Abstract

A general theorem is established concerning the effect of a transmitting hole on the lumen output of an otherwise uniform, diffuse enclosure with light-generating walls. The physical content of the theorem is first, that when a small hole is opened one loses, to first order in the area of the hole, the flux which was emitted to the outside from this area, but gains (1 − R)−1 times the flux which was absorbed in this area, where R is the reflectance of the enclosure wall; and second, that if opening an infinitesimal hole decreases the output, then opening any hole, no matter what its size, shape or position, will also decrease the output. From this it follows that opening a hole can increase the output of the enclosure if and only if the absorptance of the enclosure wall exceeds a certain critical value; the critical absorptance is calculated explicitly, and is shown to be independent of the geometry of both the enclosure and the hole. As an application, it is shown that the absorptance of standard fluorescent lamp coatings is very much smaller than the critical absorptance, and hence that if any part of the envelope of such lamps is left bare, the output and efficiency will be decreased.

© 1961 Optical Society of America

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Equations (40)

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