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310
ARTHUR C. HARDY
[J. S. M. p. K.
distance from the focal point of the projection lens to the screen, the focal length (/) of the projection lens is determined by equation (l), where m is the linear magnification of the film on the screen.
Let us first consider these elements in Fig. 1 independently of the customary source of illumination. To do this, we may imagine a ground glass or diffusing glass placed just to the left of the gate and we may ignore for the present the method by which this receives its illumination. If the diffusion is perfect, this source will appear equally bright from every direction of observation. Assuming its brightness
Diffusing Glass
Gate
Screen
FIG. 1. Blements of an optical system which determine magnification and intensity of illumination.
to be B candles per square foot, it has been shown1 that the illumination at the center of the screen is given by equation (2),
E = TT B sin2 Sf
(2)
where E is the illumination in lumens per square foot, and 6' is the half-angle of the cone whose base is the effective area of the projection lens and whose apex is the center of the screen. Equation (2) is rigorously correct when the source is perfectly diffusing, when the losses by reflection or absorption within the projection lens are negligible,2 and when the projection lens obeys the sine condition. The latter condition can be derived from the conservation of energy principle and applies only to a perfect image-forming system. No actual lens can be constructed to fulfill this condition completely nor can the losses caused by absorption and reflection be eliminated. Consequently, equation (2) gives the illumination at the center of the screen
* The transmission of the usual projection lens is between 60% and 80%, depending principally upon the number of air-glass surfaces it contains. The loss by reflection usually amounts to 5% for each air-glass surface in the system.