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Nonimaging Optics by With contributions by Narkis Shatz and John C. Bortz, Pablo G. Benitez, Juan C. Minano, Roland Winston

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Appendix L SINE RELATION FOR HYPERBOLOIDAL/LENS CONCENTRATOR

With reference to Figure L.1 the lens images the input beams inclined at angles ±θ to the axis onto the edges FF′ of the virtual source. Therefore, by Fermat’s principle [QA′] + [AF′] = [AF′], where the brackets denote optical path length, and similarly for the other beam. From the geometry of the hyperbola, [AF′] − [AF′] = 2c. Also [QA′] = 2a sin θ, since QA is normal to the beam. The desired result follows: c = a sin θ.

image

Figure L.1 The thin lens at AA′ images the input beam inclined at angle θ to the axis onto F

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