Thinking about the shape of the surface of equal contribution between two inverse square lights of different intensities.
Without loss of generality (by scaling, translating and rotating) we can use lights with this parameters:
Light 1 position:
Light 2 position:
Light 1 strength:
Light 2 strength:
We get the following equation using the inverse square law:
Operating with it:
Solving this quadratic equation:
Full 3D variant
Using the inverse square law we get an equation for the surface of equal intensity:
Using and completing the square:
Multiplying all terms by and reordering:
Replacing by the expression of as function of :
This is an sphere with
matching the results found for the 1D case.