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HANDBOOK OF PROJECTION FOR
Taking account of the minus sign before the V results in imaginary values so only the positive sign will be considered. Calculations (by 10" slide rule) are tabulated below thru the range of objective lenses recommended in this report.
Lens E.F.
4
5 6
7
E.F. 4
5 6
7 8
BD tan
17.0
13.6
11.3
9.7
8.5
2
0.085 0.068 0.0565 0.0485 0.0425
tan 2 0.00722 0.00463 0.00319 0.00235 0.00180
sec5—
1.00722 1.00463 1.00319 1.00235 1.00180
2 sec2—
2.01444 2.00926 2.00638 2.00470 2.00360
4 sec2— tan2—
0.0290
0.0186
0.01285
0.00942
0.00721
Log Cos 0 9.97924-10 9.97901-10 9.97893-10 9.97870-10 9.97887-10
17° 35' 17° 40' 17° 42' 17° 44' 17° 44' +
Thus it becomes apparent that, through the range of focal lengths recommended, the percentage of increase in picture height is practically influenced only by the projection angle, the percentage being approximately equal to the "secant minus one" of the projection angle. The present standards of the Society set the maximum projection angle at 12°, corresponding to an increase in picture height of about 2.5 per cent. Thus we see that the distortion has doubled for a 40 per cent increase in projection angle, and it becomes exceedingly apparent that it is a serious thing to add even as much as two degrees to the projection angle when designing a theatre, that it should never be done except for the most urgent reasons, and never merely to obtain architectural symmetry in a part of the theatre which the audience seldom sees.
The sidewise location of the projection equipment should be so graded as to favor those projectors which