directions from every point of the bright object O. Of this, This only a small pencil passes through the aperture A. pencil produces upon the screen a small patch of light which is the image of the corresponding point of the object. Thus in the figure pencils of light pass in the direction of the dotted lines from the head and tail of the arrow and produce images at points on the screen. From points intermediate between the head and tail of O pencils of light proceed which produce images at corresponding intermediate points on the screen. Thus a complete image I is formed. It is also clear that whereas O is an arrow with its head down, I is an arrow with its head up. The image is an inverted one. Its size is directly proportional to the distance of the screen from the aperture. In the figure it is about the same size as the object. If the screen is brought nearer to the aperture the image becomes smaller; and if the screen is moved farther off it becomes larger. The images thus produced exhibit the natural colours of the objects, but are very faint, because the amount of light that can pass through a small hole is itself small. By making the hole larger a brighter image can be obtained, but it becomes blurred and indistinct at the same time. EXPT. 3.-Remove the condensing lenses of a lantern and cover the front with a tin-foil cap. Make a pin-hole in this and place a paper screen in front. A faint image of the gas-flame (or other radiant in the lantern) is formed on the screen. Make other pin-holes near the first; each one produces a fresh image, but the images soon overlap and become confused. The same effect is produced by making one large hole. EXPT. 4.-Make two tubes (A and B, Fig. 4) by wrapping pasted paper round a wooden cylinder. Blacken the insides with lamp black varnish (p. 99) or line with n B Fig. 4. middle of the foil. Cover the end of the other with tissue - paper. You have now a 'pin-hole camera,' which you can point towards a flame or bright object. The image can be seen by looking at the tissue-paper (n). It becomes larger and fainter as the tube B is drawn out. EXPT. 5. For class demonstration the following is a good way of showing images produced by small apertures, Punch a clean hole (about 2 mm. diameter) in a large sheet of tin-plate or card-board and clamp this in a vertical position. On one side of place a white screen and on the other side three candles arranged thus-.. It is then easily seen that the images occupy this relative position . and that the distance between increases as the screen is moved away from the hole. 6. Shadows and Eclipses.-The formation of shadows is a direct consequence of the propagation of light in straight lines. When the source of light is a single bright point (S, Fig. 5) the form of the shadow thrown by any opaque object K is S K Fig. 5.-SHADOW CONE. easily seen. For the cone of light which proceeds from S to K is stopped by the latter, and the portion of this diverging cone which lies on the farther side of K is all in shadow. Sharp, well-defined shadows of this kind are thrown by electric lights (arc lights). But when the source of light is of considerable size there is B m Fig. 6.-UMBRAL AND PENUMBRAL CONES. produced, in addition to this total shadow or umbra, a half shadow or partial shadow called the penumbra. Suppose A (Fig. 6) to represent the globe of a lamp and B an opaque obstacle, such as a ball or orange. Then it will be seen from the figure that the black cone is. completely in shadow and receives no light from any part of A; this may be called the umbral cone. The shaded cone which diverges from a point between A and B is only partly in shadow, and may be called the penumbral cone. Every point in it receives light from some portion of the illuminating surface A. When a screen is placed behind B the shadow thrown upon it consists of a central umbra surrounded by a penumbra. The size of the latter increases as the screen is moved farther away from B; when the screen is in the position mn the shadow appears somewhat as shown in Fig. 7. The penumbra, however, is not of uniform depth all over. Its edge is not sharply defined: it gradually deepens from the outside inwards until it merges into the complete shadow of the umbra. Fig. 7. Fig. 6 also illustrates the way in which eclipses of the sun are produced when the moon comes between it and our earth. Suppose A to represent the sun, B the moon, and the screen mn a portion of the earth's surface. Within the umbral cone no part of the sun is visible; therefore to an observer stationed on any part of the earth within the umbra the sun will appear totally eclipsed. Within the penumbra a part of the sun is visible and the rest invisible, so that an observer stationed anywhere within the penumbra will see the sun partially eclipsed. EXPT. 6. The student should examine for himself the different kinds of shadows above described. For sharp shadows produced by luminous points use a lantern: remove the condensers and fit on a cap in which a small round hole has been pierced. Or, since the breadth of the penumbra increases with the distance from the object, any fairly small source of light (candle) will cast a sharp shadow on a screen placed near it. Farther off the shadow shows a penumbra. Hold a pencil upright between a flat fish-tail burner and a wall. Examine the shadow. When the flame is 'edge on' the shadow is sharp and well-defined. When the flame is 'broadside on' the shadow is ill defined (penumbra). In the first case the source of light is narrow, in the second case broad. Examine the shadow of an orange or ball thrown on a paper screen by a lamp with a round ground-glass globe. Prick holes through the paper in various parts of the umbra and penumbra and look through them towards the lamp. Compare what you see with Fig. 6. The penumbral cone is always divergent, as in the above figure. The umbral cone is also divergent when the object is larger than the source of light. It is convergent in Fig. 6 because B is smaller than A. When the source and the object are of the same size the umbral cone becomes a cylinder and the umbra is of the same size throughout. EXAMPLES ON CHAPTER I 1. Explain exactly how a small hole is able to produce an image of an object on a screen. What will be the effect of enlarging the hole? 2. If an image produced by a pen-hole camera is half the size of the object, what are their relative distances from the hole? Why does the image become fainter as it becomes larger? 3. By means of a small hole in the window-shutter of a darkened room an image of a house 30 ft. away is thrown on a screen 6 in. from the hole. The image is 9 in. high: how high is the house? 4. If you hold a hair in sunlight close to a sheet of paper you can see the shadow of the hair on the paper; but if you hold the hair a couple of inches away from the paper you can scarcely see any trace of a shadow. How do you explain this? 5. When has an umbra a limited length? Under what conditions is the transverse section of the umbra cast by a body larger than the body itself? 6. A circular uniform source of light, 2 inches in diameter, is placed at a distance of 10 feet from a sphere 2 inches in diameter. Calculate, approximately, the diameters of the umbra and penumbra cast on a screen 5 feet beyond the sphere. CHAPTER II PHOTOMETRY 7. Illuminating Power and Intensity of Illumination. It is evident that different sources of light give out different amounts of light. An ordinary gas-jet, for example, gives out ten or fifteen times as much light as a candle. This is expressed by saying that its illuminating power is ten or fifteen times as great as that of the candle. In this country the standard of illuminating power is the amount of light given out by a candle of a certain weight burning at a certain rate.1 When we speak of a gas-flame as being of ten candle-power (10 C.P.) we mean that it gives out as much light as ten standard candles. If such a flame were placed at a distance of a foot from a screen, it would throw upon the screen ten times as much light as a standard candle would when placed at the same distance. If the gas-flame were moved farther away, it would illuminate the screen less brightly. At a distance of four feet, for example, it would throw less light upon the screen than a candle would at a distance of one foot. We must, therefore, distinguish carefully between the illuminating power of a source of light and the intensity of illumination which it produces. The intensity of illumination produced by a given source of light on a given surface is the quantity of light received per unit of that surface. This clearly depends upon two things (1) Upon the illuminating power of the source being 1 'Sperm candles of six to the pound, each burning 120 grains per hour.' |