By A. R. Bean, D. J. Silverleaf, R. H. Simons

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Since this process can be repeated for similar pairs of points until the whole of the cap has been considered, the illumination vector for the cap must lie along CP. Another property of a circle is that the extension of chord CP (Fig. e. the direction of the illumination vector bisects the angle between the component Es producing illumination on the sphere wall and the component Ez producing illumination on the parallel plane. Since the value of each of these components is given by £ cos 0, hs = Hence _ 71L ,Λ hz.

Area Sources The general expression applies to area sources, but since an inclined plane frequently cuts the source and changes not only its size, but also its shape with respect to point P (Fig. 32), the calculation is more difficult. Plane receiving ^illumination at point p. \ FIG. 32. ILLUMINATION FROM LINE AND AREA SOURCES 51 If the change in size and shape is not taken into account, the value obtained will be the difference in the illumination on the two sides of the plane at P. EXTENSION OF THE DISC SOURCE FORMULA In the section on uniform diffuse sources we established the following: 1.

K. and CUTTLE, C , Trans. S. (Lon- don) 31, 65 (1966). 3 LP CHAPTER 3 DIRECT FLUX AND INTERREFLECTIONS CLASSIFICATION OF ROOMS Problems involving the distribution of luminous flux within an interior can be simplified if use is made of the work of Harrison and Anderson, and particularly Hisano, in classifying rooms. The classification is based on finding the square room which is equivalent to a given rectangular room, so that the calculations need only be made for square rooms. Hisano (1) has shown that if a rectangular room has the same ratio of horizontal surface area to vertical surface area as a square room, then the results of similar average illumination calculations for the two rooms will agree within 10%.