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Brain Teaser, Focus Past Infinity?

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#1 medderx

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Posted 29 May 2019 - 04:04 PM

So this is something that is mentioned a lot with camera lenses but it has a lot to do with astronomy. 

 

When you reach focus on say, a star, you are effectivly focused at infinity. But what about if you move the focus a bit further? Todays terminology is to say you are "past infinity". But how can you be passed infinity if its infinite?

 

So my question is, what would be more accurate termonology for it?

This is brought to you by jfrech14 who, "...just doesn't like it", understandably. 



#2 sg6

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Posted 29 May 2019 - 04:27 PM

I suppose that all infinity means is that the image formed is at the focal length of the len. If the object were past infinity then the image is formed at an image plane that is less then the focal length of the lens.

 

So it is more a case of refering to the image plane not the object plane where the image formed as intra-focal, focal or extra-focal.

 

In optics the past infinity object would be either negative or imaginary - and for the life of me I cannot think why these terms but they are what has wandered into the empty cavity my brain should sit in. Think I have it, the "object" is imaginary and at a negative distance.

 

Past infinity is sort of understood and is after all just a case of you can rotate the lens beyond some mark on the lens casing.

 

Not sure it is relevant to astronomy as an astro lens is fixed. You cannot go beyond infinity whereas in a way you can with a camera lens. Although what has probably happened there is the focal length of the multiple lens has changed sufficently that it can no longer be regarded as the same focal legth as you started out with. Your 50mm lens is now acting as a 45mm lens, but cannot get at the new 45mm focal plane.


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#3 Rustler46

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Posted 29 May 2019 - 04:57 PM

In the universe "infinity" is just that - infinite or with no limit as to distance. In optics, objects at "infinity" come to focus at the focal length of the lens or at the "infinity" focal point. This is just one of many possible object distances marked on a manual focus lens barrel - 1 meter, 10 meters ...., infinity, ∞. Shorter object distances require a lens to focus at a distance greater than the lens' focal length. As object distance becomes larger (approaching infinity) the focal distance becomes shorter, approaching the "infinity" focal point - that is the lens' focal length.

 

But in optics (not in the real object world) it is possible for an object "beyond infinity" to come to focus at a distance less than the lens' focal length. This is due to an optical configuration, not due to the object being beyond infinity. Of course nothing can be beyond infinity. But we speak of the lens focusing "beyond infinity", not because there is anything at that distance. It only means the lens is bringing an image to focus at less than the lens' focal length.

 

Someone versed in the language of optical science would likely use terms different than what has been given above. But the principle is the same. Clear as mud, I'm sure. 


Edited by Rustler46, 29 May 2019 - 07:00 PM.

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#4 TOMDEY

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Posted 29 May 2019 - 05:24 PM

When you focus the lens beyond its infinity setting, it is now focused properly for an object ~behind~ the camera, which range is negative. I've derived all that math for that (quite simple) but won't bore folks with that. The best intuitive unit to use for this kinda stuff is the Diopter, which is an inverse meter. Note that infinity is zero D, ten meters in front of the camera is object at +0.1D and ten behind is -0.1D. This is what we optics guys typically call phi or simply ~optical power~ That's really all there is to it; nothing paradoxical!    Tom


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#5 gavinm

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Posted 29 May 2019 - 06:46 PM

.. and the reason why camera lenses focus past the infinity point is simple due to having to possibly compensate for thermal expansion...


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#6 Rustler46

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Posted 29 May 2019 - 07:04 PM

When you focus the lens beyond its infinity setting, it is now focused properly for an object ~behind~ the camera, which range is negative. I've derived all that math for that (quite simple) but won't bore folks with that. The best intuitive unit to use for this kinda stuff is the Diopter, which is an inverse meter. Note that infinity is zero D, ten meters in front of the camera is object at +0.1D and ten behind is -0.1D. This is what we optics guys typically call phi or simply ~optical power~ That's really all there is to it; nothing paradoxical!    Tom

Thanks for that information. I've always wondered what the term diopter meant. 

 

Question:

Is the definition of diopter (inverse meter) the same for use with units other than meters? One of my old manual focus lenses has the distance scale in feet. I'm just wondering.



#7 Michael Covington

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Posted 29 May 2019 - 07:57 PM

.. and the reason why camera lenses focus past the infinity point is simple due to having to possibly compensate for thermal expansion...

And variation between camera bodies.



#8 Michael Covington

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Posted 29 May 2019 - 08:00 PM

When you focus the lens beyond its infinity setting, it is now focused properly for an object ~behind~ the camera, which range is negative. I've derived all that math for that (quite simple) but won't bore folks with that. The best intuitive unit to use for this kinda stuff is the Diopter, which is an inverse meter. Note that infinity is zero D, ten meters in front of the camera is object at +0.1D and ten behind is -0.1D. This is what we optics guys typically call phi or simply ~optical power~ That's really all there is to it; nothing paradoxical!    Tom

Another way to say it: It forms a virtual image, not a real image.  When you use a lens as a magnifying glass, you have it focused "past infinity," i.e., closer to the object you're viewing than its focal length.

 

Think of it this way: Any camera can also be a projector, if, in place of the film or sensor, you put something luminous.  Focused at 10 feet, the lens would project onto a screen 10 feet away.  Focused at infinity, it would focus on a screen infinitely far away.  Focused "past infinity" it would not form a real image at all, but if you looked into the front of the projector (and the luminous object was not too bright to look at), the lens would be a magnifier.  That is, it is producing a virtual image on the camera side of the lens rather than a real image out in front of the camera.



#9 Michael Covington

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Posted 29 May 2019 - 08:02 PM

Here is an even simpler explanation that solves your metaphysical problem.

 

When a lens is "focused at infinity" nothing is actually infinite.  The lens is focused at the point where the value of a certain mathematical function is infinite (or rather has infinity as a limit, i.e., approaches infinity (and also negative infinity) as you get closer and closer to that point (depending on which direction you approach from)).  It is positive on one side of that point, and negative on the other.  Like this series of numbers:

1/1, 1/0.1, 1/0.01, 1/0.001, 1/0 (infinity), 1/-0.001, 1/-0.01, 1/-0.1, 1/-1 ...



#10 TOMDEY

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Posted 29 May 2019 - 09:41 PM

Thanks for that information. I've always wondered what the term diopter meant. 

Question:

Is the definition of diopter (inverse meter) the same for use with units other than meters? One of my old manual focus lenses has the distance scale in feet. I'm just wondering.

Good point! The answer is no; the convention is that a diopter is specifically an inverse meter:

 

di·op·ter
/dīˈäptər/
noun
a unit of refractive power that is equal to the reciprocal of the focal length (in meters) of a given lens.

 

The ~phi~ that I referred to can be in whatever (inverse) linear units are being used in the analysis, though. So in the Geometrical Optics courses (Doug Sinclair, Rudolf Kingslake, Daniel Malacara, etc.) we would always just write out the lower case Greek letter phi --- which is extremely useful in all that math stuff. That way, the units become fungible.

 

I fondly recall one of the problems on our sweatin' bullets Optics MS ~comprehensive exam~ U of Rochester, back in the 1970s. Involved looking at a piece of graph paper through a plano-convex lens plopped flat side down on a piece of graph paper. The puzzle was quite unusual, because parametrics got coupled strangely: diameter, radius thickness and index got coupled through the "crossed chords theorem from high school algebra" --- who would have imagined Kingslake torturing us with that curve ball! And then, to express the answer in diopters!

 

PS: What I really liked about Rudolf: For the grad students, he would toss problems at us that were not specifically covered in his courses. That way, learning all the taught stuff was not sufficient to ace the course. You absolutely had to be studying beyond the assigned materials and sources, else have not a prayer of scoring an A. Maybe a B, but not an A. So, only a few students managed to earn A. That was the traditional British Tradition. He intended that high grades would mean ~going beyond~ I loved that; most students hated that.

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  • 143 Kingslake 1970 obtuse problem graph paper.jpg

Edited by TOMDEY, 29 May 2019 - 09:52 PM.

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