Calculating required extension for given distance?

[jvuokko]

I have made some focusing scales like this and used them for some years:



The place of markings are measured manually. Simply placing a target at the different distances, focusing and then measuring extension on the Field camera's rail.

These are really handy when focusing is difficult - at the dark or when there aren't enough space behind the camera and I wan't to take a simple snapshot.

But during years I have got more cameras and lenses and similar scales would be useful with these too! But using focusing target, measuring distances etc is a bit frustrating and slow process.

So I went to the math. But that didn't gave (easy) answer to my question.

The most common equation is

1/S1 + 1/S2 = 1/f

where S1 is distance between front nodal point and subject (in practical, usually distance between shutter/lens board and subject).
S2 is distance between rear nodal point and film plane/GG - usually bellows extension..
f is focal lenght.

This works fine - except it uses the distance between lens and subject - not the distance between film plane and subject which is the normal practice with focusing scales.

I am stuck with this. I could use this and calculate values for focusing scale - and accept the fact that distance is actually from the front nodal point ("from lens")..

It's okay for most purposes but...


So is it possible to calculate extension from the film plane?
Or can I calculate the place of scale markings if I know values for 1 meter and infinity?
These two numbers are quite easy to get.

For example, if the focal lenght is 210mm and I know that when focused to 1 meter, the required extension is 95mm longer than extension when focused to infinity. Can I calculate from that information where the relative extension is when focusing to 3 meters or any other range?

[aduncanson]

With f = focal length and d = distance from film plane to subject, the
displacement from the infinity focus position =

2f / [d/f - 2 + sqrt( (d/f)^2 - 4d/f)]

or if you are conversant in in Excel:

=2*$B$1/(B3/$B$1-2+SQRT((B3/$B$1)^2-4*B3/$B$1))

where B1 is focal length and B3 is subject to film distance - I've tested that; it works.

Please don't ask me to show my work, you sent me back about 40 years in school to work this out.

I provided the displacement from infinity focus because in general the film plane to rear nodal point distance cannot be measured, but you can measure this displacement from any convenient repeatable landmarks on the front and rear standards.

Good Luck - Alan

Oh Yeah, I forgot that there is still an unknown term to be considered when measuring subject to film distances. It is the Principal Point Separation, the distance between the front and rear nodal points. My math assumes it is zero. Schneider publishes this information and perhaps it can be measured accurately enough if you set up your camera with magnification = 1:1. If the actual film to subject distance is different from 4x the focal length then that difference is the Principal Point Separation - assuming that you are using the actual focal length rather than the nominal one.

Again - Good Luck

[Jack Dahlgren]

Just want to reiterate the point that nominal focal length (as marked on the lens) may be different from the real focal length.

[jvuokko]

Thank you for the equation.
I guess that it's accurate enough for making some simple rulers