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Four Useful Optical Formulas
By ROBERT MITCHELL, JR.
TO AN increasing extent during the last several years, the artistic and executive duties of a modern Director of Photography have been such as to leave him less and less time for intimate contact with many of the more basic mechanical phases of cinematography. Under these circumstances it is only to be expected that members of the profession now and again find themselves at a loss to recall the details of some of these rather elementary laws which govern their work.
For this reason the author presumes to re-state in simple form four such principles in the field of photographic optics. Any of them may be applied helpfully to problems which may arise in studio camerawork; even more frequently they may be found useful in the hobbies of miniature camera photography and substandard cinematography with which so many studio cameramen occupy leisure moments.
Apertures and Focal Length
Perhaps the basic formula of practical photographic optics is;
or that little f equals big F divided by D. It deals with lens-speed, the diameter of the aperture at that speed, and focal length.
In this "f" represents the speed of the lens in relation to its focal length, and is of course familiar to all photographers. The focal length itself is represented by "F", while "D" represents the actual diameter of the aperture at the particular f-stop in question.
In other words, speed value equals the focal length divided by the diameter of the aperture used.
For any given lens the focal length "F" naturally remains constant, while the two other factors are variable. Thus if any two of these factors are known, the formula shows us how to find the third.
Suppose, for instance, we have a lens the speed calibrations of which we doubt, or which are undecipherable. The focal length is known to be 50mm., and the maximum aperture is measured and found to be I inch or 25mm. Substituting these known values for the letters which represent them in our formula we find that the speed (f) equals 50mm. (F or focal length) divided by 25 (D or diameter of aperture). The result is naturally 2, so the maximum aperture of the lens is f:2.
The same formula will enable us to calibrate the lens, for we know its focal
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