An indirect lighting system is used to light a square room with a floor area of 400 ft2 . The luminaires in the room uniformly light the ceiling, which is 20 ft high. The walls and floor of the room are very dark and can be assumed to have a reflectance of zero. The ceiling has a reflectance of 0.8. How many lumens must be produced by the luminaires to provide 10 fc on the floor of the room?
ANSWER ==>
We will simplify the problem here. The luminaires in the room are facing upwards and they are arranged in such a way that they are uniformly lighting only the ceiling. Let the luminaires produce L lumens. Now, the ceiling has a reflectance of 0.8. Therefore, amount of lumens reflected from the ceiling = 0.8*L.
The reflected lumens from the ceiling will fall on the floor now.
Given ==>
A_{f} = Area of the floor = 400 ft^{2}
Illuminance required on the floor, I_{f} = 10 fc = 10 lm / ft^{2}
Therefore, lumens required on the floor = A_{f} * I_{f} = 400 * 10 = 4000 lm
Since, reflected lumens from the ceiling = 0.8*L = lumens falling or required on the floor = 4000 lm
Therefore =>
0.8*L = 4000 lm
==> L = 5000 lm ==> ANSWER
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