Final answer:
Using the inverse square law of illuminance, the illuminance of a torch at 5 m with a flux of 1500 lumens is calculated to be approximately 4.77 lux. None of the provided multiple-choice options match this result, indicating a possible error in the question or the options.
Step-by-step explanation:
The illuminance of a torch with a luminous flux of 1500 lm on a tree that is 5 m away can be calculated using the inverse square law of illuminance. The formula for illuminance (E) is E = Φ / (4πr²), where Φ is the luminous flux and r is the distance from the light source to the surface. In this case, Φ = 1500 lm and r = 5 m:
E = 1500 lm / (4π(5 m)²) = 1500 lm / (4π(25 m²))
E = 1500 lm / (100π m²) = 1500 lm / (314.16 m²) = 4.77 lx
However, since none of the provided options match this result, it seems there might be an error in the question or options. Typically, for a straight answer, rounding to the nearest option might be appropriate, but given that all options exceed the calculated result, the best response is that none of the provided options (A, B, C, D) correctly represent the calculation.