Increasing distance from a source

Assuming radiation in free space (and equally in all directions) and a distance $r$ from the source,

• intensity decreases by $1/r^2$

Question: If there is a doubling of distance from the source, by what factor will the intensity change?

Solution:

• Given an intensity at some initial distance:

• doubling the distance from the source yields,
  a change in intensity by a factor of of $1/2^2$.