View Full Version : finding out the focal length when focussed closer than infinity...

Hi - I have just purchased a casket set of four lenses. Unfortunately the focal lengths are not marked.

Obviously I can find out the focal length by focussing on infinity.

However in my small garden I cannot focus on anything that is far enough to use for infinity.

If I focus on an object say 10 meters away (I will measure it) is there a formula that I can use to find out the focal length at infinity?

Thank you in advance.

John Wills

www.londontramways.net

www.southernrailway.net

Here you go:

http://en.wikipedia.org/wiki/Focal_length#In_photography

If you want to check focal length at infinity, just put it under the sun light. Move the lens until the sun light focus to smallest point. The distance from that point to the lens is approx FL.

BTW it's better if you use google or forum search engine before asking :).

Leonard Evens

1-May-2012, 09:15

There is the formula

f = u v /(u + v)

where u is the distance to the subject and v is the distance to the image. Unfortunately, you have to measure the distance u to the subject from the front principal point and the distance v to image along the rail from the rear principal point. You probably won't be able to figure out where the pricipal points are. But if you measure both distances from the front of the lensboard, that should be good enough for most normal lenses. It could yield a significant error, however, for a telphoto lens.

I'm not sure why you have to do this in your garden. Just go out on the street and use a building or some other object that is not too close. That may be sufficiently far away. Also, if you use two such objects and get essentially the same distance of the image along the rail, that is a check on whether you are close enough to infinity.

Jim Graves

1-May-2012, 09:20

Good question ... glad you posted it here ... I like jumanji's solution of using the sun ... that has never occurred to me even though it seems an obvious solution.

ghostcount

1-May-2012, 10:01

... If you want to check focal length at infinity, just put it under the sun light. Move the lens until the sun light focus to smallest point. The distance from that point to the lens is approx FL.

Ahhh... the ant burning method. :cool:

Steven Tribe

1-May-2012, 10:36

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.

Ahhh... the ant burning method. :cool:

Yep that's it! A funny game when I were a child. Summers came, I took a magnifying glass, went out and burned ant and waste paper :D.

If you want to check focal length at infinity, just put it under the sun light.

The OP is in London.

The sun may not be available. :D

- Leigh

Have a look at this link it will help.

http://www.giangrandi.ch/optics/lenses/focalcalc.html

Richard Rankin

1-May-2012, 19:32

John,

The focal lengths are marked on the edge of each element - 15, 25, 35cm, etc. On the sheet I had posted with that set, it gives the focal lengths for the various combinations, but each element alone is already marked. If you need a copy of the sheet, I can email it to you.

Cheers,Richard

Leonard Evens

2-May-2012, 06:49

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

2-May-2012, 08:03

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

3-May-2012, 04:43

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

3-May-2012, 09:48

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.

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

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