Bellows Draw for a Given Diaphragm-to-Object Distance
If you could restate your question then it then it can be answered after a fashion.
In a second semester university physics course the material takes a brief look at optics. It doesn’t go into great depth and doesn’t consider more than 2-element systems. Most of the section on optics involves a theoretical “thin” lens that is thin relative to its diameter and is usually a single-element double convex lens like you’d see in a magnifying glass with each surface the same spherical radius.
I seem to recall that for the purpose of some calculations a symmetric compound-element lens is roughly equivalent to a thin double convex lens whose single element is centered at the plane of the diaphragm. With this simplifying idea it’s possible to calculate something similar to what you asked.
The Thin Lens Formula is:
1/f = 1/p + 1/i
where f = focal length of the lens, p = distance from the object to the center of the lens, and i = the distance from the image to the center of the lens.
1/i = 1/f -1/p = (p-f)/fp
i = fp/(p-f)
If by “0.7 meters away” you mean 0.7 m from the object to the plane of the diaphragm, then p = 700mm. You said that f = 240mm, so now we can calculate i, the distance from the film plane to the plane of the diaphragm.
i = 700mm*240mm/(700mm-240mm) = 365.22 mm.
To test the calculated prediction I used a 240mm f/5.6 Rodagon enlarging lens to project the image of the lit filament of a 60-watt light bulb onto a piece of white mat board. The lens was placed with the plane of the diaphragm approximately 700mm from the center of the bulb. I measured the distance from the plane of the diaphragm to the mat board where the position of the board gave the sharpest image of the filament. It’s somewhere between 355mm and 375mm so that suggests that the calculated value is close to the actual diaphragm-to-image distance. With a proper optical bench I could have refined the measurement.