FIG. 57.—A photograph at a receives four times as much light as when held at b.
100. Fading Illumination. The farther we move from a light, the less strong, or intense, is the illumination which reaches us; the light of the street lamp on the corner fades and becomes dim before the middle of the block is reached, so that we look eagerly for the next lamp. The light diminishes in brightness much more rapidly than we realize, as the following simple experiment will show. Let a single candle (Fig. 57) serve as our light, and at a distance of one foot from the candle place a photograph. In this position the photograph receives a definite amount of light from the candle and has a certain brightness.
If now we place a similar photograph directly behind the first photograph and at a distance of two feet from the candle, the second photograph receives no light because the first one cuts off all the light. If, however, the first photograph is removed, the light which fell on it passes outward and spreads itself over a larger area, until at the distance of the second photograph the light spreads itself over four times as large an area as formerly. At this distance, then, the illumination on the second photograph is only one fourth as strong as it was on a similar photograph held at a distance of one foot from the candle.
The photograph or object placed at a distance of one foot from a light is well illuminated; if it is placed at a distance of two feet, the illumination is only one fourth as strong, and if the object is placed three feet away, the illumination is only one ninth as strong. This fact should make us have thought and care in the use of our eyes. We think we are sixteen times as well off with our incandescent lights as our ancestors were with simple candles, but we must reflect that our ancestors kept the candle near them, "at their elbow," so to speak, while we sit at some distance from the light and unconcernedly read and sew.
As an object recedes from a light the illumination which it receives diminishes rapidly, for the strength of the illumination is inversely proportional to the square of distance of the object from the light. Our ancestors with a candle at a distance of one foot from a book were as well off as we are with an incandescent light four feet away.
FIG. 58.—The two shadows are equally dark.
101. Money Value of Light. Light is bought and sold almost as readily as are the products of farm and dairy; many factories, churches, and apartments pay a definite sum for electric light of a standard strength, and naturally full value is desired. An instrument for measuring the strength of a light is called a photometer, and there are many different varieties, just as there are varieties of scales which measure household articles. One light-measuring scale depends upon the law that the intensity of illumination decreases with the square of the distance of the object from the light. Suppose we wish to measure the strength of the electric light bulbs in our homes, in order to see whether we are getting the specified illumination. In front of a screen place a black rod (Fig. 58) which is illuminated by two different lights; namely, a standard candle and an incandescent bulb whose strength is to be measured. Two shadows of the rod will fall on the screen, one caused by the candle and the other caused by the incandescent light. The shadow due to the latter source is not so dark as that due to the candle. Now let the incandescent light be moved away from the screen until the two shadows are of equal darkness. If the incandescent light is four times as far away from the screen as the candle, and the shadows are equal, we know, by Section 100, that its strength is sixteen candle power. If the incandescent light is four times as far away from the screen as the candle is, its power must be sixteen times as great, and we know the company is furnishing the standard amount of light for a sixteen candle power electric bulb. If, however, the bulb must be moved nearer to the rod in order that the two shadows may be similar then the light given by the bulb is less than sixteen candle power, and less than that due the consumer.