Question

Photographers often use multiple light sources to control shadows or to illuminate their subject in an artistic manner. The illumination from a light source is inversely proportional to the square of the distance from the source and proportional to the intensity of the source. Two light sources, L1 and L2, are 10m apart, and have intensity of 4 units and 1 unit, respectively. The illumination at any point P is the sum of the illuminations from the two sources.

Hint: When a quantity y is inversely proportional to the square of another quantity x, then y= k/x^2, where k is a constant.

a) Determine a function to represent the illumination at the point P relative to the distance from L.

b) At what distance from L1 is the illumination on P the greatest?

c) At what distance from L1 is the illumination on P the least?

d) Investigate whether it would be more effective to increase the intensity of L2 or to move L2 closer to L1 in order to increase the illumination at the point found in part c). Support your findings with mathematical evidence. Consider both the illumination and the rate of change of the illumination as L2 changes intensity of position.

Answer 1