How is focal length measured?

The aperture is measured as a ratio of the focal length, but the lens elements move forward and backward when focusing. How is the focal length determined? Is it based on the infinity focus, or the nearest focus, or something in between?

Just curious.

Based on infinity. Even for lenses that never will see subjects at infinity.

Thanks, AgX.

Someone should help out Wikipedia. It is full of unhelpful jargon and formulas. It was written by nerds trying to impress other nerds, so I could not find this answer.

Ariston said:

The aperture is measured as a ratio of the focal length, but the lens elements move forward and backward when focusing.

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You hint at another important point:

Max. aperture is dependant of the effective lens opening and the focal length. As you indicated the lens/film distance varies during focusing and thus effective aperture varies too. This becomes an issue at large image scales when a correcting factor is applied depending on extension.

That is what got me thinking about it - you have to adjust for longer bellows, basically because you are changing your effective aperture, as far as I can tell.

Ariston said:

That is what got me thinking about it - you have to adjust for longer bellows, basically because you are changing your effective aperture, as far as I can tell.

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Not a change to aperture in the true sense...imagine taking a macro photo with large format --it is analogous to making a larger print with an enlarger, the larger the print the dimmer the image at the print. Similarly, the larger the magnification of the subject, the dimmer the image on the film plane simply because the overall image is larger and the same (fixed) number of photons get spread over a large image circle causing dimmer image.
Folks think of 'effective aperture' simply as a convenient way to alter the shutter speed to compensate for the dimmer image at the film plane...'effectively f/16 although the lens aperture is set to f/11'

Ariston said:

That is what got me thinking about it - you have to adjust for longer bellows, basically because you are changing your effective aperture, as far as I can tell.

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But still

-) focal length
-) max. aperture

are based on infinity

Bellows compensation is a result of wave propagation physics. If you think about it, the same number of photons are passing through the aperture, but as you extend the film plane further from the lens, you're increasing the size of the cone of light (or more accurately, moving further back within the cone) that the lens projects. It's kind of like how if you throw a stone into a lake, the waves get smaller the further they travel away from the entry point. In a camera, this means the number of photons, which remains the same, must spread out further to cover a larger area. So you get less density. This is why you need more light to get the same exposure for close up photography when using bellows cameras, but don't for SLR's and rangefinders (unless using extensions).

Some zoom lenses change their effective aperture as you change focal lengths because they don't change the physical aperture size as you change the focal length. Since the f number is a ratio, if you change the focal length, you have to change the physical size of the aperture to maintain the same effective aperture. Fancier zoom lenses do this for you automatically.

Are you wanting to know how to determine the focal length of a lens?
Or are you asking how focal length relates to other variables?
The jargon in the Wikipedia article is actually appropriate, because the answer to either question is quite complex.
For simple, single element lenses, you can determine the focal length by focusing the image from a distant source and measuring the distance between the centre of the lens and the focused image.
You use the same sort of test with a multi-element lens, except you need to measure the distance between the focused image and the rear nodal point of the lens.
The rear nodal point isn't particularly easy to locate. In the case of telephoto lenses or retro-focus lenses, the rear nodal point is actually outside the glass, and may be outside the lens body.
For cameras that rotate, like the Cirkut cameras, the rear nodal point is the point at the centre of the camera's rotation.
The rear nodal point is not the point you use as the rotational centre for panorama pictures.
Does anyone have a good suggestion for a simple way to locate the rear nodal point of a lens?

If you want a practical way of measuring the focal length of a lens, try measuring the extension required to focus it at some distance. For example focus at infinity, measure the position, then focus on an object measured to be (for example) 5 meters or 2 meters from the lens, and measure the extension relative to the first position. Use the simple lens equation 1/f = 1/d_subject + 1/d_film. In this case, we know that d_film = (focal length + extension). You can solve this equation, knowing d_subject and extension, to get focal length. (Technically, you should be measuring d_subject from the front nodal point, but this should be close enough to the lens that it doesn't introduce much error.) This will be easier in practice than trying to find the rear nodal point accurately.

Ariston said:

The aperture is measured as a ratio of the focal length, but the lens elements move forward and backward when focusing. How is the focal length determined? Is it based on the infinity focus, or the nearest focus, or something in between?

Just curious.

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as far as I understand, it's the distance between the nodal point of the lens and infinity focus, which leaves the question:'where is the nodal point'?

MattKing said:

Are you wanting to know how to determine the focal length of a lens?
Or are you asking how focal length relates to other variables?
The jargon in the Wikipedia article is actually appropriate, because the answer to either question is quite complex.
For simple, single element lenses, you can determine the focal length by focusing the image from a distant source and measuring the distance between the centre of the lens and the focused image.
You use the same sort of test with a multi-element lens, except you need to measure the distance between the focused image and the rear nodal point of the lens.
The rear nodal point isn't particularly easy to locate. In the case of telephoto lenses or retro-focus lenses, the rear nodal point is actually outside the glass, and may be outside the lens body.
For cameras that rotate, like the Cirkut cameras, the rear nodal point is the point at the centre of the camera's rotation.
The rear nodal point is not the point you use as the rotational centre for panorama pictures.
Does anyone have a good suggestion for a simple way to locate the rear nodal point of a lens?

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A one element lens only has one nodal point. It may be in the physical center of the element or not, thus here the difficulty already starts.
With lenses made from more than one element there are two nodal points: a front and a rear one.
For panoramic photography either of the two has to be used as location for the rotational axis, though the front nodal point seems to yield better image quality (statement by Seitz).
In the definition of the focal length of a lens the rear nodal point is used.
Locating of the nodal points ca be done by experimentation. The lens in swung around varying points, until there is no more virtual movement between subjects staggered in depth: https://bit.ly/2nl403q

As a linear system all optics have an input and output. Therefore a single element has two nodal points which coincide at the same plane.

There’s other stuff in this thread which could be corrected, but I don’t want to outnerd everyone.

Nodda Duma said:

As a linear system all optics have an input and output. Therefore a single element has two nodal points which coincide at the same plane.

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This is splitting hairs in its worst...

reddesert said:

If you want a practical way of measuring the focal length of a lens, try measuring the extension required to focus it at some distance. For example focus at infinity, measure the position, then focus on an object measured to be (for example) 5 meters or 2 meters from the lens, and measure the extension relative to the first position. Use the simple lens equation 1/f = 1/d_subject + 1/d_film. In this case, we know that d_film = (focal length + extension). You can solve this equation, knowing d_subject and extension, to get focal length. (Technically, you should be measuring d_subject from the front nodal point, but this should be close enough to the lens that it doesn't introduce much error.) This will be easier in practice than trying to find the rear nodal point accurately.

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The focal length is labeled on most lenses that I know but they are not 100% accurate. So if what the lens is labeled close enough then there is no need to measure. However, if you want more accuracy your method doesn't work because you don't know how far the front and rear nodal points are apart. When you measure d_subject it has to be measured from the front nodal point and the d_film has to be from the rear nodal point.

At some data-sheets as for instance from Schneider you will find both, the nominal and the actual focal length. Though I doubt a Apugger really needs that precision.

AgX said:

Locating of the nodal points ca be done by experimentation. The lens in swung around varying points, until there is no more virtual movement between subjects staggered in depth: https://bit.ly/2nl403q

Click to expand...

This method yields the front nodal point.
The rear nodal point is the one you need for determining focal length.

No, you can swing around both nodal points. And by this method locate both nodal points.

How about this:

The focal length of a lens is measured from the optical center of the lens, to the film/sensor plane. The focal point for most lenses, except telephotos is generally at the aperture. Therefore, measure from the film/sensor plane, to the aperture.

For true telephoto (not long) lenses the focal point is in front of the aperture; measure from the film/sensor plane to the focal point of the lens. A rule of thumb is to take the nominal focal length and measure that distance from the film/sensor plane. e.g. a 300mm lens will have a focal point about 12" from the film/sensor plane, and that measurement may even be in front of the front element.

Infinity is considered to be 200 times the focal length; e.g. a 150mm lens will have an infinity pointy of about 100 feet.

AgX said:

This is splitting hairs in its worst...

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Yes it is!

You are all nerds.

Ariston said:

You are all nerds.

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Tu quoque.

More seriously, why did you ask the question? How did you hope to use the information and misinformation you've been given?

Ariston said:

You are all nerds.

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When you get paid well to be a nerd, the term you use is a “professional”.

Chan Tran said:

The focal length is labeled on most lenses that I know but they are not 100% accurate. So if what the lens is labeled close enough then there is no need to measure. However, if you want more accuracy your method doesn't work because you don't know how far the front and rear nodal points are apart. When you measure d_subject it has to be measured from the front nodal point and the d_film has to be from the rear nodal point.

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Correct in principle (I dd mention the front nodal point), but in practice this method does work to amateur accuracy. The reason is that the accuracy of this measurement is limited by how well you can measure:
1) the lens to subject distance, since you don't know the exact location of the front nodal point,
2) the extension, because this is a relatively small distance and I assume that the user is an amateur with say calipers or a micrometer, measuring the extension on a camera with a homemade fixture, not some kind of incredibly rigid and aligned optical bench.

If you set it up so the lens to subject distance is several times larger than the focal length, the error from not knowing the front nodal point is a small fraction of the subject distance, so it doesn't dominate the error budget.

I will give a worked out example, sorry for the tedium. Suppose you have a lens of focal length f=100mm (but you don't know this), and you focus it at a subject distance of d=1 meter measured. The extension from the lens equation is e=11.11 mm, measured. Most of us would probably only measure that to say the nearest 0.1 mm, an accuracy of 1% on e.

The lens equation 1/f = 1/d + 1/(f+e) can be rearranged into a quadratic: f^2 + e*f - e*d = 0. You can solve this with a calculator, or analytically:
f = (sqrt(e^2 +4*e*d) - e) / 2.

Suppose that the front nodal point is 10 mm different than where we thought it was. That means we would measure d=990mm or 1010mm, You can try plugging these numbers into the formula. You'll find that the inferred focal length would be 99.5mm or 100.5mm. A 1% error on subject distance leads to an 0.5% error on focal length (due to the prefactors in the formula and the square root).

It turns out that a 1% error on measuring the extension also leads to about an 0.5% error on the focal length. IMO, measuring the extension to 1% is difficult for an amateur without fabricating a jig.

It's possible to measure focal length much more accurately (I have a process lens that is marked with true focal length to 0.01 mm), but for that I think you'll need an optical bench and techniques that are beyond the scope of this discussion.

Nodda Duma said:

When you get paid well to be a nerd, the term you use is a “professional”.

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I agree! If you are a nerd and you aren't paid well, then you are nerding wrong.

For the record, I consider myself a nerd, too. I was more curious about a laymen's explanation of what defines focal length. AgX explained it well for me.