A room requires an average illuminance of 200 lux over a 60 square meter area. If the total luminous flux emitted by the lamps is 15000 lumens and the utilization factor is 0.8, what is the actual illuminance achieved?
200 lux
To solve this problem, we need to understand the concept of illuminance, luminous flux, and utilization factor. Illuminance is a measure of how much luminous flux is spread over a given area. It is calculated using the formula:
E = \frac{\Phi \times UF}{A}
Where:
- E is the illuminance (in lux),
- \Phi is the total luminous flux (in lumens),
- UF is the utilization factor (a measure of how effectively the light is used),
- A is the area (in square meters).
Given:
- Total luminous flux \Phi = 15000 lumens,
- Utilization factor UF = 0.8,
- Area A = 60 square meters.
Substituting these values into the formula:
E = \frac{15000 \times 0.8}{60}
Calculating step-by-step:
- Calculate the product of luminous flux and utilization factor: 15000 \times 0.8 = 12000
- Divide the result by the area: \frac{12000}{60} = 200 lux
Thus, the actual illuminance achieved is 200 lux.
Therefore, the correct answer is 200 lux.
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