1. ## illumination problem

im not understanding how to set this problem up. 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. two light sources of intensities I(1) and I(2) are d units apart. what point on the line segment joining the two sources has the least illumination? huh? im definitely lost! thanks in advance..

2. "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 $\displaystyle illumination= \frac{k I}{r^2}$ for some constant k. The illumination from two sources 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:$\displaystyle r_1= x$. Then the distance from the other light source to p is $\displaystyle r_2= d- x$.

The total illumination is $\displaystyle \frac{k I_1}{x^2}+ \frac{k I_2}{(d-x)^2}$.

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