Focal Length of Convertible Lens Combinations

[Keith Pitman]

Could someone supply the formula for the resulting focal lengths when elements o f convertible lenses are combined? I haven't been able to locate this informati on on this site or in articles I have available.

[pat krentz]

Try the Ron Wisner site. Pat

[Dave Willison]

You might try Kingslake's book on Lens Design or another text which covers lens design fundamentals. I believe that Edmunds Scientifics or Amazon will have something. In general, double convertible lenses increase in focal length as the front element is removed. Triple convertibles combine all three "cells" to produce the shortest focal length. The front cell (alone) yields the longest FL and the rear cell (alone) gives something in the middle. I hope this helps.

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[Sean Billy Bob Boy yates]

It's going to vary from manufacturer to manufacturer. As far as I am aware, there was no attempt to adhere to any precise uniform code.

Typically though, a lens sold as a triple would be "normal" (or slightly wide or long of normal for the format), combined, and then 1.5X ~ 1.75x and 1.8x ~ 2.25x coverted. Turner Reich sold two 8 X 10 lenses - a 12/21/28" and a 12/19.7/25" while Wollensak sold a 13/18/25" I believe.

Protars, Pantars, Vademcums, etc. were sold singly and in casket sets, or as pairs with a shutter, so you'd get quite a variety of combinations. There is often a bit of redundancy when you combine elements from different convertibles of the same series from the same manufacturer. In other words, I can combine the 19.7" with the 21" and get a 12.5" or the 25" & the 28" and get a 14".....

[Steve Grimes.]

You can use the diopter system of lens "power" to estimate this. I forget the formula for diopters but it runs: 1000mm =1 500mm=2, 250mm = 4, etc. This is a system used to reference the focal length (known as "power") of spectacle lenses. These add together in a simple fashion. For example, two one diopter lenses placed one over the other yield a two diopter system (500mm). This is put in practice when you wear two pairs of spectacles at the same time. Similarly, a plus 1 lens (1000mm) and plus 2 lens (500mm) combined yield a plus three (333mm focal length) system.

[N Dhananjay]

The formula for combining thin lenses is as follows.

1/f = 1/f1 + 1/f2 - d/f1f2

where f is the combined focal length, f1 and f2 are the focal lengths of the individual cells and d is the space between the cells. The problem is that we're mostly not dealing with thin lenses and things get more complicated. The formula, in my experience, gets you into the ballpark but never exactly there - its easier to just measure the focal length in use. Different manufacturers utilized different criteria in the design of convertibles and depending upon the designers intentions, you could have different constraints. Cheers, DJ.