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172 PROJECTION OF IMAGES OF OPAQUE OBJECTS [Cn. VII
of the lantern slide and the reflecting qualities of the opaque object (see § 274a).
§ 275. Aperture of the projection objective for transparencies and for opaque objects. — By comparing figures 90-91 it will be seen that for a transparency, relatively small aperture for the projection objective is sufficient. This also shows that if one were to use the same objective for both transparencies and for opaque objects, that the difference in brightness would be enormously exaggerated, if one used only the necessary aperture for the transparencies. If one used the proper objective for the opaque object, it would answer well for the transparency, but only a part of the aperture would be utilized. As the large aperture makes the objective very expensive, one wastes money by having the large aperture for transparencies In the best practice, an objective of moderate aperture is used for transparencies, and one of relatively very large aperture for opaque projection.
§ 276. As will beshownlater (Ch. XIV, § 857a),with a given object and a given illumination, the brilliancy of the screen image depends upon the aperture of the objective and its distance from the screen. The larger the diameter of the lenses of an objective
§ 274a. Light flux getting through the objective with opaque projection. —
It will be shown in § 857a that the light received from a perfectly white, perfectly diffusing surface is
Sin 26 d28 _ _ ^B
= ~ (i-cos 26)
= 2QOOO (i — cos 28} lumens per square centimeter of the white reflecting
surface, where I is the intensity of illumination of the surface measured in meter candles, and 6 is the half angle of light subtended by the objective, or 20 is the angle of light subtended by the objective. The light received by the surface is I/ 10,000 lumens and the proportion of light received by the surface
which strikes the objective is then —
In this problem the angle of light subtended by the objective is 20°, i. e. 26 = 20°. The proportion of light received by the objective is then (i — cos 20°) /2 = (i — .9397) /2 = .0603/2 = .0302 or about 3%.