A photographer measures 39.8 lux from a 2,000 lumen bulb held 2.00 m away, using illuminance equals P over 4 pi r squared. If the bulb is instead measured at 3.00 m, roughly what illuminance results?
ARoughly 59.7 lux, one and a half times as much
BRoughly 39.8 lux, exactly the same as before
CRoughly 26.5 lux, two-thirds of the original value
DRoughly 17.7 lux, less than half the original value
Answer & Solution
Correct answer: D. Roughly 17.7 lux, less than half the original value
1. Illuminance is given by P divided by 4 pi r squared, so it falls as the square of the distance grows.
2. Going from r = 2.00 m to r = 3.00 m multiplies r squared by (3.00/2.00) squared = 2.25.
3. Dividing the original 39.8 lx by 2.25 gives about 17.7 lx.
4. This matches the stated follow-up result directly: at 3 m the illuminance is only 17.7 lux.
5. A value close to 39.8 lx ignores that illuminance must drop as distance increases.
6. A value like 59.7 lx would require illuminance to rise with distance, which contradicts the inverse square relationship.
_Source: OpenStax Physics (CC BY 4.0), Ch 15 "Light", section 15.2 The Behavior of Electromagnetic Radiation_
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