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Photometry and Geometrical Optics

Problem 5.8

A vertical shaft of light from a projector forms a light spot \(S=100 \mathrm{~cm}^{2}\) in area on the ceiling of a round room of radius \(R=\) \(=2.0 \mathrm{~m} .\) The illuminance of the spot is equal to \(E=1000 \mathrm{~lx}\) The reflection coefficient of the ceiling is equal to \(\rho=0.80 .\) Find the maximum illuminance of the wall produced by the light reflected from the ceiling. The reflection is assumed to obey Lambert's law.

Reveal Answer
 5.8. Emax⁡=(9/16π3)ρES/R2=0.21 lx, at the distance R/3 from the ceiling. \begin{aligned} &\text { 5.8. } E_{\max }=(9 / 16 \pi \sqrt{3}) \rho E S / R^{2}=0.21 \mathrm{~lx}, \text { at the distance }\\ &R / \sqrt{3} \text { from the ceiling. } \end{aligned}
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