How does one determine how close a given lens can focus given a given bellows draw?

I'm making initial plans for a 14x17 ULF camera. I foresee one day having a 30-inch (760mm) as my longest focal length. I'm also thinking that I'll make bellows about 40 inches long, though that is obviously a flexible factor. I'm wondering if there is a formula, or even a calculator, to determine how close I'd be able to focus a given focal length lens with a given bellows draw. I know I'd need 60 inches to focus 1:1, but what about intermediate distances? I'm not a math guy, so haven't been able to figure it out myself.

I've found some info online, but not just what I'm looking for. Figuring out what search terms to use is probably my problem.

Have a couple of magic formulas.

extension (rear nodal point to film) distance = focal length * (magnification + 1)

lens-to-subject distance (front nodal point to subject) = focal length * (magnification + 1)/magnification

For most non-telephoto lenses used on LF cameras the nodal points are very close to the diaphragm and the distance between them can be neglected.

With a 30 inch lens and 40 inches of bellows magnification = (40/30) - 1 = 0.33

Then lens-to-subject distance (remember, measured from the diaphragm) = 30 * 1.33/.33 = 120 inches

This is all slightly approximate because I don't know how far your camera's lens board sits in front of the front end of the bellows or how far your lens' diaphragm will be in front of the board.

The simple lens formula can help you: 1/p + 1/q = 1/f
p=lens to subject
q=lens to film
f=focal length

http://hyperphysics.phy-astr.gsu.edu...pt/lenseq.html

40" seems a bit short for 14x17". The V11 has 42" of bellows if memory serves me right, if you want to shoot close with a 30" lens, you might want to try for 50-60" of bellows if possible. Would also give you the possibility of using a 35" lens if you choose to go that route. If Dan's numbers above are sufficient, then fine.

All those formulas are right for the plane of focus, but in fact the camera can focus closer than what theory says because DOF when stopping.

So DOF effect has to be added to the calculations.

(To see DOF impact just install a DOF calculator App in the phone...)

And, of course, we can also use the rear/front tilt to focus closer that the theoric max film to lens board distance says.

Just noting that the practical distance may be way closer that the theory says, by adding DOF + tilt, to the point that even in the case the theory says 10m we may be able to focus at 1m.

Paul, I think that this may be a useful simulator for you: https://apenasimagens.com/en/focal-l...s-and-framing/

Sorry it's taken me so long to get back to this! Holiday travels, and then getting back on track after holiday travels.

Thanks for all the helpful comments. Looking at the numbers Dan gives, and at the link given by lungovw above, it looks like I might be okay with 1 meter bellows, especially when I keep Pere's comments in mind. Still, since I'm making them, they can be as long as I like, and it would be nice to be able to get a little closer. But plugging numbers into Dan's formulae shows me (if I'm doing it right) that going from 40 inch bellows to 50 inch bellows takes me from a closest approach of 10 feet to one of just over six feet (75 inches). I'll have to do some thinking about just how close I want to get, and how much weight and bulk I want to add to the camera to get there. I don't imagine I'll want to go longer than 50 inches, if that long.

Paul,

The difference in lensboard position between infinity focus and 1:1 (full-size image) focus equals the lens focal length.

That's true for all lenses and all formats.

- Leigh

Leigh,

Right, and that was about the extent of my knowledge before posting this question. Having the formulae to figure out intermediate distances will be very helpful. I can use a shorter focal length lens, like my 19 inch Artar, to get 1:1.

For this post, I was mostly trying to figure out what to expect with a longer focal length. I foresee the possibility of a three lens kit with this camera***: a 14 inch (355mm) for wider shots; the 19 inch (480mm) that I already have for a slightly wide normal; and a 25 inch (760mm) for slightly long images. Though the aspect ratios are slightly different, these three focal lengths on a 14x17 camera will be about comparable to a 103mm, a 140mm, and a 222mm lens on a 4x5 camera. (Folks often make comparisons to the 35mm format, but that has never made sense to me when comparing such nearly square ratios to 2:3.)

As always, thanks again to all of you for the help. I hope this is another thread that others will find helpful, too.



*** But I always start out that way, and eventually lose track of the lenses I end up trying on all my cameras. Still, I currently only have 5 lenses for my DSLR (if you don't count my telescopes; and please don't, there are too many!) and seven between my 4x5s and 5x7, five of them shared between the formats.

For those rare occasions you want to focus closer you can build a “top hat” style lens board to carry the extra extension. It can be left home to lighten the load when you know it’ll never be brought out.