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in such a way as to make the lens more convex, and thus bring into distinct focus objects which may be as close as eight or ten inches. This power of adjustment or accommodation, however, varies greatly in different individuals.

The iris, or colored part of the eye, is a diaphragm which varies the amount of light which is admitted to the retina (Figs. 428, (1) and (2)).

453. Nearsightedness and farsightedness. In a normal eye, provided the lens is relaxed and resting, parallel rays come to a focus on the retina (Fig. 429, (1)); in a nearsighted eye they focus in front of the retina (Fig. 429, (2)); and in a farsighted eye they reach the retina before coming to a focus (Fig. 429, (3)).

FIG. 429. Defects of vision

Those who are nearsighted can see distinctly only those objects which are near. The usual reason for nearsightedness is that the retina is too far from the lens. The diverging lens corrects this defect of vision because it makes the rays from a distant object enter the eye as if they had come from an object near by; that is, it partially counteracts the converging effect of the eye (Fig. 429 (2)).

Those who are farsighted cannot when the lens is relaxed see distinctly even a very distant object. The usual reason for farsightedness is that the eyeball is too short from lens to retina. The rays from near objects are converged, or focused, towards f behind the retina in spite of all effort at accommodation. A converging lens gives distinct vision because






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it supplements the converging effect of the eye (Fig. 429, (3)). In old age the lens loses its power of accommodation, that is, the ability to become more convex when looking at a near object; hence, in old age a normal eye requires the same sort of lens as is used in true farsightedness.


454. The apparent size of a body. The apparent size of a body depends simply upon the size of the image formed upon the retina by the lens of the eye, and hence upon the size of the visual angle pCq (Fig. 430). The size of this angle evidently increases as the object is brought nearer to the eye (see PCQ). Thus, the image formed on the retina when a man is 100 feet from the eye is in reality only one tenth as large as the image formed of the same man when he is but 10 feet away. We do not actually interpret the larger image as representing a larger man simply because we have been taught by lifelong experience to take account of the known distance of an object in forming our estimate of its actual size. To an infant who has not yet formed ideas of distance the man 10 feet away doubtless appears ten times as large as the man 100 feet away.


FIG. 430. The visual angle

455. Distance of most distinct vision. When we wish to examine an object minutely, we bring it as close to the eye as possible in order to increase the size of the image on the retina. But there is a limit to the size of the image which can be produced in this way; for when the object is brought nearer to the normal eye than about 10 inches, the curvature of the incident wave becomes so great that the eye lens is no longer able, without too much strain, to thicken sufficiently to bring the image into sharp focus upon the retina. Hence a person with normal eyes holds an object which he wishes to see as distinctly as possible at a distance of about 10 inches.

Although this so-called distance of most distinct vision varies somewhat with different people, for the sake of having a standard of comparison in the determination of the magnifying powers of optical instruments some exact distance had to be chosen. The distance so chosen is 10 inches, or 25 centimeters.

456. Magnifying power of a convex lens. If a convex lens is placed immediately before the eye, the object may be brought much closer than 25 centimeters without loss of distinctness, for the curvature of the wave is partly or even wholly overcome by the lens before the light enters the eye.

If we wish to use a lens as a magnifying glass to the best advantage, we place the eye as close to it as we can, so as to gather as large a cone of rays as possible, and then place the object at a distance from the lens equal to its focal length, so that the waves after passing through it are plane. They are then focused by the eye with the least possible effort. The visual angle in such a case is PeQ (Fig. 431,(1)); for, since the emergent waves are plane, the rays which pass through the center of the eye from P and Q are parallel to the lines through Pe and Qe. But if the lens were not present, and if the object were 25 centimeters from the eye, the visual angle would be the small angle pcq (Fig. 431, (2)). The magnifying power of a simple lens is due, therefore, to the fact that by its use an object can be viewed distinctly when held closer to the eye than is otherwise possible. This condition gives a visual angle that increases the size of the image on the retina.







FIG. 431. Magnifying power of a lens

The less the focal length of the lens, the nearer to it may the object be placed, and therefore the greater the visual angle, or magnifying power.

The ratio of the two angles PeQ and pcq is approximately 25/f, where ƒ is the focal length of the lens expressed in centimeters. Now the magnifying power of a lens or microscope is defined as the ratio of the angle actually subtended by the image when viewed through the instrument, to the angle subtended by the object when viewed with the unaided eye at a distance of 25 centimeters. Therefore the magnifying power of a simple lens is 25/f. Thus, if a lens has a focal length of 2.5 centimeters, it produces a magnification of 10 diameters when the object is placed at its principal focus. If the lens has a focal length of 1 centimeter, its magnifying power is 25, etc.

457. Magnifying power of an astronomical telescope. In the astronomical telescope the objective, or forward lens, forms at its principal focus an image P'Q' of an object PQ which is usually very distant. This image





FIG. 432. The magnifying power of a telescope objective is F/25

may be viewed by the unaided eye at a distance of 25 cm. (Fig. 432). The focal length of the objective is usually very much longer than 25 cm. (about 2000 cm. in the case of the great Yerkes telescope shown opposite p. 365), so that the visual angle P'EQ' is increased by means of the objective alone, the increase being F/25*, that is, in direct proportion to its focal length.

In practice, however, the image is not viewed with the unaided eye, but with a simple magnifying glass called an eyepiece (Fig. 433), placed so that the image is at its focus. Since we have seen in § 456 that the simple magnifying glass increases the visual angle 25/ƒ times, ƒ being the focal length of the eyepiece, it is clear that the total magnification

*The angle PoQ = angle P'oQ. Consider the short line Q'P' as an arc, and the angles Q'EP' and Q'oP' are inversely proportional to their radii, F and 25.

produced by both lenses, used as above, is F/25 × 25/f=F/f. The magnifying power of an astronomical telescope is therefore the focal length of the objective divided by the focal length of the eyepiece. It will be seen, therefore, that to get a high magnifying power

it is necessary to use an objec- ToP tive of as great To Q focal length as possible and an eyepiece of as short focal length as possible. The focal length of the great lens at the Yerkes Observatory is about 62 feet, and its diameter 40 inches. The great diameter enables it to collect a very large amount of light, which makes celestial objects more plainly visible.


FIG. 433. The magnifying power of a telescope is F/f

Eyepieces often have focal lengths as small as inch. Thus, the Yerkes telescope, when used with a 4-inch eyepiece, has a magnifying power of 2976.



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458. The magnifying power of the compound microscope. The compound microscope is like the telescope in that the front lens, or objective, forms a real image of the object at the focus of the eyepiece. The size of the image P'Q' (Fig. 434) formed by the objective is as many times the size of the object PQ as v, the distance from the objective to the image, is times u, the distance from the objective to the object (see § 441). Since the eyepiece magnifies this image 25/ƒtimes, the total magnifying power of a compound microscope is " Ordinarily v u f is practically the length L of the micro


scope tube, and u is the focal length F of the objective. Wherever this is the case, then, the magnifying power of the compound microscope is

25 L





FIG. 434. The compound microscope

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