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106 MOTION PICTURE HANDBOOK
aperture is found to be 29/32 of an inch (the new standard) wide. First multiply the distance from the screen in feet by the width of the aperture in fractions of an inch. To multiply 60 by 29/32 we first divide by 32 and multiply the result by 29 ; 60-7-32—1.875; 1.875X29=54.375. Next we divide this measurement by the desired width of picture in feet: 54.375 -^ 15 = 3.625, or a 3^?-inch e. f. lens. We most likely would be unable to get that exact focal length and would have to take, instead, a 524-inch e. f. lens.
It must be understood, however, that the great bulk of projection lenses now in use are cheap lenses, and cheap lenses, like all other cheap things, are inaccurate, therefore you cannot expect to arrive with certainty at precisely the result you desire in any other way than by actually testing the lenses.
The stereopticon lens is figured exactly the same way, except that instead of measuring the aperture width, we take 3 inches as the average width of the slide mat— the slide mat, in this case, being the aperture.
It is also entirely practical to make other measurements of practical value as follows: Suppose you have an objective and wish to know what size picture it will project at a given distance. First measure its e. f. as already directed and then:
Size of Image. — This can be determined by multiplying the difference between the distance from lens to screen and the focal length of the objective, by the width of the aperture and dividing the pro-rlurt by the focal length of the lens. For example: Let L be the projection distance, 40 feet (480 inches); S, the slide mat, 3 inches; F the e. f. of the lens, 12 inches; we then have the formula (in which d is the size of image) ;
S (L-F)
F
Substituting for the letters their known values, we have: 3 (480—12)
=117 in., or 9^ feet,
12
as the size picture a 12-inch e. f. stereo lens will project at 40 feet, provided the slide mat be just 3 inches wide. If. however, the mat be more or less than 3 inches, then the picture will be wider or less wide.
Distance from Slide to Screen. — With the other factors given we get this by multiplying the sum of the width of the