A designing method of reflector or lens contours for reflector and projector lamps is attemped. It has been customary, in illumination engineering, to use simple second-degree or composed surfaces for these designs, but this time we introduce a new method to calculate directly matched surfaces in the caces of various reflector type lamps and desirable light distribution.
The reflecting or refracting law exists at any arbitrary points on the unknown desirable surface, and the differential eqation between directions of light and the function of surface can be composed by the medium of gradient of normal line at these points. If the relation between light source and desirable light distribution is assumed, this eqation can be solved by formal or numerical integration.
Generally, this solution is different from second-degree surfaces. It is comparatively easy to solve this eqation in the case of a point source and uniform flood lighting. The photographs of a wide flood type sealed-beam lamp designed by this method and its light pattern compared with a medium flood type one are indicated.
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