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Probably a dumb question but....


Clarkey

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I have been pondering a though which I am sure has a very simple answer. However, my old and naddled brain is not coming up with the answer. (Physics was never my strong point).

Why does focal length dictate the FOV of a scope? For example, a simple refractor of a given focal length will show a certain amount of sky. Why could you not alter the lens shape to focus the same area of sky at a different point? Same with a mirror system.

Any guidance to put me out of my misery would be appreciated. (Be aware, I do have a penchant to miss the glaringly obvious 😀).

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Hopefully a couple of calculations will help explain...

Field of view (Degrees) = field of view of the eyepiece/magnification

Magnification = focal length of the telescope/focal length of the eyepiece.

Hopefully that will put you out of your misery, but if all I have done is muddy the waters further, I will be equally pleased :D

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19 minutes ago, M40 said:

Hopefully a couple of calculations will help explain...

Field of view (Degrees) = field of view of the eyepiece/magnification

Magnification = focal length of the telescope/focal length of the eyepiece.

Hopefully that will put you out of your misery, but if all I have done is muddy the waters further, I will be equally pleased :D

I understand these bits but it does not answer my initial question regarding WHY the focal length defines the FOV. At least the water is no muddier🤣

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Ok, how about this ... Focal length of a telescope is the distance between lens and eyepiece where the image is focused. If you change the shape of the lens, to focus, the distance will change so the focal length changes. Using the same lens but with a different focal point will mean the length of the tube has changed, because the length of tube has changed the field of view must change. Time for a cup of tea 😅

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13 hours ago, Clarkey said:

 

Why does focal length dictate the FOV of a scope? For example, a simple refractor of a given focal length will show a certain amount of sky. Why could you not alter the lens shape to focus the same area of sky at a different point? Same with a mirror system.

 

You're getting focus and fov mixed up there. You can change the lens shape to change the view of the sky, it's called a zoom lens.

With any particular lens operating within its parameters you can also focus along the plane of where it can "see" from near to far if that makes sense

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"Why could you not alter the lens shape to focus the same area of sky at a different point?"

That's exactly how a refractor with a wide angle of view, differs from a refractor with a narrow angle of view - the lenses have a different shape.

Those Fish Eye lenses you can screw onto the front of a camera lens do that too.

And a Focal Reducer on the back of an OTA appears to widen the angle of view, aka the Field of View FOV

Reflectors alter the FOV by having deeper or flatter mirror shapes.

Ultimately the focal length, which is determined by the lens or mirror shape, determines the FOV.

Michael

 

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17 hours ago, Clarkey said:

Any guidance to put me out of my misery would be appreciated. (Be aware, I do have a penchant to miss the glaringly obvious 😀).

See if this article helps in your understanding https://www.edmundoptics.co.uk/knowledge-center/application-notes/imaging/understanding-focal-length-and-field-of-view/. The diagram explains it quite nicely.

Edited by AstroMuni
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Since your question is posted in the starting imaging forum, I presume you intend to use a camera without an eyepiece. Physics is not your thing, but a simple calculator can provide you the answer:

If the camera active sensor width is W millimeters, and the focal length of the telescope is L, the rigorous equation for FOV (field of view) is:

FOV = 2*atan(W/(L*2))

a good approximation for the FOV just drops the two "twos" and is:

approximate FOV = atan(W/L)

That is for a camera with no eyepiece involved.

Hope that helps :)

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20 hours ago, Clarkey said:

Why does focal length dictate the FOV of a scope? For example, a simple refractor of a given focal length will show a certain amount of sky. Why could you not alter the lens shape to focus the same area of sky at a different point? Same with a mirror system.

That one is simple.

You have to look at chief ray for either lens or mirror - it does not bend (in case of lens).

image.png.ba3ace9af3bf88f9872800aa0ff8319e.png

In above image it is ray passing thru point B.

That ray is always straight. It does not bend - for lens. Similarly for reflector - it is also ray that "does not bend" - or rather one that is reflected like of ordinary mirror - look at this diagram:

image.png.fa7ddb9fcaeea307a413572dbc88c40e.png

In above image - ray that hits center of the mirror - might as well hit flat mirror - it will be reflected at the same angle it came in - it will be symmetric to optical axis.

Now that we know what chief ray behaves like - it is very easy to understand why FOV depends on focal length - if we examine this diagram:

image.png.90b511dc5f3e6efca92c38f242280773.png

Here we have lens and chief ray that hits "edge of FOV".

If our focal length is short - it will hit focal plane closer to center, and if focal length is long - it will hit it further away. In fact - there is relationship between focal length and height in focal plane for given angle - all those triangles are similar and have same angle.

Now if you fix sensor size - following happens:

image.png.cc967575a6abb0e7279cef714279b84b.png

If sensor is further away from lens because focal length is greater - then line connecting center of the lens and edge of sensor forms smaller angle - and again, angle is function of sensor size and focal length.

Don't need any ray bending to explain this - chief ray that stays straight is enough to show this dependence.

 

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Thanks for the guidance. From the multitude of different answers I don't think I made myself too clear but I think I now get it. In effect, there is one primary ray that is effectively straight and not refracted. All the other light needs to be aligned to the same focal plane.

Just to add to my confusion, cameras have a fixed distance to the focal plane but can have any focal length lens. You could have one scope with multiple lenses😁

I think if I had drawn a diagram my query would make more sense, but I'm on holiday and using my phone.

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7 minutes ago, Clarkey said:

Just to add to my confusion, cameras have a fixed distance to the focal plane but can have any focal length lens. You could have one scope with multiple lenses

That one is also easy to solve. If we look at geometrical optics - then combination of the lens can usually be replaced with single lens.

For monochromatic light there is really no difference in singlet, doublet or triplet telescope. They all act the same - as simple/singlet lens with given focal length. Additional lenses are there just to correct for optical aberrations that are "on deeper" level than simple geometrical optics (chromatic aberration, spherical, flattening the field with camera lens, etc ...).

 

 

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9 minutes ago, vlaiv said:

That one is also easy to solve. If we look at geometrical optics - then combination of the lens can usually be replaced with single lens.

Yes, I understand this from the other explanations and I appreciate the differences. It would be a lot cheaper though😀

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On 14/08/2022 at 20:15, Clarkey said:

Why does focal length dictate the FOV of a scope? 

Well, mostly because it does not. The focal length defines... the focal length. The field of view is defined by the ratio between the size of the image projection and the focal length. For instance, if you use a full frame capteur, you will enlarge your apparent field of view compared to if you use a webcam with a 5mm*4mm sensor. 

There is no mathematical limits (only practical/optical limits) to the FoV you can get with any given FL. It is mathematically possible (but practically impossible) to design a fish-eye with a 1200mm FL. It is also mathematically possible to have a .5arcsec FoV with a 20mm FL. 

FoV and FL are often mentioned interchangeably or to give an indication of the other simply because in practice there is a limit to the size of the image projection, from a few mm to a few centimeters - say, roughly 5mm to 5 cm, the vast majority of practical applications being around the 20/25mm mark.  But that's just a practical constraint, not really a physics/optics law.

Edited by FrenchyArnaud
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7 minutes ago, FrenchyArnaud said:

Well, mostly because it does not. The focal length defines... the focal length

As I said above I probably needed to clarify my original query. Such as for the same sensor size.

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