

The intensity is proportional see ∝ to the multiplicative inverse of the square of the distance thus:

In mathematical notation the inverse square law can be expressed as an intensity I varying as a function of distance d from some centre. To prevent dilution of energy while propagating a signal,methods can be used such(a) as a waveguide, which acts like a canal does for water, or how a gun barrel restricts hot gas expansion to one dimension in profile to prevent damage of energy transfer to a bullet. Radar energy to direct or establish expands during both thetransmission in addition to the reflected return, so the inverse square for both paths means that the radar will receive power to direct or determine according to the inverse fourth power of the range. The fundamental hit for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space. In inversely proportional to the square of a distance from the character of that physical quantity.
