The inverse square law states that the intensity of light from a point source falls off with the square of the distance. Double the distance and the light reaching the subject is one quarter as intense, equivalent to a loss of two stops. Triple the distance and the loss is nearly four stops. The relationship holds for any unobstructed point source in free space and is the single most useful equation in lighting because it explains why small changes in source distance produce dramatic changes in exposure and falloff.
The most visible consequence is shadow falloff across a subject. A softbox placed one meter from a face delivers similar intensity to the nose and the ear; the same softbox at four meters delivers nearly identical intensity to both because the proportional distance from source to each feature has changed. Photographers exploit this by moving lights close for dramatic falloff, where the side of the face nearer the source is two stops brighter than the side farther away, and far for even, almost flat illumination.
The same math governs background separation. Placing a subject close to a wall lights both at similar intensity and leaves no tonal separation. Moving the subject away from the wall makes the wall fall darker (since the wall is now proportionally farther from the source) while keeping the subject bright. A four-foot gap can drop a background by two stops, which is why studio setups so often pull the subject off the cyc rather than placing them against it.
Bounce flash demonstrates the cost in exposure. A flash aimed at a ceiling travels up, hits the ceiling, scatters, and travels back down to the subject. The total path is roughly four to six meters in a typical room, against a direct path of two to three meters. Squared, the bounce path loses three or more stops compared to direct flash, on top of the additional loss from the ceiling absorbing some of the light. This is why bounce flash often needs full power on a speedlight that would deliver the same direct exposure at 1/16 power.
The law is technically valid only for true point sources. Large area sources (an enormous softbox or a wall acting as a giant reflector) follow it less strictly when the subject is closer than the source’s longest dimension, because the source is effectively many points overlapping. The practical takeaway is that big sources up close behave more linearly than the law predicts, while small sources behave exactly as predicted at any distance.
Ambient sources outdoors (the sun, the sky) are at essentially infinite distance and do not show useful falloff across human-scale scenes. The sun on the foreground rocks is the same intensity as the sun on the distant mountain. Inside a studio or a small location, however, lights are close enough that the law dominates every decision about distance, falloff, and ratio. Guide number math for flash, light meter readings, and lighting ratio calculations all derive from this same square relationship.