# Math Help - Optimization Problems - Illumination

1. ## Optimization Problems - Illumination

Need help on the illumination problem, i have no idea where to start. Any help would be appreciated and thx in advance

Illumination
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 I1 and I2 and d units apart. What point on the line segment joining the two sources has the least illumination?

2. The light at some point 'a' units from L1 could be represented by:

$k\frac{L_{1}}{d^{2}}+k\frac{L_{2}}{(d-a)^{2}}$

Now, differentiate:

$\frac{dL}{da}=\frac{-2kL_{1}}{a^{3}}+\frac{2kL_{2}}{(d-a)^{3}}$

Now, set to 0 and solve for a.