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Photometry and Geometrical Optics

Problem 5.3

Find the mean illuminance of the irradiated part of an opaque sphere receiving (a) a parallel luminous flux resulting in illuminance E0E_{0} at the point of normal incidence; (b) light from a point isotropic source located at a distance ll =100 cm=100 \mathrm{~cm} from the centre of the sphere; the radius of the sphere is R=60 cmR=60 \mathrm{~cm} and the luminous intensity is I=36 cd.I=36 \mathrm{~cd} .

Reveal Answer
(a) ⟨E⟩=1/2E0\langle E\rangle=1 / 2 E_{0} (b) ⟨E⟩=1−1−(R/l)21−R/lIR2=50 lx\langle E\rangle=\frac{1-\sqrt{1-(R / l)^{2}}}{1-R / l} \frac{I}{R^{2}}=50 \mathrm{~lx}
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