Surface Environment, Mine Ventilation and Underground Hazards · Underground Hazards · 2 marks · Numerical answer
An 8×6×4 m workshop has one roof-corner luminaire at each corner. Each uses 100 W and produces 100 lumen/W uniformly into a full sphere. Neglect reflections. Find horizontal floor-centre illumination in lux, to two decimals.
Each lamp emits 10000 lumens, so intensity is I=10000/(4π) candela. Distance to floor centre is r=√(4²+3²+4²)=√41 m, with incidence cosine 4/r. Illumination from one is Icosθ/r²=4I/r³. Four lamps give E=16×10000/[4π×41^(3/2)]=48.50 lux. The cosine factor accounts for the horizontal receiving plane.
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