IMAGES FORMED BY SMALL HOLES.

951

image of A. In like manner B' will be the image of B, and points of the object between A and B will have their images between A' and B'. An inverted image A'B' will thus be formed of the object A B.

As the image thus formed of an external point is not a point, but a spot, whose size increases with that of the opening, there must always be a little blurring of the outlines from the overlapping of the spots which represent neighbouring points; but this will be comparatively slight if the opening is very small.

An experiment, substantially the same as the above, may be performed by piercing a card with a large pin-hole, and holding it between

a candle and a screen, as in Fig. 644. An inverted image of the candle will thus be formed upon the screen.

When the sun shines through a small hole into a room with the blinds down (Fig. 645), the cone of rays thus admitted is easily traced by the lighting up of the particles of dust which lie in its course. The image of the sun which is formed at its further extremity will be either circular or elliptical, according as the incidence of the rays is normal or oblique. Fine images of the sun are sometimes thus formed by the chinks of a venetian-blind, especially when the sun is low, and there is a white wall opposite to receive the

image. In these circumstances it is sometimes possible to detect the presence of spots on the sun by examining the image.

When the sun's rays shine through the foliage of a tree (Fig. 646), the spots of light which they form upon the ground are always round or oval, whatever may be the shape of the interstices through which they have passed, provided always that these interstices are small. When the sun is undergoing eclipse, the progress of the eclipse can

be traced by watching the shape of these images, which resembles that of the uneclipsed portion of the sun's disc.

939. Theory of Shadows. The rectilinear propagation of light is the foundation of the geometry of shadows. Let the source of light be a luminous point, and let an opaque body be placed so as to intercept a portion of its rays (Fig. 647). If we construct a conical surface touching the body all round, and having its vertex at the luminous point, it is evident that all the space within this surface on the further side of the opaque body is completely screened from the rays. The cone thus constructed is called the shadow-cone, and its intersection with any surface behind the opaque body defines the shadow cast upon that surface. In the case which we have been supposing-that of a luminous point-the shadow-cone and the shadow itself will be sharply defined.

Actual sources of light, however, are not mere luminous points, but have finite dimensions. Hence some complication arises. Consider, in fact (Fig. 648), a luminous body situated between two opaque bodies, one of them larger, and the other smaller than itself. Conceive a cone touching the luminous body and either of the opaque bodies externally. This will be the cone of total shadow, or the cone of the umbra. All points lying within it are completely excluded from view of the luminous body. This cone narrows or enlarges as it recedes, according as the opaque body is smaller or larger than the luminous body. In the former case it terminates at a finite distance. In the latter case it extends to infinite distance.

Now conceive a double cone touching the luminous body and either of the opaque bodies internally. This cone will be wider than the cone of total shadow, and will include it. It is called the

cone of partial shadow, or the cone of the penumbra. All points lying within it are excluded from the view of some portion of the luminous body, and are thus partially shaded by the opaque body. If they are near its outer boundary, they are very slightly shaded. If they are so far within it as to be near the total shadow, they are almost completely shaded. Accordingly, if the shadow of the opaque body is received upon a screen, it will not have sharply defined edges, but will show a gradual transition from the total shadow which covers a finite central area to a complete absence of shadow at the outer boundary of the penumbra. Thus neither the edges of the umbra nor those of the penumbra are sharply defined.

The umbra and penumbra show themselves on the surface of the

opaque body itself, the line of contact of the umbral cone being further back from the source of light than the line of contact of the penumbral cone. The zone between these two lines is in partial shadow, and separates the portion of the surface which is in total shadow from the part which is not shaded at all.

940. Velocity of Light.-Luminous undulations, unlike those of sound, advance with a velocity which may fairly be styled inconceivable, being about 300 million metres per second, or 186,000 miles per second. As the circumference of the earth is only 40 million metres, light would travel seven and a half times round the earth in a second.

In

Hopeless as it might appear to attempt the measurement of such an enormous velocity by mere terrestrial experiments, the feat has actually been performed, and that by two distinct methods. Fizeau's experiments the distance between the two experimental stations was about 5 miles. In Foucault's experiments the whole apparatus was contained in one room, and the movement of light within this room served to determine the velocity.

We will first describe Fizeau's experiment.

941. Fizeau's Experiment.-Imagine a source of light placed directly in front of a plane mirror, at a great distance. The mirror will send back a reflected beam along the line of the incident beam, and an observer stationed behind the source will see its image in the mirror as a luminous point.

Now imagine a toothed-wheel, with its plane perpendicular to the path of the beam, revolving uniformly in front of the source, in such a position that its teeth pass directly between the source of light and the mirror. The incident beam will be stopped by the teeth, as they successively come up, but will pass through the spaces between them. Now the velocity of the wheel may be such that the light which has thus passed through a space shall be reflected back from the mirror just in time to meet a tooth and be stopped. In this case it will not reach the observer's eye, and the image may thus become permanently invisible to him. From the velocity of the wheel, and the number of its teeth, it will be possible to compute the time occupied by the light in travelling from the wheel to the mirror, and back again. If the velocity of the wheel is such that the light is sometimes intercepted on its return, and sometimes allowed to pass, the image will appear steadily visible, in consequence of the persistence of impressions on the retina, but with a