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Folygonal Floodlight Mirror — Benford and Palmer 113
back spun to a parabolic form, and lined on its concave side by numerous pieces of flat mirror glass. It has been demonstrated* both mathematically and by actual test that if certain proportions are observed in forming the individual mirrors the resultant beam will be free from images and highly uniform in intensity in its central part. The basic equation of such a mirror is :
a ^ a
la-\-So COS^ COS a = pa slu (Z + ^o COS
2 2
where
la is the angular length of a section, measured along a radial centerline ;
Pa is the angular width of a section, or 360 divided by the number of mirrors in the zone;
So is the angular diameter of the light source measured from the vertex of the complete mirror ;
a is the angle, measured from the axis to the center of the particular section being designed.
When the conditions of this equation are fulfilled each mirror will give a beam that coincides in direction and in average size with all the other individual beams. With all beams covering the same field it is self evident that the action of any one particular section is not of vital importance. Several trial mirrors were built with a commercial grade of rolled glass mirrors, but it was found that the imperfections in the glass set up zones or images in the beam. These images were not of great strength or of much visual prominence, but they rendered the beam defective, particularly if it was moved during the taking of a scene. Later, mirrors of plate glass were used, and they gave a beam almost wholly free from this defect. Only the outer zones of the beam show traces of the individual beams .
In Fig. 4 is illustrated a front view of a 36 inch diameter mirror designed to give a beam 30 degrees in diameter. There are three zones of mirrors. The central zone contains four sections, the intermediate zone nine, and the outer zone twelve sections. The beam from each section has a general resemblance in outline to the form of the sections in the diagram. The sections are here seen in perspective and are foreshortened somewhat, which has the effect of making them appear more nearly equal in length and breadth than they actually
* Benford, "Studies in the Projection of Light," General Electric Review Dec, 1925, and March, 192o.