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March, 1930] OPTICS OF MOTION PICTURE PROJECTORS 315
short as possible with due consideration for lens aberrations on the one hand, and over-heating or pitting of the surface of the condenser on the other.
Let us now examine the system shown in Fig. 4, in which the arc is focussed directly on the gate. With this arrangement, it is impossible for the arc to be the aperture stop of the system, but it may be the field stop unless the magnification of the image formed by the condenser more than covers the gate. As before, the size of the arc will be a minimum when the magnification of its image is a maximum. The condenser, in this case, may limit both the field and the aperture if it is too small. Its minimum diameter may be quickly determined by applying the method outlined in the preceding section. This consists in determining the image of the condenser formed by the projection lens, and treating this image in the same manner as the stop shown in Fig. 2.
If the two major conditions are satisfied, the screen illumination in both systems that we have just considered will be substantially the same. However, one system or the other will satisfy these conditions with a smaller source, depending upon the relative sizes of the gate and the projection lens. Since the gate is ordinarily smaller than the projection lens in projecting motion pictures, it is somewhat easier to fill the gate with the image of the source than to fill the projection lens. In other words, if we assume the same magnification in the image of the arc by the condenser, the two major conditions can be satisfied with a smaller source with the system shown in Fig. 4. On the other hand, in the projection of lantern slides, or the wide motion picture film that is now being discussed, the gate may be larger than the projection lens, and it is then more economical to image the arc on the latter. In comparing the two systems in this way, we are tacitly assuming that the surface of the arc crater is sufficiently uniform in brightness to focus directly on the gate. This assumption is seldom completely justified and is never possible with incandescent lamp sources. Consequently, when the maximum efficiency would result from imaging the source on the gate, a compromise is usually made by moving the image of the source toward the projection lens until the illumination of the screen is sufficiently uniform. The proper size of the arc can be determined by finding the size and position of its image by the condenser, and then determining the image of this image formed by the projection lens. The second image is then treated as a real stop in the manner described with reference to Fig. 2