The inverse square law states that the intensity of light from a point source is inversely proportional to the square of the distance from that source. In photography lighting, it means that doubling the light-to-subject distance reduces the light to one quarter, a loss of exactly two stops, while halving the distance makes it four times brighter.
The law explains two effects that every lighting setup depends on: how much power a light must deliver at a given distance, and how quickly brightness falls off from the subject to the background. Understanding it turns light placement from trial and error into a predictable calculation.
Why light follows the inverse square law
Light leaving a small source spreads out in all directions. At any distance, the same total energy is distributed over the surface of an imaginary sphere, and the area of that sphere grows with the square of its radius. When the distance doubles, the same light covers four times the area, so each square centimeter receives one quarter as much.
In formula form, illuminance at distance d is proportional to 1/d². Because photographers count light in stops, where each stop is a factor of two, the relationship is easiest to remember in stop terms: a factor of about 1.4 in distance equals one stop, and a factor of 2 equals two stops.
The table below shows how distance changes translate into light intensity and exposure.
| Distance multiplier | Relative light | Change in stops |
|---|---|---|
| 0.5x | 4 times as much | Plus 2 stops |
| 0.7x | About 2 times as much | Plus 1 stop |
| 1x | Unchanged | 0 stops |
| 1.4x | About one half | Minus 1 stop |
| 2x | One quarter | Minus 2 stops |
| 3x | One ninth | About minus 3.2 stops |
| 4x | One sixteenth | Minus 4 stops |
Light falloff between subject and background
The most useful consequence of the law is falloff, the difference in brightness between objects at different distances from the same light. What matters is not the absolute distance but the ratio of the distances, because the law compares squares.
With a light 1 m from a subject and a background 1 m behind, the background is twice as far away and receives two stops less light. Moving the light to 3 m keeps the same 1 m gap, but the background at 4 m is now only about 1.33 times farther, so it is less than one stop darker.
| Light-to-subject distance | Light-to-background distance | Background darker by |
|---|---|---|
| 0.5 m | 1.5 m | About 3.2 stops |
| 1 m | 2 m | 2 stops |
| 2 m | 3 m | About 1.2 stops |
| 4 m | 5 m | About 0.6 stops |
This gives the photographer a creative control. A close light produces dramatic falloff and a dark background, while a distant light produces even illumination across a group, a set or a product line. The trade-off is power: the distant light must be much stronger to achieve the same exposure.
Where the inverse square law holds and where it does not
The law is exact only for an ideal point source in free space. Real photographic light sources follow it closely in some situations and deviate in others, so knowing the exceptions prevents wrong conclusions.
| Light source | Agreement with the law | Reason |
|---|---|---|
| Bare flash or bulb | Close | Small source radiating broadly |
| Softbox at long distance | Close | Small relative to the distance |
| Large softbox very close | Weaker falloff than predicted | Extended source, not a point |
| Fresnel or focused spot | Weaker falloff over a range | Partly collimated beam |
| Sunlight | No visible falloff in a scene | Source distance is effectively infinite |
| Room with light walls | Weaker falloff | Reflected light adds fill everywhere |
A practical guideline is that an extended source behaves approximately like a point source once the distance is several times its largest dimension. Distances should also be measured from the effective light source, such as the front diffusion panel of a softbox, rather than from the stand.
Using the law in practical lighting
The inverse square law underlies several everyday lighting tools and decisions.
- Guide number calculations for flash rely on it: the guide number equals distance multiplied by f-number, so doubling the distance requires opening the aperture by two stops.
- Lighting ratios between key and fill lights can be set by distance alone, without changing power settings.
- Feathering a light across a group places the nearest person at the edge of the beam and the farthest one in its center, balancing exposure.
- Background control is achieved by moving the subject away from the background or the light closer to the subject.
A light meter or a test frame remains the final check, because reflections, modifiers and spill make real sets more complex than the formula.
Common misunderstandings
The law is frequently simplified in ways that lead to wrong exposure decisions. The most common misunderstandings are listed below.
- Believing that doubling distance halves the light; it reduces it to one quarter.
- Assuming the law makes close lights harsher; hardness depends on the apparent size of the source, which actually grows when the light moves closer.
- Measuring distance to the stand rather than to the effective source surface.
- Expecting falloff outdoors in sunlight, where distance differences are negligible compared with the distance to the sun.
Explained without jargon
Light spreads out as it travels, like paint from a spray can. Close to the can, the paint is thick. Farther away, the same paint covers a much larger area and looks thin.
Move twice as far from a lamp, and the light is spread over four times the area. The subject receives only a quarter of the light. This is why a person near a lamp looks bright while the wall behind falls into shadow.
A typical use case
A portrait photographer wants a moody headshot with a nearly black background in a small studio with a gray wall. The subject sits 1.5 m from the wall. With a softbox 0.75 m from the face, the wall is three times farther from the light and receives about 3.2 stops less light, so it renders as a deep charcoal tone.
For a corporate group portrait the next day, the photographer needs even light across three rows of people standing 1 m apart in depth. The softbox is moved back to about 8 m from the front row and its power is raised, so the last row at 10 m is only about two-thirds of a stop darker than the first. The front-to-back difference falls within what the photographer can balance easily in post-processing.