Fig. 24.

intensity. From this experiment we deduce the law, that the intensity of light varies inversely as the square of the distance. (Exercise IV.)

Shadows and Penumbræ.-In Fig. 25 suppose

Fig. 25.

luminous rays to proceed from a point m to the screen o; in their path they meet with an opaque ball n, from which what is called a shadow on the screen is derived. Here the light proceeds from a point, and the shadow is well defined; this is not commonly the case, for the light has generally some magnitude, and produces outside the shadow a rim called a penumbra (almost a shadow). For instance, in Fig. 26 let L represent a luminous ball and M an opaque ball, P being the screen, then the part 1 of the screen will be

fully illuminated, part 2 partially so, part 3 will be a complete shadow. Part 2 is called a penumbra. These are geometrical shadows, natural shadows are by no means so well defined.

The relative intensities of light are ascertained by the shadow-test. Photometers (light measurers) are used. Rumford's photometer has an upright spindle

Fig. 27.

c on a wooden stand; at a short distance there is a plate of ground glass d in sliding grooves. To use this simple instrument, suppose a candle b to be at a known distance, and that a gas flame e is placed at three times this distance to give a shadow of the same intensity on the ground glass from the upright spindle as is given by the candle, then the intensity of the light from the gas flame is nine times that of the light given by the candle. An estimate of the power of a gaslight may be thus made, a fixed standard candle being used.

Ritchie's photometer is on the same principle. The light is admitted from the lights to be compared at opposite ends of a rectangular box, in the middle of which there is a wooden partition flanked on each side by a mirror placed at an angle of 45°. Therefore the light is thrown off at an angle of 90° with the incident rays, and passes to the upper side of the box, in which is placed a ground-glass screen to receive the two quantities of light. Here the lights to be compared are arranged so that the reflections on the glass are equal; then their distances measured; say one is at two feet, and the other at eight. Then the latter at four times the distance has equal intensity to the former; i. e., its intensity is sixteen times that of the smaller flame.

Bunsen's Photometer.-A grease spot is made on bibulous paper, and the lights are placed on opposite sides until this part of the paper looks like the rest, when the distances are measured.

Wheatstone's Photometer.- This instrument gives more accurate results. It consists of a steel bead fixed on a small toothed wheel, and this again is placed on a moveable disc surrounded by teeth. By turning a handle the disc and the small wheel are made to rotate, and the bead, with the light reflected on opposite sides in turning round with the double motion imparted, gives two lines of light, somewhat in the shape of a rose. As before, these are made equal, and distances of lights measured.

Reflection of Light from Plane Mirrors.The angle of reflection is equal to the angle of incidence. The image of any point is formed behind the mirror at a distance equal to that of the given point from the mirror. We always seem to see an object in the direction in which the rays of light enter the eye.

It is a common mistake, especially with young students, to picture to themselves the rays of light proceeding from the eye. To guard against this, bear in mind that we see objects by means of light which comes from them. The eye is only an instrument for receiving impressions from the light as it arrives.

A Plane Mirror is one in which the reflecting ́surface is plane. Ordinary plane mirrors, or lookingglasses, are plates of smooth glass with one side. covered with a thin layer of mercury and tinfoil. The images formed by a looking-glass are produced by the reflection of the rays of light from the metallic covering. If the surface of a plane mirror could be so highly polished as to reflect all the rays incident upon it, the mirror itself would be invisible, and an observer would see nothing but the images of the objects before it. Such a mirror placed vertically against the walls of a room appears like an opening leading to another apartment, and a person is only prevented from walking through it by meeting his own image. We always seem to see an object in the direction in which the rays of light enter the eye. A mirror which changes the direction of the rays proceeding from an object will change the apparent place of that object. Let a looking-glass be placed horizontally on a table, and let the rays of a candle fall obliquely on the mirror and be reflected to the eye, on the opposite side we shall seem to see the candle inverted, and as much below the surface of the glass as the candle is above it. Vary the position of the candle and of the observer, drawing a diagram for each new position, which shall fully account for the apparent change of the image in position. The reader will then obtain accurate views of the lateral inversion of objects by plane mirrors.

When a person stands before a looking-glass, the rays of light which proceed from each point of his body will, after reflection, proceed as if they came from points occupying corresponding positions behind the glass, and will produce an effect upon the eye as if they had actually proceeded from those points.

Fig. 28.

The image, therefore, appears as much behind the glass as the person is before it. Let (Fig. 28) AB be a plane mirror or looking-glass, and c an object placed before it. Let c D and E be two rays diverging from the object, and reflected from D and E to the eye at F. After reflection they will proceed as if they had come from a point a, as far behind the surface of the glass as c is before it. The two triangles a D A and A D c are equal. For the angles at A are right angles, and the angles at D are equal by construction. The side A D is common, therefore the base a A = the base Ac. (Euclid, i., 4.) Hence whatever the length of A c, the distance a A will be the same. For this reason our reflection in a mirror appears to approach when we move towards it, and retire when we walk away.

When trees or houses are reflected from the smooth