finding out the focal length when focussed closer than infinity...

[Leonard Evens]

Perhaps it is easier to use the formula

u/f = 1 + M

where u is the distance to the subject and M is the ratio of the subject size to the image size. You measure a linear dimension in the subject and the corresponding dimension in the image on the ground glass. M is the ratio of the former to the latter. You add 1 to M. You then measure the distance to the subject. In principle, this should be measured from the front prinicpal plane, but if you measure it from the front of the lensboard or even the front of the lens, it probably won't make a lot of difference in the calculation, You know u/f = 1 + M because you know 1 + M. You take its recipprocal f/u and multiply it by your measured distance u. That gives you f in the units you used for u. If, as you say, u is 10 meters, you will get the focal length in meters. Multiply by 1,000 to get the focal length in mm.

This method will only be an approximation because of possible errors in measuring the subject size, the image size, and the distance u to the subject. If you do the calculation for different subject distances and take the average of the results, you will get a better aproximation. Finally, it might make sense to round it up or down to the nearest probable lens focal length. For example, if you measurments give you 104 mm, it is more likley the focal length is 105 mm.

[Brian Ellis]

When I needed to focus on infinity to set the infinity stops for different lenses on my Linhof Technika camera I just went out to a highway and focused on billboards a mile or so away.

[Struan Gray]

I always use the comparison method.
Hold two lenses up and focus the window frame on a white wall. One of these must have a "known" focal length. Swap the known lens until you get a match - or a very close match. If you have a measuring scale on this wall, you can "measure" the size of the window frame image with a "known" lens and unknow lens. Then do a simple division calculation. This method also gives an indication of the F value of the unknown cell. You can see the difference between and F5 and F6 (as an example) very easily.

Just for completeness, it is worth pointing out that this method makes a small angle approximation. It will be around 10% out if the window fills an angle of view of around 60° (think of an equilateral triangle formed by points at the edges of the window and the lens). The error gets worse fast after that.

The simplest way round the problem is to draw a graph of projected window size for the known lenses, and interpolate a smooth curve for the unknown values. Hard to do for those with few lenses, but most of us can cobble together a reasonable collection from our various formats. This way will work even in a small room where the distance from wall to lens is a significant portion of the distance from lens to window.

Otherwise, it's easy enough to do a bit of trig. An object an angle theta off the axis of the lens gets focussed to a point which is a distance f*tan(theta) from the same axis.

[desertrat]

There are several good formulas for measuring the focal length of a lens directly, giving the focal length at infinity even though the object focused on is much closer. These can be done in a room:

http://archive.org/details/photographicfact00wall

The formulas begin on page 35. The simplest one works if you have enough bellows to get the lens to 1:1 magnification. Move the object back and forth until its image on the GG is the same size as the object. With a tape measure, measure the distance between the object and the GG. Divide this by 4. You will have the focal length of your lens at infinity. If you can't extend the bellows that far, there is another formula on page 37 that you can use for an object across the room. It only requires the size of the object, the size of the object image in the GG, and the distance between the object and the GG. It also gives the focal length at infinity. If you like complex formulas, there is one on page 35 that involves two measurements of object and image at different distances in a room. It also gives focal length at infinity. What I like about these three formulas, is there is no need to know the position of the nodal point in the lens, and no need to measure the distance between the nodal point and the GG, which some formulas require. Some of the simpler scale formulas only give the focal length of the lens at the distance focused, not infinity.

[numnutz]

Thank you for all your replies. As it has been raining in London almost without a stop since a drought was declared I though I would set up the camera in the house and focus through a window at an object. This will give me something to do until the rain stops!

John, The focal lengths are marked on the edge of each element - 15, 25, 35, 45cm

Thanks for your reply Richard, I only saw the markings on each lens after I looked at the lenses through a magnifier. I did download the info sheet you posted and will have a further look at that.

Focussing on the sun is good idea unfortunately the sun has not been seen in London for a while and in any case the windows in my flat point to the north.

I repeat thank you for your replies.

john Wills
www.southernrailway.net
www.londontramways.net