Why does the intensity of radiation vary inversely to the square of the distance?

The intensity of radiation varies inversely to the square of the distance primarily because the x-ray beam diverges from its point source. As the distance from the point of origin of the radiation increases, the same amount of radiation is spread over a larger area. This geometric spreading results in a decrease in intensity at greater distances.

When radiation is emitted from a point source, it radiates outward in all directions, creating a sphere of influence. As you move away from this source, the area over which the radiation is distributed expands with the square of the distance. Hence, for every doubling of the distance from the source, the intensity (measured as the number of photons per unit area) decreases by a factor of four. This principle is consistent with the inverse square law, which is fundamental to understanding radiation exposure and safety in medical imaging.

The other options do not accurately capture the fundamental reason behind the inverse square law as it applies to radiation intensity.