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Basic facts about magnifying glasses by Dr Zyun Koana Professor of Optics, Sophia University Professor Emeritus, the University of Tokyo

Select the magnifying power to suit your purpose

A magnifier or magnifier glass, also called a loupe, is a lens or a lens-system that can form a magnified virtual image of an object. When a magnifier is placed between the object and the observer’s eye, the observer can inspect fine details of the object by viewing the magnified image of it. Magnifiers of various “magnifying power” are manufactured according to the purpose for which they are used. The same object can be seen in larger scale by a magnifier of higher magnifying power. However, magnifiers with higher magnifying power have the shortcomings of a smaller image field and a shorter working distance (i.e. the distance between the object under inspection and the magnifier); the latter effect makes their use less convenient. The magnifier with a magnifying power of 2x to 3x is usually a single convex lens, relatively low in cost; those with high magnifying power are composed of 2 to 5 pieces of convex and concave lenses made of different kinds of optical glasses in accordance with elaborate optical design for the correction of aberrations, and so are more expensive.

For reading documents with smaller letters, magnifiers of 2x to 3x magnifying power, consequently with wider image field, are suitable. Those with 5x to 7x magnifying power are most adequate for daily desk use. For the inspection of very fine details, magnifying power of 10x to 15x is recommended. However, if you tried to read a newspaper with a 10x magnifying power magnifier, you would have to move the magnifier along each letter because of the small image field, with the result that you would be unable to catch the import of the sentences. Therefore you should select a magnifier with an magnifying power that suits your purpose, and to realize that expensive magnifiers with high magnifying power are by no means universally usable. This is the first basic point about selecting magnifiers.

Observation with a magnifying power of 20x or more is usually accomplished by a compound microscope, which is composed of an objective lens and an eye-piece separated by a definite distance. The objective lens forms a magnified but inverted real image of the object under inspection, and the eye-piece, which is a special kind of magnifier, further magnifies the real image. Thus the compound microscope can be compared to a two- step amplifier, wheras a magnifier is considered as a single-step one. Hence the former can have a very high magnifying power, such as 100x to 1000x; and when used at low magnifying power of 20x to 30x, it has a wider image field and a longer working distance than a magnifier with the same magnifying power

The compound microscope does however have some disadvantages; it is massive and expensive, the object under inspection must be placed on its stage, and the observed magnified image is inverted. Here one sees the advantage of having 20x to 30x magnifiers, which make possible the observation of the erect (i.e. not inverted) image of each part of a large object that cannot be laid on the microscope stage. Such magnifiers are indispen- sable, for instance, in photo-mechanical processes. These high magnifying power magnifiers, however, have a very short working distance, and further, the opti- cal axis of the observer’s eye must coincide correctly with that of the magnifier. This latter condition requires some experience on the part of the user, and incorrect use of these magnifiers prevents the user from taking full advantage of their performance. It should be emphasized again that one should carefully select the magnifying power of magnifiers, now available from about 2x to 30x.

Magnifying power changes with conditions of use

Hithero the term magnifying power has been used without precise explanation. It is different from the “mag- nification” of the image, i.e. the physical quantity defined as the ratio of the lateral length of the image of a small object itself. The magnifying power refers to the combination of a magnifier (or a compound microscope) and an observing eye. It is defined as the ratio of the view angle of the magnified virtual image of a small object to that of the same object viewed with the naked eye at 250 mm (ca. 10”) distance from it, which is approxi- mately equal to the ratio of the length of the image formed on the retina of the eye in each respective case. Thus if the magnifying power of a magnifier is 7x, the lateral length of the image viewed through it is 7 times that one of the same object seen with the naked eye at a distance of 250 mm. In this case, the area is magnified about 72 or 49 times.

The magnifying power of a magnifier is not a constant, but varies continuously within a certain range with changes in distance between the magnifier and the eye, as well as with changes in the working distance. So its value is indefinite as long as the condition of use is not specified. The value of the magnifying power of a magnifier engraved on its barrel or listed in catalogues is the so-called „normal magnifying power“, which is the magnifying power under the condition that the object under inspec- tion ist placed on the „focal plane in the object space“ of the magnifier. In this case, the rays of light emitted from each point of the object become parallel with each other after passing through the magnifier, as is shown in Fig. 1, and hence the virtual image of the object is formed at infinite distance from the eye with an infinetely large length. Hence the value of the „magnification“ of the image is infinite, but the magnifying power in this case, or the normal magnifying power of the magnifier takes a finite value, and is given exactly by the formula

normal magnifying power = 250 (mm)/focal length (mm) of magnifier

being independent of the distance between the magnifier and the eye. From the formula it is easily calculated that a magnifier with a 25 mm focal length has a normal magnifying power of 10x, and one with a 50 mm focal length has 5x normal magnifying power It can be seen also that the normal magnifying power of a „weak“ magnifier with a 250 mm focal length is 1.0x, meaning that no benefit can be obtained by using such a magnifier. Furthermore, a weaker one with a 300 mm focal length has a normal magnifying power of 0.83x, which means that the size of the virtual image viewed through it is smaller than that of the objekt viewed with the naked eye at a distance of 250 mm! These results are absolutely correct so far as the „normal magnifying power“ is concerned.

The „normal using condition“ described above, however, is by no means recommended in using ordinary magnifiers. The most efficient method is to bring the eye as close as possible to the magnifier, and adjust the distance between the object and the magnifier so that the virtual image ist formed at a 250 mm distance from the eye as shown in Fig. 2. If the eye is brought in contact with the magnfier, or more strictly speaking, if the „nodal point in the object space“ of the eye is made coincident with the „nodal point in the image space“ of the magnifier, and the virtual image is formed at the position stated above, then the magnifying power takes a maximum value magnifying powermax given by the following formula

magnifying powermax = 1 + normal magnifying power

It may usually be impossible to realize this condition exactly, but the nearer the eye is brought to the magni- fier, the more closely the magnifying power takes a value given by the above formula. Hence the magnifying power of a 300 mm magnifier will be approximately (1 + 0.83) or 1.83x, and that one of a 250 mm one will be about (1 + 1.0) or 2x. This means that the magnifying power of a magnifier is always greater than 1x, however weak it may be, as long as it is used under the condition stated above. The medium power magnifier with a normal magnifying power of 5x or 7x can also have a magnifying power of nearly 6x or 8x respectively if used under the above condition. To realize this condition, hold the magnifier with one hand and keep it as close as possible to your eye, while adjusting the position of the object under in- spection with the other hand until the magnified virtual image can be observed sharply. This is the second basic point about using magnifiers.

Special magnifiers for special purposes

Several kinds of special magnifiers have been manufactured for special purposes, with the same value of nor- mal magnifying power as ordinary ones but with some unusual features. For instance the „Anastigmatic Loupe 4x“ with a very wide and flat image field is suited for inspecting fine details of 35 mm size microfilm negatives or for viewing color slides, without having to move of the object or the magnifier. The „Telecentric Loupe 7x“ fitted with a glass scale can be used to read accurately the deflected position of a meter needle that moves in a plane slightly different from that of the ruled scale. The „Retrofocus Loupe 7x“, because of its very long working distance, allows one to inspect the bottom of a small and deep hole, or to observe the fine structure of electrodes in a vacuum tube from outside the bulb. At present, however, only one or two kinds of magnifying power are available in such special magnifiers. If you want a special magnifier with a different magnifying power, the manufacturer can design and make it to your specifications, but the cost will be extraordinarily great due to a lot of mental labor and time required in the optical design. The fact is common in every order-made optical instrument, and the only way of reducing the cost is to order a large number of the same product by gathering the demand of persons equally interested in using it. This is the third basic point about ordering special magnifiers.