Question

# An indirect lighting system is used to light a square room with a floor area of...

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?

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 ==>

Af = Area of the floor = 400 ft2

Illuminance required on the floor, If = 10 fc = 10 lm / ft2

Therefore, lumens required on the floor = Af * If = 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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