CH. XIV] EFFECT OF APERTURE IN PROJECTION 613 



per sq. cm. ( 85 ;a) 50 sq. cm. gives 76 candle-power. At a dis- 

 tance of 4 meters from the screen this gives ^ = 4.8 meter candles. 

 Counting the losses due to the lens as 30% the illumination of the 

 screen would be 3.16 meter candles. This is about a third of the 

 minimum illumination for projection in a perfectly dark room, and 

 about one-tenth of what would be required for good projection. 



If the intrinsic brilliancy of the source is the same and the closing 

 angle is the same the illumination will be the same, thus, if the 

 screen is twice as distant and the objective has twice the diameter 

 the illumination would be the same (fig. 344-345). 



In the above example no use has been made of the focal length of 

 the objective nor the magnification of the object, these having no 

 direct influence on the screen illumination. If a higher magnifica- 

 tion were desired a shorter focus objective would be substituted 

 and the object brought nearer to it. The apparent brightness of 

 the paper seen through the objective will not change if the paper 

 is moved closer to the objective. Therefore, if the objective has 

 the same diameter the illumination on the screen will be just as 

 before. 



Another way of looking at the matter is this : with the shorter 

 focus objective a certain small area of the object will be spread 

 over a larger area on the screen, but bringing the object nearer the 

 face of the objective, more light from the small area of the object 

 will enter it. These two effects exactly counterbalance each other, 

 the increased light taken in by the objective being sufficient to 

 illuminate the larger area. 



857a. Formula for finding the candle-power of a surface illuminated at a 

 given intensity. -Suppose a perfectly diffusing, perfectly white surface to be 

 illuminated at a given intensity, say the intensity of the incident illumination 

 is I meter candles, i. e., the incident light flux is I lumens per square meter. 

 The light falling on one square centimeter will be 1/10,000 lumens. This light 

 will be scattered in all directions so that the surface appears equally bright 

 when seen from any direction, but as the surface appears fore-shortened when 

 seen from any other direction than the perpendicular, more light will be 

 reflected perpendicular to the.'surface than in any other direction. The candle- 

 power of one square centimeter of this surface in any given direction can be 

 expressed as B cos 9, where the constant B, is the intrinsic brilliancy in candle- 

 power per square centimeter of the surface considered as a source of light, and 

 6, is the angle between the normal to the surface and the given direction. 



