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magnifying glass

, magnifier
a convex lens used to produce an enlarged image of an object



an optical instrument for examining small objects not readily discernible by the naked eye. The object being observed is positioned slightly less than a focal length away from the magnifier. Under these conditions a magnifier provides an upright, magnified virtual optical image of the object. After passing through the magnifier, the rays from the object are again refracted in the eye and are collected at its most remote point. They enter the eye at an angle greater than do the rays from the object without a magnifier; this is the reason for the magnifying effect (see Figure 1).

Figure 1. Path of rays when viewing a small object / in a magnifier L The object is positioned in the immediate vicinity of the focal plane OO1, of the magnifier. The rays coming from point S of the object are collected at point S” on the retina of the eye. The rays from point S″ would also be collected at point S” if there were no magnifier (point S’ is the’virtual image of point S).

The magnification M is defined as the ratio of the angle α at which the virtual image of the object is seen from the center of the eye’s pupil to the angle at which the same object is seen without the magnifier at the distance of distinct vision D (Figure 2; for the normal human eye, D == 0.25 m). The magnification depends on the focal length f’ of the magnifier (usually expressed in millimeters) according to the ratio M = 250/f; the value of M may range from 2 to 40 or 50, depending on the design of the magnifier.

Figure 2. Observation of a small object /. (a) With naked eye at the distance of distinct vision D; 0 is aperture angle of rays from the object that enter the eye. (b) Through a magnifier; rays from the object enter the eye at an angle a > <£; d is the distance from the magnifier to the object, d’ is the distance from the magnifier to the image it forms of the object as seen by an observer.

The simplest magnifiers are converging lenses; their magnification is usually low (about 2-3 X). Two-lens and three-lens systems (Figure 3) are used for magnifications of 4-10 X. The field of view of the images in space for magnifiers having low and medium magnification does not exceed 15°-20°. The design of magnifiers having high values of M is similar to that of complicated eyepieces; their field of view reaches an angle of 80°-100°.

Figure 3. Magnifiers: (a) “twin” lenses, (b) aplanatic

Figure 4. Telescopic magnifier

In a magnifier with high magnification the distance from the object to the surface of the magnifier is very short. This drawback is avoided in telescopic magnifiers (Figure 4), which are capable of observing remote objects with M ~ 2.5 and nearby objects with M ~ 6. Binocular (stereoscopic) magnifiers, a diagram of which is shown in Figure 5, are also in use.

Figure 5. Stereoscopic magnifier consisting of prismatic achromatic lenses combined with low-power binoculars

Magnifiers are also used to measure linear dimensions. The object to be measured is brought into coincidence with a flat glass or metal scale placed in front of the focal plane of the measuring magnifier (in practical terms it is in the plane). The images of the object and the scale are compared. The magnification of a measuring magnifier is usually 4-16X; the focal length, 10-40 mm; and the scale divisions, 0.1 mm. Such magnifiers are used to measure the width and length of letters and scratches and the distance between points.


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