"the illumination from a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source"

So for some constant k. The illumination fromtwosources is the sum of the two separate illuminations:\frac{k I_1}{r_1^2}+ \frac{k I_2}{r_2^2}[/tex]

Let x be the distance from the first light source to a point p on the line between the two light sources: . Then the distance from the other light source to p is .

The total illumination is .

The minimum illumination will be where the derivative of that, with respect to x, is 0.