The radiation intensity from a point source varies inversely as the square of the distance from the source. Which equation expresses this relation?

The radiation intensity from a point source varies inversely as the square of the distance from the source. Which equation expresses this relation?

• A. I1/I2 = (R1)^2/(R2)^2
• B. I1/I2 = (R2)^2/(R1)^2
• C. I1/I2 = R2/R1
• D. I1*I2 = R1^2 R2^2

Answer: (B)

The main idea is that the intensity from a point source decreases with the square of the distance: I ∝ 1/r^2. For two distances, R1 and R2, with corresponding intensities I1 and I2, you have I1 ∝ 1/R1^2 and I2 ∝ 1/R2^2. Taking the ratio gives I1/I2 = (1/R1^2) / (1/R2^2) = R2^2 / R1^2. This matches the stated relation. Why this form fits: it reflects how the emitted energy spreads over the surface of a sphere whose area grows as r^2, so doubling the distance reduces intensity by a factor of four. Other forms would misrepresent the dependence. For example, R1^2/R2^2 would invert the relation, implying intensity scales with the reciprocal of the inverse square, and R2/R1 would imply a linear, not quadratic, dependence. The product I1I2 = R1^2R2^2 also contradicts the separate 1/r^2 dependence for each intensity.

The main idea is that the intensity from a point source decreases with the square of the distance: I ∝ 1/r^2. For two distances, R1 and R2, with corresponding intensities I1 and I2, you have I1 ∝ 1/R1^2 and I2 ∝ 1/R2^2. Taking the ratio gives I1/I2 = (1/R1^2) / (1/R2^2) = R2^2 / R1^2. This matches the stated relation.

Why this form fits: it reflects how the emitted energy spreads over the surface of a sphere whose area grows as r^2, so doubling the distance reduces intensity by a factor of four.

Other forms would misrepresent the dependence. For example, R1^2/R2^2 would invert the relation, implying intensity scales with the reciprocal of the inverse square, and R2/R1 would imply a linear, not quadratic, dependence. The product I1I2 = R1^2R2^2 also contradicts the separate 1/r^2 dependence for each intensity.