Magnifiers: a closer look (VIII)
Focal length measurements - continued

Okay, agreed, they are cute, our tardigrades. But, as most of our readers will have noticed anyway, we have a tendency to smuggle some serious information among the sentiments. When screening the literature about scientific magnifiers we noticed that many authors and collectors are not able to specify the actual magnification of the respective items. And in fact most magnifiers with ages of 100 and beyond are not bearing any inscription at all.

In the previous magazine issue we had demonstrated that in some cases the sun projection method might be sufficient in order to measure the focal length of folding magnifiers. This statement is valid if the precision requirement is moderate and the lens system easily accessible for measurement (i.e., not recessed or made up of a complex assembly of various lenses).

Nevertheless there exist some more advanced methods in order to measure the focal length. Those can serve as comfortable work-arounds when fighting the above-mentioned problems. In this issue we are going to present a more professional focal length measurement for magnifiers with low magnification. And in the July issue we will demonstrate a truly professional precision measurement method for complex and strong magnifiers - up to 30x and beyond!

Fig. 1: A so-called lensmeter or focimeter. The German language has a dedicated word for it (calling it "Scheitelbrechwertmesser") but we were not able to find an English equivalent. This type of instrument is mostly used by opticians in order to find out appropriate spectacle lenses for their customers. There are old fashioned, analogue and more modern digital versions, but basically the function and outcome are all the same: when a given lens is placed on the socket the optics can be adjusted to the respective lens by viewing through the big top eye-piece. Afterwards, the diopter value is indicated in a second, smaller viewing tube (in addition most of those instruments wil be able to deliver further informations for opticians, e.g. about the character of asymmetrical lenses, but we will skip this particular instrument capability here).

The measurement procedure is simple
(1) The object under investigation is mounted on the support and fixed by spring pins (see fig. 1).
(2) Then the black wheel at the base of the instrument is used to focus a control circle of tiny light points in the center of the eyepiece image (see fig. 2):

Fig. 2: View through the main (big) eyepiece, with the optics already focused for subsequent diopter value reading (in the secondary eyepiece).

(3) The diopter value can be read off a scale which is visible through a second, smaller viewing window on the backside of the instrument. In our example the diopter value viewing window is delivering a value of ca. +5.55 diopters (fig. 3).

Fig. 3: View through the smaller (diopter) eyepiece of the lensmeter. The mechanical (moving) scale has a slightly yellow tinge but it is still fit for the job.

The reciprocal value of the diopter number is delivering the focal length f = 1 [m] / diopter_value. In the case shown this is 1/5.55 = 0.18 m. On the basis of this value we can calculate the magnification V as 250 mm / 180 mm = 1.4. A magnification value of 1.4 is a clear indicator that the object under investigation (the one shown in fig. 1) is by no means a "scientific" magnifier but instead a reading aid for the elderly (long-sighted) people.

Techical hints for reliable results: most of those lensmeters are precision instruments. Nevertheless it is still possible to receive wrong values, e.g. when the eye-pieces are not properly adjusted. In order to play safe it is best to check the instrument by means of lenses with known diopter values. These can be easily acquired via internet. On this basis the diopter measurement and the subsequent focal length/magnification result precision can be as good as 1%.

But there is a strong drawback: most commercial lensmeter instruments are able to display values up to 25 diopters maxiumum, which is roughly equivalent to a 6x magnifier. For all stronger lenses we will need a different method which will be shown in the issue to follow.

© 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.

Main Page