612 EFFECT OF APERTURE IN PROJECTION [Cn. XIV 



BRIGHTNESS OF THE SCREEN IMAGE 



857. The brightness of the image can be calculated in either 

 of two ways. 



1. The relative area of the object and image and the illumina- 

 tion of the object. 



2. The intrinsic brilliancy of the source and the closing angle 

 of the rays forming the image. 



The first case is more applicable to directed light where all of the 

 light illuminating the object gets through the objective. For 

 example, with a magic lantern, let the area of the slide be 50 sq. cm., 

 7.1 x 7.1 cm. and the area of the screen 2x2 meters = 40,000 sq. 

 cm. or 800 times as much surface. Let the brightness of the slide 

 illumination be 48,000 meter candles. The illumination of the 

 screen will be - [ of this or 60 meter candles. 



BOO 



Actually only 70% of the light from the slide will get through the 

 objective, and the illumination will be 42 meter candles. For 

 ordinary reading with artificial light one needs an illumination of 

 from 30 to 50 meter candles. 



The second case is most useful where the entire aperture of the 

 lens is filled with light, as with a large light source with the micro- 

 scope, and with opaque projection. Consider the same example as 

 above except that the object is a white opaque body illuminated 

 from the front. More data concerning the lens will be needed. 

 Let the lens be one of 14 cm. (sJ^in.) focus, 6.25 cm. (2^in.) diam- 

 eter, the size of the picture being two meters square as before ; and 

 as before the object illuminated with an intensity of 48,000 meter 

 candles. To secure the same magnification as before requires a 

 distance of 396 cm. (4 meters approximately) from the screen with 

 this focus objective. Suppose the objective is looked at from the 

 screen. Its entire opening will appear of the same brightness 

 (except for absorption) as if there were no glass present and the 

 illumination on the screen will be just the same as if the light 

 reaching it were from a piece of white paper having an area of 50 

 sq. cm. illuminated by 48,000 meter candles. Considered as a 



48,000 

 source of light this paper disc would have a can die-power of 



