View Full Version : Close Focusing Distance Formula Question

3-Mar-2017, 12:43
From doing some diligent checking, the formula for calculating close focusing distance for a given lens and bellows is the following:

1/f = 1/d + 1/b

f = focal length
d = distance
b = bellows draw

Using this, for a 240mm lens, and 11 inches of bellows draw, the result that I come up with is a close focusing distance of 1.7 meters or roughly 5.6 feet. Somehow that sounds way too close. I hope that I'm not overlooking something here. Is this correct?



3-Mar-2017, 13:07
Hi Ed,

That's sort of correct, and sort of not.

First off, "bellows draw" is meaningless and not related to that equation in any way.

The proper equation is: 1/f = 1/Df + 1/Ds where
Df is the distance from the rear node of the lens to the film, and
Ds is the distance from the' front node of the lens to the subject.

The two lens nodes may be close together, but they may also be very far apart.
Telephoto or ultra-wide lens designs usually have one or both nodes significantly shifted.
For example, a telephoto design has the rear node waaaaay out in front of the front element.

You must consult the manufacturer's datasheet to determine the node locations.
You can use the diaphragm location as a close approximation on lenses of roughly "normal" focal length.

- Leigh

Dan Fromm
3-Mar-2017, 13:35
Ed, what Leigh wrote is correct. I find it easier, though, to think in terms of magnification.

First magic formula: rear node-to-film distance = focal length * (magnification + 1) whence magnification = (rear node-to-film distance - focal length)/(focal length)

Leigh is right that you should look for documentation to find out where your lens' rear node is located. However, lenses of normal construction -- not telephoto, not retrofocus -- have both nodes very close to the diaphragm.

Assume that y'r 240 mm lens' focal length is really 240 mm and that its shutter's diaphragm is at the flange. This last is approximately what Leigh suggested. Extension will be 25.4 mm/inch * 11" =279 mm, magnification will be (279 - 240) = 39/240, ~ 0.17

Second magic formula: front node-to-subject distance = focal length * (magnification + 1)/magnification = 240 mm * 1.17/.17 = 240 mm * 6.88 = 1930 mm.

Adding, film-to-subject distance will be 240 mm + 1930 mm = 2170 mm give or take a little to allow for non-zero internodal distance and the possibility that the lens' focal length isn't exactly 240 mm.

Mark Sawyer
3-Mar-2017, 15:11
Don't tell anyone, but there's a secret method only a few of the mysterious Large Format Illuminati know. Measure your bellows draw (focal length), and your aperture size. Divide the former by the latter and you get a secret number we clandestine cult members call the "f/stop". Maybe you've heard rumors of it. Some say it's only a myth, an urban legend, but it really exists!

Remember to keep it secret, we don't want anyone else to know...

Jim Graves
5-Mar-2017, 20:39
The League of the Secret Illuminati meets on the second Tuesday following the third full moon of even numbered years.

Only those knowing the foot-candle power of the full moon will be admitted.

Appropriate dress is a dark cloth cape and a 8X loupe necklace.

Be sure to bring your Petzval Sums as price of admission.