Measuring the objective focal length (1 Viewer)

[jcbouget]

For those who are interested in optics, here is a rather accurate method for measuring the focal length of the objectives in binoculars with an external focusing mechanism.

The useful formula is : 1/F = 1/D1 + 1/D2
F is the objective focal length
D1 is the minimum focus distance
D2 is the corresponding focal length. One can write D2 = F + X, where X is the travel of the eyepiece between infinity and focusing at a distance D1.

First, I focus the binocular at a very distant object, several kilometres away. In order to make a precise measurement, I use a 5x monocular behind the eyepiece. This avoids the accommodation of the eye, which would lower the accuracy of the method. The monocular is focused at infinity beforehand. When it is done, I measure the position of the eyepiece relative to the prism housing with a calliper rule.
Then I pull back the eyepiece at maximum, and I measure again the position of the eyepiece. The difference is X.
Of course I also measure D1 when the eyepiece is completely pulled back : this is the distance between the objective and the location of best sharpness. Again I use the monocular behind the eyepiece to get a very precise measurement.

Then it is possible to find F by resolving the equation : 1/F = 1/D1 + 1/(F + X)

My estimation of the accuracy is about 3%.

Here are some results :
Nikon 12x50 SE: 187 mm
Zeiss 15x60 BGAT : 194 mm
Fujinon 16x70 FMT SX2 : 267 mm

Jean-Charles

 

[ronh]

Jean Charles,
That is a good idea. Thank you for sharing it.

But I find your choice of words a little confusing. This is the result of mixing popular binocular terminology with firm optical concepts. I have no problems with F, but I think it may clarify matters to say:

D1 is the "object distance", the distance from the lens to the object being viewed. (The shortest D1 of which an instrument is capable is commonly called minimum focus, but that is ambiguous with the fact that focus is something that occurs behind the lens.)

D2 is the "image distance", the distance from the lens to where the image is focused. (This distance varies with object distance, and could be called a focal distance, but that is ambiguous with "focal length".)

So by measuring the travel of the eyepiece at the settings for the closest object and an object at infinity, the objective focal length is obtained. I hope this does more good than harm, and does not detract from your idea. At least, it explains it to myself!

Once again, the 15x60 Zeiss amazes us, this time with its very fast focal ratio. It might very well be an ED triplet, don't you think?
Ron

 

[elkcub]

Jean-Charles,

Have you cross-validated the method against direct measurement of an objective from one of your Porros?

Regards,
Ed

 

[jcbouget]

Ed, I have cross-validated the method with a Meade 10x50. It’s a wonderful lab instrument, because I can take it apart without fear. If something goes wrong, I lose only 20 € !
In fact, measuring directly the focal length of the objective is not easy, because the objective lens remains in its conic barrel, and there is an uncertainty about the point from which the focal length must be measured. So I think that the indirect method is more accurate.


Ron, your clarifications are welcome. I can’t edit my post any more, but I agree that your definitions for D1 and D2 are the right ones.

I can count four reflections on the objective of the Zeiss 15x60, so it’s an air spaced doublet. I asked Zeiss some details about these objectives, but they are not willing to give any technical information, even for discontinued models.

Jean-Charles