The brightness of any point-source illumination diminishes rapidly with distance. This weakening of light is called fall-off.
It diminishes according to the inverse square law, which states that the effect of a light shining on a surface weakens at a rate comparable to the square of the distance between source and surface.
As the diagram above demonstrates, at twice the distance, the light is only one fourth as bright because the same rays must cover four times the area. At three times the distance, it drops to one ninth as bright.