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Magnifiers: a closer look (VII)
Focal length measurements - beginning with the basics

As has been shown in the previous issue, nowadays commercial magnifier inscriptions needn't be correct, some might even be considered as fraudulent. Furthermore, there are many older instruments with no inscriptions at all. So, at least from a collector's point of view, it might be worth while to perform own comparisons and measurements. We will start with some simple concepts and methods in this issue and continue with focal length (= magnification) precision measurements in the issues to come.

Lenses and simple magnifiers with low to medium magnification power are easy-going objects (fig. 1): sunlight can be directed on the respective lens and the outcoming light focused on a white wall. The distance between the center of the lens an the resulting tiny, condensed light circle spot can be easily measured. This distance is called the focal distance and designated by a small letter f. By definition the magnifying power V is calculated by division of the standardized shortest human eye close-focus distance (arbitrarily defined as 250 mm) through the measured focal length (again in [mm]):

     V = 250mm / f

Easy. But be warned that any lens tested by this method is acting as a burning glass as well! So don't let the experiment go on by its own and walk for a pause in the nearby cafeteria!

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Abb. 1: The most simple focal length measurement method. Here sunlight is directed through a no-name "10x" magnifier by means of a mirror and concentrated on a white material (not an inflammable white paper!). The millimeter paper on the bottom of the setup comes in handy in order to measure the distance between the approximate center of the magnifier lens and the wall: 25 mm. When inserting this value in the above formula we can calculate the magnification power value V to be 250 mm / 25 mm = 10. So we can conclude that the inscription on this magnifier housing is fully correct.

Problems are beginning to arise at the moment when we plan to investigate stronger magnifiers and combined magnifier systems (made up of several lenses): now the smaller focal length distance is more difficult to assess. Moreover, the exact starting point of our measurement is hidden somewhere in the inner "soul" of the instrument, adding one more uncertainty to our analysis.

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Fig. 2: Measurement of the focal length of a very old brass and tortoise shell, two lens folding magnifier (bearing no inscription). In this case the measurement is still appearing to deliver a reasonable result: we measured ca. 10 to 11 mm focal length. This is indicating a true and very impressive, ca. 23x to 25x magnifying power!

Nevertheless there are limits: e.g. a "Coddington" type magnifier (like the one shown in our previous issue) with meager three millimeters working distance and a recessed lens mount will already range beyond the limits of our direct sunlight method.

But be consoled - we are not alone with those limits. The following scientific anecdote might help to illuminate the risks of measuring any of those subtle optical properties: the so-called "Utrecht lens" microscope, made by the famous amateur Antoni van Leeuwenhoek centuries ago, is housing an extremely tiny lens (1.3 mm in diameter). Due to understandable handling restrictions it was strictly forbidden to dismantle the precious instrument in order to investigate this lens directly. Only non-destructive tests (NDT) were permitted. As a consequence this instrument marked a particular challenge for optical analysts.

A reknowned Dutch specialist, Jan van Zuylen (see link below), had developped a dedicated and sophisticated method in order to measure the optical properties of the Utrecht lens. In 1981 he published his results with the conclusion that the Utrecht lens was aspherical, probably produced by a complicated glass-blowing variant. This finding contributed to the enormous fame of Antoni van Leeuwenhoek, adding a first "aspheric" to his long list of achievements.

But as time and technoloy went on, a modern NDT method came up: the so-called neutron tomography was able to prove by means of direct image that the Utrecht lens is in fact a rather primitive, normal though tiny globular glass sphere. This interpretation was corroborated by the fact, that a small glass stem fragment became visible on one side of the sphere. This stem can easily be explained as the typical trace of the most easy-going micro glass lens production method: melting the end of a slim glass stick in a flame until it is forming a glass sphere. This method is described in the respective and impressive experimental work by a German Leeuwenhoek specialist and microscope collector [Klaus Meyer 1991].

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Fig. 3: Small glass spheres, produced by melting the end of a slim glass stick [product and courtesy of Klaus Meyer]. An almost ideal spherical geometry and remains of the glass sticks are visible in the photograph. Obviously, those glass stick fragments are clear indicators of the production method that was used.

All this is not described in order to diminish the tremendous merits of Jan van Zuylen. Instead it is intended as a warning that one should never run to quick conclusions when investigating historic optical instruments!

Internet sources and literature

Tiemen Cocquyt, Zhou Zhou, Jeroen Plomp, Lambert Eijck (2021). Neutron tomography of Van Leeuwenhoek’s microscopes. Science Advances. 7. eabf2402. 10.1126/sciadv.abf2402. https://www.science.org/doi/10.1126/sciadv.abf2402

Klaus Meyer: Die Geheimnisse des Antoni van Leeuwenhoek. Lengerich 1998.
ISBN 3-931660-89-3.

Jan van Zuylen: The Microscopes of Antoni van Leeuwenhoek.
Journal of Microscopy 121 (1981) 309-328.

Further background literature about Antoni van Leeuwenhoek and his microscopes

Brian J. Ford: Single lens. The Story of the Simple Microscope. New York 1985.
ISBN 0-06-015366-0.

© Text, images and video clips by  Martin Mach  (webmaster@baertierchen.de).
The Water Bear web base is a licensed and revised version of the German language monthly magazine  Bärtierchen-Journal . Style and grammar amendments by native speakers are warmly welcomed.

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