Formula for calculating focus distance from extension & v. versa.

[walter23]

With a normal, non-retrofocus or telephoto lens design, how does extension correlate to the distance you've focused?

For example, say you've got a 355mm G-claron. You extend your rail to 400mm. How close have you focused? What's the formula?

 

[Bruce Osgood]

I have no idea.
I just posted to get a flag if somebody else does know.

 

[Ole]

1/F=1/x+1/d

where F= focal length, x= extension, and d= distance from lens to subject.

 

[walter23]

Thanks a lot, Ole.

 

[Dan Fromm]

1/F=1/x+1/d

where F= focal length, x= extension, and d= distance from lens to subject.

Hmm. Isn't extension measured from rear node and lens to subject distance from front node?

Yes, at normal distances this is a nit. But close up it isn't quite.

Oh, and by the way, Walter, Ole's formula with my slight correction of definitions works for all lens types, including retrofocus and telephoto.

 

[Sparky]

measurement points are usually the film plane, which is frequently indicated on 35mm cameras (say- I wonder why more LF cameras don't have that??) and the lens nodal point - normally very close to the aperture plane, but not exactly on it (really depends on specific lens design).

 

[Ole]

Hmm. Isn't extension measured from rear node and lens to subject distance from front node?

So it is. The "nit" is most important around 1:1, less important at 1:3 and 3:1 (notice the equation gives the same results at 1:3.and 3:1), and can mostly be forgotten (except with tele and retrofocus lenses) once you get to 1:10 (or 10:1) or so.

 

[Sparky]

are you guys suggesting that lenses have TWO nodal points?? (that would be news to me..!)

 

[walter23]

How do you determine the nodal point(s?) for lenses, without having access to them? This is something of a hypothetical question with practical implications (camera building / design issue - figuring out some configurational stuff based on projected lenses that I don't yet own).

The real question I'm trying to figure out is: how much extension, lens board to film, for a ~355mm / 14" lens to focus to 5 feet (and also to 10 feet)?

The knowledge will be useful for other design considerations though.

 

[Ole]

How do you determine the nodal point(s?) for lenses, without having access to them? ...

You can assume the internodal distance is 0, or look up the manufacturer's specification in many cases. Look for H-H'.

Knowing the back focal distance at infinity and the actual focal length as well should give enough data to calculate just about everything.

 

[Dan Fromm]

Walter, for most lenses of "normal" construction (not telephoto, not retrofocus) the front and rear nodal points are quite close together and are near the diaphragm. When in doubt, focus the lens on a distant subject and the film plane-to-rear node distance will be the focal length. And then you'll know where the lens' rear node is.

If you want real precision, remember that nominal and actual focal lengths may differ by as much as several percent. For example, the QC slip with my 260/10 Nikkor-Q (looks like a Process Nikkor to me) says that the actual focal length is 266.6 mm. In its intended use, it was to have been focused by measurement, not on a GG, that's why Nikon QC told the purchaser the lens' true focal length. Another example: I once extracted 20 38/4.5 Biogons, nominal focal length 38.5 mm, from some aerial cameras. The camera manufacturer's QC department had marked actual focal length on them, the range was 38.3 - 38.8 mm.

Sparky, buy a book. If you have the money to get it, you'd probably enjoy S. F. Ray's Applied Photographic Optics. Yes, lenses have two nodal points, front and rear.

Walter, you might want to buy a book too. For both of you, probably the least expensive book on photographic optics in English is Cox' Photographic Optics. Many many editions, there are lots of copies floating around.

Walter, as a practical matter the distances you're interested in scale linearly with focal length. So a 7" lens needs half as much extension to focus to 5' as a 14" lens. If you have a camera and a lens (I know you do ... ), set up and focus to 5', measure film plane-to-diaphragm distance, multiply appropriately, and stop worrying. Repeat at 10'.

 

[Sparky]

Sorry Dan - i've read 'em ALL... it'd make your head spin! Just been too long or something I suppose. I suspect that the nodal point discrepancy we seem to be having between us is an issue of using the lens forwards/backwards... However it seems to me fairly preposerous that the rays passing through the lens would cross at TWO points.

If that were in fact true, a lens would not invert it's virtual image - it would be re-inverted back to the same orientation.

 

[Dan Fromm]

Sparky, from memory, a ray entering a lens at the lens' front nodal point will exit the lens' rear nodal point at the same angle at which it entered the front nodal point. There's no crossing over at either.

 

[Helen B]

Sparky, from memory, a ray entering a lens at the lens' front nodal point will exit the lens' rear nodal point at the same angle at which it entered the front nodal point. There's no crossing over at either.

Dan,

I know that what you meant to say was more like

'a ray entering a lens that is heading towards the lens' front nodal point will appear to exit the lens' rear nodal point at the same angle at which it appeared to enter the front nodal point.

The ray does not actually cross the optical axis at the nodal points, unless they are coincident. It crosses at the aperture stop.

Best,
Helen

 

[Dan Fromm]

Thanks, Helen.

 

[Sparky]

Dan - I don't know you so well - so I can't call anything you say into question - but Helen - I'm surprised at your statement. Why on earth would it be called a 'nodal' point if there's no 'crossover' happening..? And how on can a lens invert an image without having 'crossover'...? I guess - for the sake of illustration we can consider a landscape photo - where the image-forming rays can, for all intents and purposes, be considered parallel (assuming that's what you meant to say..?).

To the best of my knowledge - most lens designers (except under special circumstances) try to place the aperture AT or close to the nodal point - which is why one would see the inversion happening there.

I need to look into this a bit more to make my case though...

 

[Dan Fromm]

Sparky, you thought I was mistaken and said so. I think you just said the same about Helen. Could be, neither of us is always right.

But it really would be helpful if you could direct us to a source other than you that supports what you're saying. I have on hand Cox' Photographic Optics, Brandt's The Photographic Objective (title from memory, could be wrong), Kingslake's Lenses In Photography (same comment applies), and S. F. Ray's Applied Photographic Optics, 3d ed. I believe that Helen has these books and more.

Look in your library, ideally in a book I own too, and direct me to a source. If you can't find one, please reconsider your position.

Thanks,

Dan

 

[Sparky]

Dan - Hi. Truth be told - I really don't have the energy to get into it... but I BELIEVE there's a little confusion going on here. I think it stems from the fact that a nodal point is not, in fact, a real 'point' as it were, so much as a conceptual tool. As you (I think) HINTED at - it exists as a projection of a ray within a limited optical system. One may consider each individual element to have it's own nodal point - or each individual CELL, or a given GROUP. In common photographic terms we refer to a single nodal point of the lens as a whole - taken from the film - as a neat and tidy means of establishing focal length (that's how it's defined). ONE CAN, however, get as technical as one would like (as we are now, painfully, doing). When I spoke of 'nodal points' it was in the general term of discussing the establishment of focal length (please see the title of the thread to understand why this is). And so - yes - if you reverse an optical system - we can establish the existence of a SECOND nodal point for that system - in that orientation. I agree with you if that's the situation we're talking about. But in most cases - I think it is far simpler and more convenient to think about a lens functioning with a 'front' and a 'back'.

Anyway- I'm not too interested in dropping the names of authors of books I like - but you seem very concerned with this so - I guess - the two sets I generally refer to and consider excellent are LP Clerc and Langford. Though I like to go back to the old Halliday and Resnick (fundamentals of physics) if there's anything I REALLY need to take apart.

 

[Ole]

A nodal point is a point - it's the intersection between the optical axis and the principal plane.

I think - I'm off to bed in 10 minutes.

 

[Helen B]

... but Helen - I'm surprised at your statement. Why on earth would it be called a 'nodal' point if there's no 'crossover' happening..? And how on can a lens invert an image without having 'crossover'...?
...

Sparky,

I didn't say that there is no crossover. I said that it happens at the aperture stop (a single entity) rather than a nodal point (of which there are two in a complex lens).

When I spoke of 'nodal points' it was in the general term of discussing the establishment of focal length (please see the title of the thread to understand why this is). And so - yes - if you reverse an optical system - we can establish the existence of a SECOND nodal point for that system - in that orientation. I agree with you if that's the situation we're talking about.

That is the situation we are talking about, but it applies all the time, no matter which way round the lens is. Object-side distances are measured from the front (aka forward and first) nodal point and image-side distances are measured from the rear (aka second) nodal point. It is possible for the two nodal points to be coincident.

[As an aside, a lot of the tequinical* information on the web about stitched panoramas refers to 'the nodal point' of a lens as being 'where the rays cross the axis' or somesuch.]

Maybe it is worth starting from the basic definitions. You will already know a lot of this, but I am trying to clear up what appears to be some confusion.

For a simple single-element symmetrical lens a ray that is headed into the centre of the lens emerges from the other side undeviated. For a complex lens the equivalent ray that is headed towards the front nodal point will appear to emerge undeviated from the rear nodal point. That is the property that defines the two nodal points.

There are a couple of catches:

-The front nodal point may be behind the rear nodal point.

-The ray may not exist, because the image is projected from the exit pupil, not the rear nodal point. Furthermore, even if an object point is within the field of view of the lens the ray between it and the front nodal point may not be capable of entering the lens - it may be outside the bounds of the front element.

Neither of these two catches matter when you are doing calculations involving object distance, image distance and magnification, if you measure image distances from the rear nodal point and object distances from the front nodal point. If you use only one nodal point, such as the rear nodal point, for these calculations they will be incorrect. The error may not be significant: for example when the distance between the nodal points is very small in comparison to the object distance.

This is a lot more simple than it sounds. If I get the time and can find a scanner I will either scan a page from one of the textbooks, or draw it out myself. For now, here is a very simple sketch drawn for a completely different reason. I was a bit naughty when I drew all the lines as solid, instead of partly solid and partly dashed. It is of a Zeiss Distagon 35 mm f/3.5 for the Contax 645. It was drawn "to show different entrance and exit angles for ray heading towards centre of entrance pupil and then out of centre of exit pupil. Also shows that lens aperture may be too small for parallel ray heading towards front nodal point to actually enter lens". The ray that is headed towards the centre of the entrance pupil and shown to exit from the centre of the exit pupil actually crosses the optical axis at the centre of the aperture stop (just to the left of the exit pupil).

Dead Link Removed

Best,
Helen

*A word for something that poses as being technical, but is not. It was named after Terence Tequinical, the anarchist.

 

[Sparky]

Thanks for all your work Helen - I suppose (in my badly formed argument) - I was trying to simplify the discussion to suggest that when one refers to a lens' nodal point in relation to determinations of focal length - that we are talking about something a bit 'different' or more practical.

This was always the simple view I've taken - but surely you agree that if you can say that a given lens has TWO nodal points - that it also has more than that (at LEAST one per element - should you choose to consider each in vitro...?). I'm just trying to suggest (in my own sheepish way) that it's a convention (i would say an arbitrary one - as is having a 'single' nodal point for the purposes of understanding issues of focal distance and back focus). But maybe my point is kind of obscure and academic and I shouldn't push it.. (?)

I have to say though - I still take issue with your suggesting that the 'crossover' or image inversion happens at the aperture. I'm not totally convinced that that's the case. But I suppose I'll have to satisfy my curiosity for myself if I care to... it's certainly not your problem... anyway - thanks for the thoughts.

 

[Dan Fromm]

Helen, I continue to admire your patience. Do visit Sparky's site and read his campaign biography. It and his comments in this thread give me a bad case of cognitive dissonance.

Sparky, you should have the mathematical background to understand and appreciate http://www.optics.arizona.edu/ot/Opti502/MIL_HDBK_141.html

 

[Sparky]

Nooooo...!! Don't read it - it's pathetically bad...!!!! (I have to change it!) Dan - I think you're being passive-aggressive. Perhaps you can explain the problem (specifically) you have with my reasoning..? Can you pick up the general principle of what a nodal point is...? Can you see that each ELEMENT in a lens would therefore have it's own separate pair of nodal points? I think you're looking at things a little bit prescriptively.

 

[Dan Fromm]

Sparky, a person with the education you say you have -- and I believe what you say -- shouldn't need to be spoon fed. If you work your way through MIL-HDBK-141 you'll learn how to do ray tracing, and then you'll have your answers.

 

[Sparky]

Okay Dan - sure thing.