According to the inverse square law, when changing the PID length from 8 to 16 inches, how does the beam's intensity change?

The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source. This principle can be articulated mathematically as:

[ I_1 / I_2 = (D_2 / D_1)^2 ]

where ( I_1 ) and ( I_2 ) are the intensities at distances ( D_1 ) and ( D_2 ), respectively.

In the case of changing the PID (position indicating device) length from 8 inches to 16 inches, the distance is effectively doubled. Plugging these values into the inverse square law provides a clear calculation:

[ I_1 / I_2 = (16 / 8)^2 = (2)^2 = 4 ]

This indicates that the intensity at the greater distance of 16 inches (I_2) is one-fourth of the intensity at 8 inches (I_1), hence:

[ I_2 = I_1 / 4 ]

Thus, when the PID length increases, the beam's intensity decreases to one-fourth of its original intensity. This understanding is crucial in radiation safety practices, as it illustrates how increasing the distance from a radiation source