So this is an interesting question to me: How do I calculate the magnification of my macro lens if I throw extension tubes on the lens? Is there a formula you can use? To provide hard data I have the Sigma 150mm lens.
So this is an interesting question to me: How do I calculate the magnification of my macro lens if I throw extension tubes on the lens? Is there a formula you can use? To provide hard data I have the Sigma 150mm lens.
Try this link.
1/f = 1/D + 1/F
f is focal length. D is subject distance. F is focus distance. Magnification is M = F/D, the ratio of subject distance to focus distance. For 1:1 magnification, D and F are equal and twice the focal length f.
For a 20mm extension tube on your 150 mm lens (assuming it was capable of 1:1):
1/150 = 1/D + 1/320.
M = (1/150 - 1/320) / (1/320) = 1:1.1333
All the stuff in the link can be derived from the lensmakers equation, 1/f = 1/p + 1/q, where f is the focal length of the lens, and p and q are the distance between the subject and the lens and the distance between the ccd and the lens respectively.
From this and some high school algebra (together with the fact that magnification = q / p), one can conclude that if your extension tubes have length t, they add t/f to your magnification.
The only problem is, that's all wrong. []
Ideal lenses obey the equation, but at least one canon lens I have measured does not. There is a word that describes lenses that do not obey, but I forgot what it is. Thus the above is just an approximation. But it is close enough to true that I never noticed it was wrong until I measured.
The link above says their answers are only approximate (they say you can use it to get a feel for how extension tubes act), so maybe they just use the lensmakers equation (in which case I would think the equation itself is far more informative than the spreadsheet).
Maybe they take more into account, though.
Originally Posted by MikeWhy
You beat me to it, and said it much quicker
But again, not all lenses obey this equation exactly. Most don't, I believe.
I've never measured, and would put it to the test except I don't have extension tubes. Could your measurements be off by the lens's inter-nodal distance? An ideal lens is assumed to have zero thickness. Real lenses had non-zero nodal thickness, and so have front and rear principal nodes. Focus distance is measured from the rear principal node; subject distance from the front principal node. On a telephoto, the rear node can be forward of the front node. If you measure the distances when focused at 1:1, you can mark the respective nodes on the lens body. I wouldn't bother... haven't bothered.
I don't bother doing those measurements either. But if I add 68mm extension to my canon 100mm macro (non IS), I get about 2x magnification. It should take 100mm of extension to get 2x magnification from 1x no matter what the inter-nodal distance is.
This puzzled me for a while. Daniel once mentioned that effective focal lengths of lenses often change as you get close to a subject- I think he called this "breathing"- so I thought this might be it (though, he didn't seem to expect it to vary that much). Later I learned that it is not at all uncommon for modern lenses to simply not obey the law.
Yes. (Pedantry forces me to point out that it's the act of changing focus, not subject distance, that causes the effective focal length to change. Of course, in reality the difference is moot, since we tend to want our subject to be in focus if we move closer [].)
Any lens that is front, rear, or internally focusing does this to some degree or other, which includes most Canon lenses. Many times the change is pretty small (10-20%), but one of the best Nikon macro lenses, the 200mm f/4, goes down to 105mm (!) when focused at 1:1.
Yes, of course; makes perfect sense. The lens elements are moving around inside, unlike a view camera which just moves the film holder nearer and farther. Physical realities would prevent that Nikon from finding another 200mm of back extension. Something else has to give, and I hadn't noticed the impossibility of holding focal length constant even on my shorter 100mm macro.
Okay, I was confused here. I'm not sure if this is true or not. What seems to be true is that magnification might not be the ratio between subject-lens distance and the lens sensor-distance.
Some lenses for which this seemingly obvious property fails are called telecentric lenses. For a particular type of telecentric lens, magnification is independent of lens-subject distance. For another type, magnificaiton is independant of lens-sensor distance. According to wikipedia: "Many lenses that have been specially optimized for digital SLR cameras are nearly telecentric on
the image side, to avoid the vignetting
and color crosstalk that occur in color filter array-based digital image sensors with
oblique incident rays. The Four Thirds System uses this
approach."
I now regard all calculated magnifications as approximations. They might be off due to breathing, or they might be off due to a strange telecentric-like effect.
If anyone knows more about this, I would be happy to be enlightened.
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