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as regards brightness of the surface. For example, a dusty or dirty screen lighted to an intensity of five foot-candles will not appear so bright as a white one, for a greater proportion of the light falling upon the screen is absorbed and lost. The brightness of an object depends upon both the intensity of illumination on it and the percentage of light that it reflects.
Having defined the foot-candle as a unit of intensity of illumination, we are naturally interested in seeing how the intensity of illumination varies as the candle-power of the source varies, and also as the area over which a given beam is spread varies. It is obvious that if, in Fig. 4, instead of an intensity of one candle along the line SA^ we have an intensity of two candles, the illumination at 'A' would be twice as great, and that if we have an intensity of five candles the illumination at ''A' will be five times as great. Now, if we consider a source of one candle as shown in Fig. 6, we know that the intensity of illumination on 'A' which is one foot distant is one foot-candle. If, however, we remove the plane ''A' and allow the same beam of light that formerly was intercepted by 'yf' to pass on to the plane '5,' two feet away, we find as shown in the diagram that this same beam of light would have to cover four times the area of 'yf' ; and, inasmuch as we cannot get something for nothing, we would find that the average intensity on '^,' two feet away, would be one-fourth as high as that on 'A' i foot.
Fig. 6 The Illumination on a surface varies inversely as the square of the distance from the source to the surface.
away, or one-fourth of a foot-candle. In the same way, if *5' also is removed and the same beam allowed to fall upon plane 'C,' three feet away from the source, it will be spread over an area nine times as great as 'A^ and so on; at a distance of five feet we would have only one-twenty-fifth of a foot-candle. From this we deduce that the intensity of illumination falls off not in proportion to the distance ,but in proportion to the square of the distance. This relation is commonly known as the inverse square law.
Important Relation Between Foot-Candle and Lumen.
If we refer back to Fig. 3B, we see that the surface OP§R is illuminated at every point to an intensity of one foot-candle. We also know by definition that the quantity of light falling on the plane OPR^ is one lumen. This gives us the important law that if one lumen is so