Question

1. according to the inverse square law, if you double the distance from a radiating source, the intensity will decrease by the _____ of the distance.

Explanation:

Step1: Recall Inverse Square Law

The inverse square law for radiation intensity (\(I\)) and distance (\(d\)) is \(I \propto \frac{1}{d^{2}}\).

Step2: Analyze Effect of Doubling Distance

Let initial distance be \(d_1 = d\), intensity \(I_1\). New distance \(d_2 = 2d\). Using the law, \(I_2 \propto \frac{1}{(2d)^{2}}=\frac{1}{4d^{2}}\). Compare \(I_2\) to \(I_1\) (\(I_1 \propto \frac{1}{d^{2}}\)): \(I_2=\frac{I_1}{4}\). So intensity decreases by the square of the distance factor (since factor of distance is 2, square is 4, so intensity is \(1/4\) of original, i.e., decreases by the square of the distance's multiple).

Answer:

square