Final answer:
The correct formula to describe the variation of illumination (I) on a surface is c. I= kc/d², where k is a constant of proportionality, c is the candlepower of the light source, and d is the distance from the source to the surface.
Step-by-step explanation:
The question involves understanding the concept of the inverse square law for light, which describes how the illumination (I) varies with the distance (d) from the light source and its intensity, measured in candlepower (c). The inverse square law tells us that as you move away from a point light source, the illumination decreases in proportion to the square of the distance from the source, meaning that if the distance is doubled, the illumination is reduced to one-fourth of its original value. Conversely, the illumination varies directly with the candlepower of the source, so doubling the candlepower doubles the illumination.
To write a general formula based on this rule, the illumination I will be directly proportional to the candlepower c and inversely proportional to the square of the distance d. This relationship can be represented mathematically by a constant of proportionality k. Thus, we can derive the correct formula:
I = \( \frac{kc}{d^2} \)
This means that the correct option from the provided choices is:
c. I= kc/d2
As an example, if a lightbulb has a certain candlepower and is observed from a distance of 2 meters yielding an illumination of 2.4 W/m2, and if the distance is doubled to 4 meters, according to the inverse square law, the new illumination would be 2.4 W/m2 times 1/4, which equals 0.6 W/m2.