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Filmmaking Dictionary: Number 1 / 1/r² (Inverse-Square Law)
Definition
The inverse-square law describes how illuminance from an effectively point-like source changes with distance. Under the appropriate conditions, illuminance is proportional to 1/r², where r is the distance from the source.
For a surface facing the incoming light, the relationship can be written E = I/r², where E is illuminance and I is luminous intensity in that direction. Doubling the distance gives one quarter of the illuminance, a reduction of two stops.
A Simple Distance Example
Suppose an effectively point-like source provides 400 lux at a distance of 2 metres. Keeping its output, direction and other conditions unchanged, the inverse-square estimate gives 100 lux at 4 metres and 25 lux at 8 metres.
Moving from 2 metres to 4 metres therefore does not merely halve the light. The distance doubles, and the square of that change is four. Moving closer reverses the relationship, within the limits of the model.
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Why It Matters for Blocking
When a subject moves near a small source, a modest change in distance can produce a noticeable exposure change. The same movement can have a smaller effect when the source is much farther away because the proportional distance change is smaller.
For example, moving from 1 metre to 2 metres doubles the distance. Moving from 10 metres to 11 metres changes it by only 10%. This is one reason a crew may place a suitable source farther away when seeking more even illumination across a performer’s movement.
Where the Simple Rule Needs Qualification
- Large nearby sources: Different parts of a soft source sit at different distances from the subject.
- Beam optics: Changing focus or beam angle changes the source’s intensity distribution.
- Bounce and reflections: Walls, ceilings and other surfaces add light through additional paths.
- Surface angle: A surface tilted away from the incoming light receives a different illuminance.
- Atmosphere and obstructions: Transmission losses can change the result.
The law is not wrong when a large softbox behaves differently at close range; the point-source approximation is no longer an adequate description of the whole setup. Meter the actual subject positions.
Exposure Versus Softness
Moving a light changes more than exposure. It can change apparent source size, shadow softness, spill and background relationships. Compensating the output to restore a meter reading does not automatically restore the original look.
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Frequently Asked Questions
Does doubling distance remove one stop?
For the point-source inverse-square case, it removes two stops.
Can I use it to predict every LED panel at close range?
Not reliably. The panel’s size, diffusion and optics can make near-field behaviour differ from the simple model.
Related Terms
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