494 ELEMENTS OF ELECTRICAL ENGINEERING. 



172. An open-arc lamp is placed at a distance of five feet from 

 a converging lens and an image of the arc is formed at a distance 

 of one foot beyond the lens. The light from the lamp has a 

 conical intensity of 2,500 candles. Assuming that the luminous 

 surface of the lamp is negligibly small, and ignoring loss of light 

 at the lens by reflection and absorption, find the conical intensity 

 of the beam beyond the image. Ans. 100 candles. 



Note. Consider the cone A formed by lines drawn from the arc to the periphery 

 of the lens, the cone B formed by lines drawn from the image to the periphery of the 

 lens, and the cone a formed by lines drawn from the center of the lens to the per- 

 iphery of the luminous surface of the lamp. The size of the luminous area of the 

 lamp is negligibly small when the solid angle of the cone a is negligible in compari- 

 son with the solid angle of the cone B. 



All of the light in cone A is in cone B after it passes through the lens, so that the 

 conical intensities of the light in cones A and B are inversely as the solid angles of 

 these cones, and these solid angles are inversely proportional to the squares of the 

 distances of the lens from the lamp and from the image, respectively. 



173. Calculate the spherical-candle-power of a bare glow lamp 

 from the data given in Fig. 175, Chap. X. Ans. 13.33 spherical- 

 candles. 



174. Calculate from the data given in Fig. 176, Chap. X., 

 the spherical-candle-power of the glow lamp of problem 173 

 when it is provided with an aluminum cone shade, and express 

 the amount of light absorbed by the shade as a percentage of 

 the spherical-candle power of the bare lamp. Ans. 8.26 spher- 

 ical candles ; 3 8 per cent, of the light is lost. 



175. (a) How many 16 candle-power lamps are required to 

 illuminate a lecture hall 50 x 75 feet with a moderately high 

 ceiling? (ft) How many 16 candle-power lamps would be re- 

 quired to give exactly the same average intensity of illumination 

 in a room twice as long, twice as wide and twice as high with the 

 same kind of walls and ceiling and the same kind of furniture ? 

 Why? (c) The mean coefficient of absorption of walls, ceiling 

 and furniture in the room specified under a is 40 per cent. How 

 many i6-candle-power lamps would be required to give the same 

 illumination in a room of the same size in which the mean coeffic- 

 ient of absorption of walls, ceiling and furniture is 5 5 per cent ? 



