apparent field of view has started to reduce rather than get larger. The max AFoV at 32mm is around 52 degrees while at 40 mm it's decreased to 43 degrees and you don't see any wider true field of view. In the 2" fitting the story is the same but the AFoV's are larger than the 1.25" size because there is room for larger field stops. You can actually get 3" and 4" barrel eyepieces but we are talking about industrial sized scopes for those.

The key thing when making anologies between telescopes and modern camera lenses is to think of the camera lenses at their wide open aperture and forget about the iris. A zoom lens for example, used with the iris wide open will have a wider aperture at the wide end and a narrower aperture at the long end. Typical cheap zooms might be something like a 80mm f4.5 to a 200mm f6.3 - even with the iris fully open. The reason the f number rises in this case is nothing to do with the iris but is caused by the focal length getting longer - just like the difference between a ST80 and a class refractor.

They imply that the eyepiece apparent field of view makes zero difference to the amount of sky that your telescope can see (the number of stars and how much jupiter is magnified). One of those fancy Naglers or an ortho that yield say 50x magnification will see identical patches of sky with exactly the same subject matter inside the frame. What does change instead, is how close the circle you see feels to the eyepiece. In other words some eyepieces make the circle look like it's down the end of a long tunnel, while others make the circle seem really close, in your face with no wasted space outside the circle frame. It's similar to the difference between the viewfinder of an APS-C format SLR camera and a full frame SLR. With the APS-C camera, the viewfinder puts the frame down the end of a long dark tunnel where it looks small and far away while full frame viewfinders are bigger and closer. In fact, often so big and close that you can't always see the edges with your eye in one position but have to move it around the eyepiece to scan the frame.

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An eyepiece with a larger apparent field of view will show more sky than one with a narrower apparent field. If the focal length of the eyepieces is the same and the scope is the same then the magnification will be the same.

Suppose we can move your house to half distance to the building, then we see the building is twice as big as before, still, how much you can see, depends on the size of the window.

- Lenses designed for different size sensors produce larger or smaller image circles, The diameter of the image circle needs to be sufficient to cover the format of film or sensor you are using. For example a lens designed for 35mm format will typically produce a 43mm diameter image circle, while a lens designed for 5"x4" sheet film will produce an image circle larger that 5" across. How that is achieved I don't understand.

- Apparent field of view. This is the spec that keeps getting quoted in adverts. What confuses me is the descriptions in the adverts always imply that if you use an eyepiece with a wider apparent field of view, it's like fitting a wide-angle lens on your camera - yet it can still magnify x300. This must surely be nonsense. The youtube diagrams imply something quite different:

Suppose we can move your house to half distance to the building, then we see the building is twice as big as before, still, how much you can see, depends on the size of the window.

For Cassegrain scopes it is usually the primary baffle that limits the field size, shortening the baffle would allow stray light into the focuser so it is not really practical to change this.

But the increase in depth of field that applies to stopping down a camera iris must also apply to the telescope, yes? One of the reasons why my simple f16 achromat gives views the equal of an expensive APO is because the increased depth of field at f/16 makes chromatic aberration go away. The same achromat type objective with an f2.8 focal ratio would give appalling image quality because of all the out of focus colour fringing.

Telescopesimulator

The key thing for me about this camera analogy is that what is in the frame of both viewfinders is exactly the same subject and the pictures you take will look identical. The difference is basically cosmetic - how comfortable the viewfinder is to use and how bright and impressive the view is. The framing doesn't change. Likewise with telescope eyepieces, what is contained within the circle is the same for a Nagler and an ortho, what changes is how much wasted space there is outside the image circle and how "close" the circle itself appears. It's basically like watching your TV from a foot away or across the room. The same field of view is in the TV picture either way.

........here's a quick image from a simulator I have input the measurements of the two scopes you suggested, A- 3" (75mm) F-300 & A- 3" F- 1250mm

In my 35mm days and now the digital revolution, anything to do with a focal ratio was simply adjusting the aperture, which gave a larger or smaller depth of view.

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Here are examples of the view with a normal and wide angle eyepieces of the same focal length used in the same scope. The magnification is the same so the angular size of an object within the field of view stays the same size. The amount of sky that frames it is larger in the wide field eyepiece:

Telescope field of viewapp

The Focal ratio is indeed a throwback from the photographic world, but a non-entity for visual only observations. I`m still reading your question though!

The size of the field will be further effected if you add more optics into the light path, a Barlow lens will make it bigger whereas a reducer will make it smaller, hence you can introduce vignetting with a reducer.

The limiting factor for the illuminated field size depends on the scope, for a Newtonian design it is the size of the secondary mirror, you can use a bigger secondary to get a bigger field but this will then block more light from reaching the primary.

Field of viewcalculator astrophotography

Also note, when you change the aperture on your camera, f/number, your actually stopping down the aperture closing the aperture / iris ( old 35mm talk) and this opening / closing of the aperture will affect the depth of view, and the amount of light passing through, in conjunction with the shutter speed. In a telescope the aperture is fixed. so for my use, as described, visual only, I`ve no way of changing the aperture ( I lie, I can leave the dust cap on and go from 200mm to 25mm?).

Which gives me a clue. Is it perhaps, that the image circle produced by the objective is quite large in diameter, somewhat like the large image circle produced by a plate camera lens. And the eyepiece doesn't see the whole circle, just the centre of it. I have always assumed that the boundary of the view you see through the eyepiece is the edge of the image circle produced by the objective - but actually that can't be true because the edge of the objective image circle will be quite fuzzy and the eyepiece view is very clean cut. So there must be an artificial edge introduced in the eyepiece - an artificial vignette essentially. Which suggests that these fancy eyepieces make use of more of the objective image circle than the basic ones. That would make sense. It is like replacing an APS-C sensor with a full frame of twice the area. It could see more of the objective image circle without having to zoom out. Which leads to a question: are there eye pieces whose apparent field of view is so wide it exceeds the objective image circle so you can actually see the whole thing with its fuzzy edges blurring into darkness...

A scope does not use an iris. The aperture is defined by the diameter of the objective lens or primary mirror. The focal ratio is defined by the focal length of the objective lens or primary mirror divided by it's aperture.

The only way I know to duplicate the effect your images show is by stitching a pano - basically taking two or more photos and joining the frames together. There is no camera that can do what you are showing here. How does a telescope do the impossible????

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Telescope field of viewcalculator

Some eyepieces with short focal lengths, which produce high magnifications in scopes, do have very large apparent fields of view. It is their focal length that determines the magnification they give in a particular scope though, not their AFoV.

- However, there doesn't seem to any absolute angle of view/magnification determined by focal length; you always have to consider the sensor size as well. So, for example, a 300mm lens on 35mm is a longish telephoto but on a 10x8 plate camera it is merely a standard lens.

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To create another analogy: imagine you are watching TV, say the evening news. The TV cameraman zooms out to show the studio and sometimes zooms in to the face of the news reader. This is analogous to swapping from say a 25mm eyepiece to a 4mm eyepiece: everything on the screen is magnified. Now imagine that you are viewing the TV not with you eyes but through the zoom lens of your camera. You can zoom in so the TV exactly fills the viewfinder. Then when the TV cameraman zooms in or out, your viewfinder view follows suit. Now zoom your camera in a bit further so you fram only the centre of the TV. Again, when the TV cameraman zooms into a close up you see that in your viewfinder. But when he zooms out again for the studio shot, your viewfinder chops off the edges and you can't see the wide view.

I use eyepieces with apparent fields of view that range from 50 degrees to 100 degrees and using two eyepieces of the same focal length but with differing AFoV's in the same scope produces just the effects that the picture above illustrates.

- What size image circle does a telescope objective project? If I were to place a sheet of paper at the focal point without an eyepiece installed what would be the diameter of that circle? Is it the same for all telescopes (i.e. is there some kind of standard) or does it vary? If it varies what is the cause of the variation.

No great mystery there. (I know this isn't the point of your post, but since you mention it...) Basically larger format cameras use similar optical designs to those used on smaller formats - but with correspondingly longer focal lengths to cover the larger frame with the same field of view.

- this gets really confusing for me. You read about eyepieces of the same focal length having different fields of view. I don't understand this. How can this be - magnification and field of view are the inverse of one another: if one goes up, the other goes down in lockstep. It is impossible to have a wide-angle telephoto, yet eyepiece specs imply that some eyepieces are simultaneously wide angle and telephoto! A 100 degree angle of view is inconsistent with high magnification, it is by definition the opposite. A high magnification would surely be a 1 or 2 degree angle of view!

What little understanding of optics I have comes from the photography world. There are many similarities in the concepts and terminology but sufficient differences to utterly baffle me ;-)

A wide aperture low f number lens has a very thin depth of field and focusing has to be very precise - too precise for all the colours to be in focus at the same point unless exotic glass in used. A narrow aperture high f number lens has a thick depth of field sufficient to include the focus point of all the colours even with a simple objective - hence chromatic aberration is gone. F number is still important in discussions about telescopes for this reason.

Ignoring the eyepiece for a moment, what difference does the objective make? Let's compare a 3" 300mm short tube refractor with a 3" 1250mm refractor. They have the same size objective lens so they collect the same total light and offer the same absolute resolution potential. However, one has a focal ratio of f4 and the other f16.4. And I know from my photography that when the f number gets bigger, the image gets darker. What is the explanation for this? The answer must logically be that the long focus refractor objective magnifies more than the 300mm refractor even without an eyepiece. That's why it's darker. If it were possible to view the image created by the objective with a 1x eyepiece, you'd see that that the 1250mm refractor was more zoomed in that the 300mm. I think this means the image created by the objective is not like what you see with naked eye - it will vary from scope to scope depending on the focal length of the objective. To mimic the naked eye, the objective would have to have a focal length of 40-50mm (and I don't believe telescopes this short are that common).

It seems to me that more mathematical formulae or words I read, the more confusing it gets! However, I just watched a Youtube tutorial in which the words used were so confusing it was better with the sound off (!) but in which the pictures might have provided some illumination. Let me try it on you...

The Focal ratio is indeed a throwback from the photographic world, but a non-entity for visual only observations. I`m still reading your question though!

And with higher (ie narrower) f numbers comes a greater depth of field (zone of sharp focus either side of the actual focus point). This largely happens because the narrow aperture blocks off the light rays at the edge of the light cone that are diverging, letting in only the ones that are more parallel. This is significant because Chromatic aberration is caused by colours coming to focus at different points.

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I like your analogy as an aid to visualising what you will actually see. But it does not seem to explain my central condumdrum of why telescopes can do the impossible! With my camera I can use a telephoto to get a close up view or I can use a wide angle to get a lot in. But I cannot swap out my telephoto to another telephoto of the same focal length that will also show me the wide view at the same time. The two are mutually incompatible. Yet in eyepiece land I appear to be able to buy a high magnification eyepiece that has a wider view than a low magnification eyepiece of a different design. That's pretty counter-intuitive, you must admit. Again I come back to my idea that the objective must project a large circle most of which is wasted by cheap eyepieces. Only the expensive multi-element designs can "see" the outer regions of the objective's image circle.

.......... With my camera I can use a telephoto to get a close up view or I can use a wide angle to get a lot in. But I cannot swap out my telephoto to another telephoto of the same focal length that will also show me the wide view at the same time.

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Camerafield of viewsimulator

For example, a 'normal' lens for a 5x4 camera isn't hugely different in design from a simple 50-55mm 'standard lens' that you might have used on 35mm. The crucial difference is that it will be a 150mm lens, or even 180mm, if we're really trying to compare like with like. Similar design leads to a similar angle of view, which, with a longer focal length results in a larger image circle. I'd guess that most LF photography is done with lenses of that quite basic type (most of mine is, or was, anyway). For properly wide angles the designs resemble the old Zeiss Biogon type from the 1930s - the angles are comparable, but again you're just dealing with longer focal lengths for the same field of view.

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If it helps, just think of the lens as a glorified pinhole - if the light coming out of the back of the pinhole spans a certain angle, then the further back you place the film plane, the larger the diameter of the image circle.

CA can cause a secondary limitation, whilst the field may be fully illuminated the star shapes may be too distorted to be useful for imaging (unless you like Star Trek style warp drive effects!).

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The first "stops" used in photography were literally metal plates with different size holes in them the were inserted into slots in the lens barrel to vignette the incoming light cone.

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If I have a zoom lens on my camera, there is only one way to get more stuff in and that is to zoom out to a wide angle view: which makes everything smaller. It is impossible to zoom in a way that keeps the centre of the field the same size while making the edges show more. A lens is either zoomed in close or pulled out wide. Your images appear to show a view which is simultaneously wide angle and zoomed in! Does not compute...does not compute...illogical Kirk, illogical...

For example a lens designed for 35mm format will typically produce a 43mm diameter image circle, while a lens designed for 5"x4" sheet film will produce an image circle larger that 5" across. How that is achieved I don't understand...

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........here's a quick image from a simulator I have input the measurements of the two scopes you suggested, A- 3" (75mm) F-300 & A- 3" F- 1250mm

.......dont be concerned about asking over and over again. Thats what the forums are about, and someone, from somewhere will have an answer to satisfy / or not, your answer, I know, I've been there before talking about Barlow eyepieces. I had a firm belief in their method, how they worked, but I know adopt a different approach when discussing them. Your not alone?

- keep the telescope and don't change the EP focal length but swap the EP for a different design that has a wider apparent FOV