How does light intensity vary with distance?
The intensity of light is proportional to the inverse square of the distance from the source. For example, If the distance from the source doubles, the intensity is 1/4 the original intensity. If the distance triples, the intensity goes down to 1/9 the original value.
Intensity is power/area.
A light bulb emits light that travels in all directions in a spherical pattern. It is spread over an increasingly larger surface as the distance increases. Think about how the illumination from a flashlight spreads over a larger area as you move it farther from a surface. If you think of the distance as the radius of the sphere of illumination then the surface area of the sphere is `4/3pir^3` . The luminous intensity, power/area, is `I = (3P)/(4pir^2)`
which shows that intensity is inversely proportional to r^2, the square of the distance from the source.