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.