Determining aperture of antique brass lens?

[BrianShaw]

“I would think that this issue of equivilant aperature determination had come up before.“

It has. It is a rather well-understood situation. Have you checked out the comparison table?. It’s old but. For me at least, accurate enough.

Just because it’s old is no reason to think that there can’t be trust. .

But I’m with you on “trust but verify”. I verify by looking at negatives (or Polaroids back in the olden days) rather than calculating and extensive testing.

[Drew Bedo]

Steven: Sounds good. But I am confused about x/y . . .which is which?

If: GG measurement of the known focal length is...………………….M1
` The marked focal length of the known lens in mm is...………...f1
GG measurement of the unknown focal length is...………………..M2
The actual focal length of the unknown lens in mm is …………...f2

Then the equation would be............................................……...f2=f1(M1/M2)

Do I have that right?


Drat! I cannot get everything yto line up nicely.

[Steven Tribe]

Correct!

You talk about GG, but it is far easier to compare known and unknown focal lengths by keeping the lenses away from flanges, lens boards and cameras!

Just go to an interior wall ( white or light wood) - in a place that will not attact attention to other members of the household! Point lens #1 towards a well lit window. Adjust distance to wall to "engage" focus - make one pencil mark with one hand, and then another when the focus is stable again. It is fair easier to do this than with the height of the nearest tower/chimney because of the light/darkness transition around the edge of the window frame.

I suppose the dedicated nerd could mount a kind of "trophy board/kids growth through the years" board, recording previous measurements and removing the need for new focal length bench marks everytime an "unknown" lens arrives in the post!

[Emmanuel BIGLER]

Hello from France!

The method proposed by Steven Tribe is one of the best and simplest, provided that you know the real focal length of the reference lens, and will allow you with a simple ruler to determine the unknown focal length within an accuracy of a few percent.

However may I dare to propose another method, probably less precise, but which does not require any other reference lens. And of course, like Steven's method, which does not require to know where the principal or nodal points of the lens are located. You only need a large format camera, a wooden stick, some gaffer-tape, a table, a piece of paper and a pencil

The method is based on the fundamental relationship between the focal length "f" and the image displacement "y" (for a far-distant object) on the ground glass when you rotate the whole camera by an angle "theta".

The formula is : y = f tan(theta) when starting from an image centered on the optical axis of the lens, i.e. in the middle of the ground glass with all shifts zeroed.

Now assume that we rotate only with a small angle, less than 10 degrees, tan(theta) can be approximated by theta (in radians) or approx. theta/57 in degrees. And with small angles we do not need to measure from the center of the ground glass, we simply measure the whole displacement of the image across the ground glass, provided of course that during the rotation, our reference object (a distant spire, a distant electric pole etc) projects an image staying within the limits of the ground glass.

Find a wooden stick, about one meter (20") long. Firmly attach one end of the stick to the tripod head, just under the camera and above the panoramic movement, so that the stick will rotate exactly like the whole camera. Support the other end of the stick on a table, this requires to set the tripod to the proper height. When the camera rotates, the end of the stick will move on the table. Tape a piece of paper underneath and measure the displacement of the end of the stick for a given displacement of the image on the ground glass.

Let, for example, the image move by 50 mm (one inch) on tr ground glass.
If the unknown focal length is one meter, like the wooden stick, the end of the wooden stick will move by 50 mm when the image moves by 50 mm.
If the unknown focal length is 500 mm, the end of the wooden stick will move by 2x50 = 100 mm
If the unknown focal length is 250 mm, the end of the wooden stick will move by 4x50 = 200 mm

In general, for a displacement "d" at the end of a one meter long stick (20"), and for a displacement of the image of 50 mm (1") on the ground glass, the focal length of the unknown lens is simply
f (in mm) = 50x1000 / (d in mm).

For example, if the focal length is 300 mm, the displacement "d" will be 50 x 1000 / 300 = 167 mm.

I like very much this way of defining the focal length, because it is totally independent from the actual lens design, you do not have to care for the rear nodal or principal plane H', located one focal length ahead of the focal point. But on an antique brass lens, the location of H' is never engraved and if it is a telephoto design, H' will probably float somewhere in air in front of the lens!

It is important that the reference object is located as far as possible from the camera, but if this condition is respected, you can rotate the camera around any rotation point, the displacement of the image will be the same for a given focal length.



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This for finding the value of the focal length.

Now regarding the f-number "N", it is defined with reference to the diameter "a" of the entrance pupil, not the actual size of the iris.

N = f/a

You can measure the diameter "a" of the entrance pupil by illuminating the lens backward, with a small flash light located on the optical axis, at the focal point. Focus the lens at infinity with the ground glass, remove the ground glass and try fix the small flashlight at the center of the ground glass, without the ground glass.
In front of the lens you'll see a beam of light, intercept this beam with a piece of paper, placing it as close as you can from the first lens element. You'll see a parallel projection of the iris, its size is the size of the entrance pupil. This size can be significantly bigger than the physical diameter of the iris, but now you do not care for the physical iris, since you got the right measurement!
If the iris is not perfectly circular, estimate approximately the diameter, no precision is required here, you are allowed an error of about 10% on the measurement of the diameter of the entrance pupil !

Have fun!

[David Lobato]

Hey Drew, good luck with your lens. Keep us posted.