A Little Help Calculating Working Distance, Please.

Dan Quan · Jan 10, 2012

I am considering a lens purchase for still life close-up work, but I can't seem to find the formula to calculate working distance when I know the magnification and focal length and bellows draw, a formula I did find. I presume there is such a formula and I am hoping one of you will point me in the right direction or post it.

Caveat: I am not a math person, I struggled through Algebra, several times.

MattKing · Jan 10, 2012

Dan:

IIRC, any such formula would only tell you the working distance:

1) from the lens, if the lens was a simple meniscus lens; or
2) from the nodal point, which depending on the type of lens being used, could be inside the lens, in front of front element of the lens, or behind the rear element of the lens.

Dan Quan · Jan 10, 2012

I appreciate your quick response.

I'm considering a G-Claron or an Artar, and I may be able to find the nodal point info for those.

David A. Goldfarb · Jan 10, 2012

Or you can just use what's conventional for 8x10" (assuming from your profile info that that's the format you're shooting), which would be about 19" or 480mm if you have the bellows draw to shoot still life with a 19" lens (you'll probably want around 40", which is a pretty long bellows). For practical purposes, if you want to maximize working distance with the camera you have, start from the maximum bellows draw, and pick the lens that gives you the maximum magnification you need with the bellows draw you have, and then you just have to deal with the working distance or get a camera with a longer bellows.

Dan Quan · Jan 10, 2012

Hi David, Thanks for posting. I do have a 19" RDA and a Kodak Copying Ektanon 16 3/4 , but only 30" of bellows draw and I want to shoot some really small stuff, peppers, flowers etc. So I am thinking of a 305, 270, 210 ish but I want to have room to light the subject as well. I need some idea of the working distance these offer so I can guess-timate my lighting requirements.

BradS · Jan 10, 2012

Dan,

the general equation is

1/f = 1/w + 1/v

where:
f is the focal length
w is the distance from lens to object (roughly what you call working distance)
v is the distance from lens to film plane (image distance)

so, for example,
if your focal length is 305mm and your bellows is 700mm (~27 inches) then

1/f = 1/w + 1/v
1/305 = 1/w + 1/700
1/w = 1/305 - 1/700
and so,
w = 1/( (1/305) - (1/700) )
and when I punch this into my trusty pocket calculator, I get...
working distance = 540.506 mm (~21.3 inches)

(EDIT: the two distances v and w are actually from the nodal point of the lens. This can be assumed to be roughly at the lens board for lenses that are not telephoto nor wide angle).

Dan Quan · Jan 10, 2012

Oh, I get by with a little help from my friends...

Ian C · Jan 11, 2012

I presume that you mean working distance = lens-to-subject distance.

Let s = the subject distance (from the optical center of the lens to the subject)

f = focal length of the lens

m = magnification

E = total extension = f + b, where b = displacement of the lens forward of its infinity focus position

As a function of m and f

s = (m + 1)f/m

Example: f = 100mm, m = 1X. Then

s = (1 + 1)100mm/1 = 200mm

As a function of E and f

s = Ef/(E f)

Example E = 200mm (b = 100mm), f = 100mm

s = 200mm*100mm/(200mm 100mm) = 200mm

You could also calculate the distance from the film plane to the subject if you find it more practical.

Dan Quan · Jan 11, 2012

Thanks Ian, I appreciate your response and I am sure it makes perfect sense to the smart people. I however, (frequently boasting of an IQ in the high double digits) needed something I could just plug into my TI-83 Plus, hit enter, smile with satisfaction and move onto my next task.

I appreciate the effort it takes to answer questions and everyones contribution. Thanks so much.

BradS, thanks for spelling it out, that really made it work for me.

BradS · Jan 11, 2012

Dan Quan said:
BradS, thanks for spelling it out, that really made it work for me.

My sincere pleasure. I always wanted to "be a Math teacher when I grow up".....somehow that never happened. No regrets though.

Dan Quan · Jan 12, 2012

I bought a G-Claron 150 and 240 to try out.

The 150 should give me 4:1 @~27" with ~ 7" working distance. And the 240 2:1 with ~ 10" working distance.

Thanks again for all your help.

A Little Help Calculating Working Distance, Please.

Dan Quan

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A Little Help Calculating Working Distance, Please.

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