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ent points in the object mix with each other on the receiving screen ; much more, then, would rays from contiguous points of the object mix. In such a case the mixing is so great that no recognizable image is formed at all. As the hole becomes smaller, the circles of dispersion, a' b' c', become sinaller in the same proportion; and, therefore, the light from different points of the object is more and more separated on the receiving

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screen, and the image becomes first recognizable, then more and more distinct. But, in the mean time, the quantity of light is becoming less and less, and therefore the image fainter and fainter. If we suppose the hole to become a mathematical point, then one ray only passes from each point to the object, and goes to its own place in the image (Fig. 6, B), and the conditions of distinctness are fulfilled ; but the image is now infinitely faint, and therefore invisible. If, now, we try to increase the brightness by increasing the size of the hole, in proportion as we get brightness do we lose distinctness. We can not get both at the same time.


Experiment.Let a room with solid shutters be darkened ; let one shutter have a hole of a few inches in diameter; cover the hole with an opaque plate of sheet iron, in which there is a very small hole one tenth to one twentieth of an inch in diameter. If, now, a sheet of white paper be held a little way from the small hole, an inverted image of the external landscape

will be seen on the sheet. If we increase the size of the hole, the image will be brighter, but also more blurred.

Illustrations.—Many simple experiments may be made illustrating this principle. A pinhole in a card will make an inverted image of a candle flame. When the sun is in eclipse, it may be examined without smoked glass, by simply allowing it to shine through a pinhole in a card upon a suitable screen. In the shade of

very thick tree-top the sun-flecks are circular like the sun; but during an eclipse they are crescentic, or even annular, according to the de?ree of obscuration. They are always images of the sun. Such an image may be called a pinhole image.

This principle is utilized in some animals. In the nautilus, e. g., the eye is a mere empty hollow lined with the retina, and opening in front by a small hole which forms a pinhole image in the retina.

Property of a Lens. — Now a lens has the remarkable property of accomplishing both these apparently opposite ends, viz., brightness and distinctness at the same time. If an object, a c, be placed before a lens, L (Fig. 7), of suitable shape, then all the rays diverging from any point, b, are bent so as to come together again at the point b'. Of the divergent pencil, b L L, the central ray passes straight through without deviation ; rays a little way from the central are bent a little; rays farther

away are bent more and more according to their angle of divergence, so that they all meet at the same point, b'. Similarly all the rays proceeding from a, and falling on the lens, are brought to the same point, a', and from c to the point c', and so also for every intermediate point. Thus an image is fornied which is both bright and very distinct if the receiving screen is suitably

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placed—i. e., at the exact place where the rays meet. The billions of rays from millions of points of the surface of the object are, as it were, sifted out by the law of refraction, and each safely conveyed to its own point in the image ; so that for every radiant point of the object there is a corresponding focal point in the image. But it is evident that the screen must be suitably placed, for if it be placed too near, at S' S, the rays have not yet come together; if too far, at S" S", the rays have already met, crossed, and again diverged. In both cases the image will be blurred.

Observe: 1. The image is inverted. It must be so, because the central rays of all the pencils cross at a certain point in the lens. This is called the nodal point. 2. The place of the receiving screen must be exactly at the focal point. 3. The size of the image will be to the size of the object as their relative distances from the nodal point. 4. As the object moves farther away, the image comes nearer to the lens and becomes smaller. 5. It is not every lens that will make a perfect image. The lens must be of suitable shape.

Application to the Eye.In all dioptric instruments images are formed in this way. It is in this way that images are formed in the eye. In Fig. 8 it is seen that the diverging pencils, from points A and B of the object,

FIG. 8.




ab, the image ; rr, retina of the normal eye.

which enter the pupil, are refracted by the lenses of the eye, and if the eye be normal, brought to a focus on the retinal screen at a b. Now, since the rays from every intermediate point of the object will be similarly focused, we will have a perfect image of the object painted on the retina. In the same figure p q shows the position of the retina in the myopic and p" go" in the hyperopic eye. Of these defects we will speak more fully hereafter.

The fundamental fact of the existence of the retinal image may be proved in many ways by observations on the dead eye : 1. If the eye of an ox be taken from the socket and the sclerotic carefully removed, so that the back parts of the eye are somewhat transparent, a miniature image of the landscape may be seen there; or, 2. If we remove the eyeball of a white rabbit, we will find that, on account of the al sence of black pigment in the choroid of these albinos, the transparency of the coats of the eye enables us to see the image, even through the sclerotic, or much more distinctly if the sclerotic be removed; or, 3. We may remove all the coats of the dead eye and replace them by a film of mica—the image will be very distinct; or, 4. The image may be seen in the living eye by means of the ophthalmoscope.

By reference to the diagram, Fig. 8, it is seen that the central rays from all radiants cross each other in the lens. This point of ray-crossing is called the nodal point. It is a little behind the center of the lens, and about 0:6 inch (15 mm.) in front of the retina. The size of the retinal image is as much smaller than the object as the former is nearer to the nodal point than the latter, and therefore for distant objects it must be extremely minute.

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