## Bizarre: Image size stays constant as lens is extended

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Lou Jost
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### Bizarre: Image size stays constant as lens is extended

I wrote about my "poor man's Repro-Nikkor" here.

http://www.photomacrography.net/forum/v ... highlight=

It is made of two 50mm Olympus Four-thirds macro lenses stacked front-to-front. It acts as if it were an f/1.0 lens with fixed magnification of 1x.

I figured I could move it up from 1x to a bit higher m by bringing the subject closer and adding extension, like any other lens. To my surprise, when I added 26mm of extension and refocused the lens on the subject (which had to be brought much closer to the lens), the size of the image stayed about the same size! In fact it shrunk slightly, by approx by 2%. What on earth is going on?

Edit: Ah, that's what a "Measuring objective" does. Perhaps by varying the spacing between the two lenses, or putting my paper aperture exactly in the middle instead of 2mm higher, I could turn my "Repro-Nikkor" into a perfect double-telecentric lens????

rjlittlefield
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### Re: Bizarre: Image size stays constant as lens is extended

Lou, welcome to yet another of the often unexpected behaviors of lens combos!

The relevant formula is given at https://en.wikipedia.org/wiki/Lens_(optics)#Compound_lenses :
If two thin lenses are separated in air by some distance d, the focal length for the combined system is given by

1/f = 1/f1 + 1/f2 - d/(f1*f2)
When d = 0, this reduces to the classic thin-lenses-with-no-separation formula that 1/f = 1/f1 + 1/f2.

When d = f1+f2, it reduces to 1/f = 0, which implies that f, the effective focal length of the combined system, is infinite! Probably confusingly, this combination that has infinite focal length is nonetheless capable of focusing at finite conjugates with no problem.

The catch is that the combined system still obeys the extension formula that
and with EffectiveFocalLength = infinity, that formula correctly predicts zero change in magnification as you change extension!

The particular combo that you're testing apparently has d > f1 + f2. That drives the effective focal length of the combined system into the negative range, which in turn implies that as you add extension you get less magnification. The change is small because the focal length has large magnitude, because d is not much greater than f1 + f2.

Personally I find it quite counterintuitive that a lens combination with negative effective focal length can nonetheless focus with finite conjugates, but yep, that's the way it works. Interestingly, the ray tracing diagrams don't seem confusing at all. The problem is only that I'm so used to the simplified formulas that ignore lens spacing. Those simplified formulas become increasingly inappropriate as the spacings get large, and in cases like you have here, they make wildly crazy predictions.
Lou Jost wrote:Perhaps by varying the spacing between the two lenses, or putting my paper aperture exactly in the middle instead of 2mm higher, I could turn my "Repro-Nikkor" into a perfect double-telecentric lens????
Perhaps. What's needed is to have lenses be exactly the correct distance apart, and to have the central aperture be located at the focus point of each lens individually. When you do that, you will have completely fixed the magnification as the ratio of focal lengths, and the combination will be telecentric on both sides.

However, it's worrisome that your image size shrank slightly as you added extension. That indicates you need to slightly reduce the separation between the lenses, and I can imagine that might be mechanically challenging to accomplish.

--Rik

Lou Jost
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Thanks for the explanation Rik. As you said, this effect is quite counter-intuitive, but I see now that it follows from the full formula. Ray Parkhurst had asked about the effective focal length of this combination on my original thread, but I didn't dare answer because I couldn't figure out what "focal length" even means in this context. I'm glad I didn't try to answer!!!

The male-male ring I used to join them was an especially fat one. Maybe I can find a thinner one and hit that special spot.

I wonder if the real Repro-Nikkor has similar behavior.

rjlittlefield
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Lou Jost wrote:I wonder if the real Repro-Nikkor has similar behavior.
I expect it would, based on published descriptions that indicate the lens is bilaterally telecentric or close to it.

--Rik

Lou Jost
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According to that formula and my measured data, d= 101.9 so I would have to shave off about 2mm to get perfection....

My male-male ring has a three-millimeter spacer between the threads. I could sand down the lenses' front threads a bit, or destroy the ring and mount the threads on the outside of a 50mm cylinder with epoxy....

Lou Jost
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I see there is nothing special about the lenses having the same focal length. I can replace one of the 50mm lenses by my 70mm lens (also excellent) and then I only need to add a bit of distance, not shave it off.

Could I find that distance, and the proper place to put the aperture, by finding the front focal plane of each lens when the rear element is aimed at the sun, and making sure that the two planes overlap?

If so, then just about any pair of stacked lenses that don't have deeply recessed front elements can be made telecentric on image and object sides. That could be useful.

Is there some cost in IQ? We usually find that large distances between lenses causes aberrations.

rjlittlefield