Advanced Geometry by H.C. Rajpoot-2014
A uniform point-source of light is mounted at a normal height from the centre of an infinitely long rectangular plane having width . If the plane intercepts of total radiation emitted by the source, find the ratio of height to width .
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The lamp illuminates a half sphere with the radius R. The surface of a spherical cap (actually two half spherical caps) that must have 75% of the surface of the half sphere is calculated. W/2 is the radius R minus the height H of the sperical cap. The ratio would therefore be R/2(R-H). The ratio of ½ would mean that H=0. This cannot be the case here.