Question

The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one four times as strong as the other, are placed 14 ft apart, how far away from the stronger light source should an object be placed on the line between the two sources so as to receive the least illumination? (Round your answer to two decimal places.)

Answer 1

Answer:

$d=4.67ft$ from the weaker source

Explanation:

The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source:

$Illumination=k*S/d^{2}$   first source

$Illumination=k*4S/(14-d)^{2}$   second source (stronger)

If the illumination is the same for the two sources:

$k*S/d^{2}=k*(4S)/(14-d)^{2}$

We solve to find d:

$2d=14-d$

$d=14/3=4.67ft$ from the weaker source