Prismatic elements are typical devices of natural light illumination system for redirecting and collecting daylight. Based on the principles of optics, this paper presents a simple mathematical matrix ray-tracing methodology through which a detailed intensity distribution of parallel light beam incident onto a right angled prism from different incident angles can be calculated precisely. We also present the distribution of the secondary emerged intensity from a prism illuminated by the emerged light of an adjacent prism. The direction, concentration, and distribution of intensity of the emerged light from the parallel light incident onto a surface of the right-angle prism, as well as daylight illuminate on a prismatic collector, are precisely calculated. The detailed calculation of the emerged light re-incident onto the adjacent prism or emerged out of the prismatic element presented that most of daylight are directly emerged out and are confined in some directions at earlier morning and afternoon, and the emerged light re-incident into the adjacent prism at noon around. This detailed calculation model of parallel light beam incident to a prismatic element can be applied to the hybrid natural light illumination system, as well as to the prism-relative solar illumination system for the improvement of efficiency.
Prismatic elements are widely used in daylight illumination systems. The characteristics of the light that emerges from the surface of a right-angled prism vary with the apex of the prism and the incident angle of the sunshine illuminating the surface of the prismatic daylight collector. This paper investigates the effect of the apex angle of a right-angled prismatic collector on the performance of the collector using a matrix ray-tracing model and the edge principle. It was found that the majority of the light emerges from the hypotenuse of the right-angled prism when sunshine is incident on the surface of the prismatic daylight collector; furthermore, the flux of the light emerging from the hypotenuse that directs illuminating space decreases as the apex of the right-angled prism is increased. The intensity distribution of the majority of the light emerging from the hypotenuse of a right-angled prism can be used to guide the design of natural light illumination systems and enhance their performance. The percentage of light emerging from the hypotenuse decreases with the number of prismatic elements because the relative area of the emerging light that reaches the adjacent prism increases with the number of prismatic elements. The analysis of the relative area of the hypotenuse, where the emerging light that reaches the adjacent prism according to the edge ray principle shows that the total area is constant when the number of prismatic elements is greater than 10; an economical prismatic daylight collector can be realized with less material due to the larger number of smaller prisms with the same apex.
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