Inverse Square Law

The inverse square law states that the illuminance (or received intensity) from a point light source decreases proportionally to the square of the distance from that source. Doubling the distance divides the illuminance by 4. This law is part of the high school physics curriculum.

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How to measure it in class

With the FizziQ app, the light meter allows you to experimentally verify the 1/d² law.

Steps:

Open FizziQ and select the “Light Meter” instrument
Use a point light source (lamp, LED)
Measure the illuminance at different distances: 20, 40, 60, 80, 100 cm
Plot E versus d and E versus 1/d²
Verify that E × d² = constant
Discuss deviations: source size, stray reflections

Scientific activities on this topic

Learn more

Physical origin:

A point source emits light in all directions. This light spreads over spheres of increasing radius. Since the surface area of a sphere is 4πr², the energy per unit area decreases as 1/r².

Applications:

This law applies to any isotropic point source:

Visible light
Infrared radiation (heat)
Sound waves
Gravitation and electrostatic force

Model limitations:

The source must be point-like (or the distance must be large compared to its size)
No stray reflections (free-field measurement)
No absorption by the medium

Formula

Illuminance as a function of distance:

E = I / d²

where:

E: illuminance (lux or W/m²)
I: luminous intensity of the source (candela or W/sr)
d: distance from the source (m)

For two positions: E₁ / E₂ = d₂² / d₁²

If the distance doubles (d₂ = 2d₁): E₂ = E₁ / 4

Application examples

A candle at 1 m gives 10 lux, at 2 m only 2.5 lux
Solar illuminance on Mars (1.5 AU) is 2.25 times weaker than on Earth
Photographers use this law to calculate the lighting of a scene
Astronomers measure the distance of stars from their apparent brightness

FAQ

Q: How to verify this law with FizziQ? A: Measure the illuminance E at several distances d. Plot E versus 1/d²: you should get a straight line passing through the origin.

Q: Why doesn’t the Sun appear smaller at sunset? A: It is an optical illusion. The Earth-Sun distance varies by only ±1.7% over the year. The law applies, but the atmosphere modifies perception.

Q: Does this law apply to a fluorescent lamp? A: Approximately, if you are far away. Up close, the lamp is not point-like and the law is not exactly verified.

Q: Does a camera flash follow this law? A: Yes! That is why the flash has a limited range. At 4 m, the illuminance is 16 times weaker than at 1 m.

Illuminance