Calculating Lens Extension and Subject Distance

[bbinboulder]

I would like to understand how to calculate the lens extension (i.e. total bellows draw) and lens to subject distance when I know the following:

Reproduction ratio, aka magnification ratio-
Focal length of lens-

Example: I wish to photograph a flower subject that measures 10" across. I want to image this at 4" at the film plane. I think that this would give a magnification ratio of .40 My lens is 6.5" and the optical axis of the lens is at 90 degrees to the film plane.

Seems to me a couple of quick calculations would do it, but can't quite get my brains around this one...

[Ian Grant]

It's very easy just start with 1/f=1/u + 1/v where f is the FL and u is the subject distance from lens nodal oint and v is the focus. The test is simmple geometry.

Ian

[Q.G.]

Magnification = (Total extension - Focal length) / Focal length

So if i'm not mistaken (which - given my math skills - is more likely than not):
Total extension = (Magnification * Focal length) + Focal length.

The conjugate equation mentioned by Ian will then produce the lens to subject distance.

But mind you, that's not the front lens to subject distance.

Just as the total extension calculated above is measured from the rear principal plane of the lens, which depending on the lens design may lie somewhere in, in front of or behind the lens. So it's not necessarily (and most likely not) the exact amount of bellows draw needed.

Life just isn't easy...

[RalphLambrecht]

Ian gave you the classic lens equation, which is correct, but takes a little mathematical acrobatic to get to the answer of your question. I don't recognize Q.G.'s equation and actually think, there is something missing (-1), but I can offer this equation for the magnification 'm':

m = (v/f)-1 = f/(u-f)

where 'v' is the lens or bellows extension, 'u' is the lens to subject distance, and 'f' is the focal length.

I assume, you can solve those for 'u' and 'v', if not let me know.


By the way, if you intent to do more of this, check this out:

http://www.darkroomagic.com/DarkroomMagic/Camera.html

and scroll down to 'Bellows Traget & Ruler'.

[Q.G.]

I don't recognize Q.G.'s equation and actually think, there is something missing (-1),

It's correct as it is, Ralph.
I checked.

[RalphLambrecht]

Yes, you are right. Both our equations lead to the same result.

[Q.G.]

Magnification = (Total extension - Focal length) / Focal length

So if i'm not mistaken (which - given my math skills - is more likely than not):
Total extension = (Magnification * Focal length) + Focal length.
[...]

Just as the total extension calculated above is measured from the rear principal plane of the lens, which depending on the lens design may lie somewhere in, in front of or behind the lens. So it's not necessarily (and most likely not) the exact amount of bellows draw needed.

Life just isn't easy...

It will be easier, however, if you measure the bellows draw of the lens you happen to be using when focussed to infinity (make a note of it), and modify the above formula to read:

Extra extension = Magnification * Focal length.

Add the result to the measured 'infinity' bellows draw, and the effect of principal plane positions should disappear.