Optic projection : principles, installation and use of the magic lantern, projection microscope, reflecting lantern, moving picture machine, fully illustrated with plates and with over 400 text-figures (1914)

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CH. XII] SIZE OF SCREENS 467 If the lantern cannot be at the back of the room, but must be closer to the screen, then the projection objective must be of shorter focus than 25 to 30 cm. (10-12 in.). To determine the proper objective to use to give the desired size of image in any case one must proceed as follows : 1 i ) The size of screen image is decided on by remembering that it should be between one-fourth and one-fifth the distance to the farthest seat in the room. (2) The distance from the screen to the lantern must be measured. (3) Following the simple optical law founded on the geometry of similar triangles that: "The size of object and image vary directly as their distance from the center of the objective," one can by simple proportion get the focus which the objective should have for a given screen image. § 637. Examples. — For example, suppose the distance from the screen to the farthest seat is 20 meters (66 ft.), the width of the screen should be not less than one-fourth this distance, i. e., five meters (16.5 ft.). Now suppose that instead of the lantern being 20 meters from the screen it is only n meters (36 ft.) from it, what should be the focus of the projection objective to give a screen image 5 meters (16.5 ft.) wide? The formula best adapted for this calculation is: f d where f is the distance of the object from the center of the objective (focus of the objective). 0 is the size of the object. d is the distance from the objective to the screen. 1 is the size of the screen image. It is assumed in all the calculations for the magic lantern that the width of the lantern-slide opening or picture is 7.5 cm. or 3 inches.