Which equation expresses the inverse-square law for radiation intensity from a point source?

Which equation expresses the inverse-square law for radiation intensity from a point source?

• A. Directly with distance
• B. Inversely with the square of distance
• C. With the square of distance
• D. With distance only

Answer: (B)

The key idea is that radiation from a point source spreads out over the surface of a sphere as it travels. The energy delivered per unit area therefore drops with the area of that sphere, which grows as the square of the distance. In practical terms, if the source emits a fixed power, the irradiance at distance r is proportional to 1/r^2 (often written as I ∝ 1/r^2 or E = P/(4πr^2)). That’s why doubling the distance reduces the intensity to one quarter. Saying the intensity is directly proportional to distance, or to the distance squared, or to distance only, would imply the energy spreads over a smaller area as you move away, which isn’t the case. The inverse-square relationship accurately describes how intensity falls off with distance from a point source.

The key idea is that radiation from a point source spreads out over the surface of a sphere as it travels. The energy delivered per unit area therefore drops with the area of that sphere, which grows as the square of the distance. In practical terms, if the source emits a fixed power, the irradiance at distance r is proportional to 1/r^2 (often written as I ∝ 1/r^2 or E = P/(4πr^2)). That’s why doubling the distance reduces the intensity to one quarter. Saying the intensity is directly proportional to distance, or to the distance squared, or to distance only, would imply the energy spreads over a smaller area as you move away, which isn’t the case. The inverse-square relationship accurately describes how intensity falls off with distance from a point source.