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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 \(E_{0}\) at the point of normal incidence; (b) light from a point isotropic source located at a distance \(l\) \(=100 \mathrm{~cm}\) from the centre of the sphere; the radius of the sphere is \(R=60 \mathrm{~cm}\) and the luminous intensity is \(I=36 \mathrm{~cd} .\)

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