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A2 Daily A Level Physics question

2026-03-05 OCR A Synoptic set B: order-of-magnitude estimates H556/03 Unified physics (synoptic): estimation and limiting-case reasoning Module 4 Waves — intensity as power per unit area; point-source inverse-square behaviour

An LED bike light emits about 2 W of light uniformly in all directions (approximate point source). A light meter records the power per square metre at 2 m and then at 4 m in air, with absorption ignored. Which statement must be true about how the reading changes, and give a reasonable estimate for the reading at 2 m?

  1. A It drops by a factor of 4; at 2 m it is about 0.04 W m−2. (correct)
  2. B It drops by a factor of 2; at 2 m it is about 0.04 W m−2.
  3. C It drops by a factor of 4; at 2 m it is about 0.4 W m−2.
  4. D It stays the same; at 2 m it is about 0.04 W m−2.

Answer

The correct answer is A.

Correct: A — It drops by a factor of 4; at 2 m it is about 0.04 W m−2. A uses spherical spreading: area = 4πr², so doubling r quarters the irradiance; at 2 m, I ≈ 2 W / (16π m²) ≈ 0.04 W m−2. B is wrong because it assumes 1/r rather than 1/r², so it halves instead of quarters. C is wrong because the factor of 4 is right but the estimate ~0.4 W m−2 neglects the 4π in the area (overestimates by about 10×). D is wrong because the power per square metre does not stay the same; it decreases with distance as 1/r².

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