Calculate Brightness vs. Distance
Inverse-square law for illuminance and relative brightness
Brightness calculator (JavaScript)
Inverse-square law
For point-like light sources, the approximation E = I/r² applies. If distance doubles, brightness drops to one quarter.
Example calculations
Example 1: Illuminance at 2 m
Given: I = 400 cd, r = 2 m
Result: E = 100 lx
Example 2: Brightness ratio from 1 m to 3 m
Given: r₁ = 1 m, r₂ = 3 m
Interpretation: At 3 m, only about 11.11% remains compared with 1 m.
Example 3: Double distance
Rule: r₂ = 2·r₁
Result: Doubling distance means one quarter brightness.
Formulas and comprehensive description
Perceived brightness on a surface decreases with distance from a point-like light source, not linearly but quadratically. The inverse-square law is a fundamental model in photometry, stage lighting, street lighting, photography, and sensor design. It helps estimate illuminance at different distances and design efficient lighting systems.
Absolute illuminance
Relative ratio
Illuminance unit
Practical rule
Notes for real applications
Detailed Description
What is Brightness?
Brightness (also called illuminance or illumination) is a measure of the amount of visible light falling on a surface. It is measured in the unit Lux (lx), where 1 Lux = 1 Lumen per square meter. The brighter a surface is, the more light hits it per unit area.
The Inverse-Square Law
The Inverse-Square Law is a fundamental principle in photometry and radiometry. It states that the brightness (or intensity) from a point light source decreases with the square of the distance:
- E – illuminance (lux)
- I – luminous intensity of the source (candela, cd)
- r – distance from the light source (meters)
Physical Interpretation
The Inverse-Square Law arises from geometric reasons: the light energy from a point source is distributed uniformly over a spherical surface. As the radius r increases, the surface area grows proportionally to 4πr². Thus, the intensity per unit area decreases in proportion to 1/r².
Practical Consequences
- Doubled distance: Brightness drops to one quarter (2² = 4)
- Tripled distance: Brightness drops to one ninth (3² = 9)
- Relative change: \[\frac{E_2}{E_1} = \left(\frac{r_1}{r_2}\right)^2\]
Luminous Intensity vs. Brightness
| Quantity | Symbol | Unit | Meaning |
|---|---|---|---|
| Luminous Intensity | I | cd (Candela) | Luminous flux per solid angle of the source |
| Luminous Flux | Φ | lm (Lumen) | Total visible light energy |
| Illuminance | E | lx (Lux) | Luminous flux on a surface: 1 lx = 1 lm/m² |
| Luminance | L | cd/m² | Perceived brightness from a given direction |
Typical Brightness Values
| Light Condition | Illuminance (lx) |
|---|---|
| Clear starry night sky | 0.0003 |
| Full moon night | 1 |
| Dark room (artificial light) | 50 |
| Office lighting (standard) | 200 – 500 |
| Workplace (good lighting) | 500 – 1000 |
| Operating room | 10000 – 50000 |
| Overcast sky (noon) | 10000 – 20000 |
| Sunny sky (noon) | 100000 |
Applications
- Architecture & lighting design: Calculate number and position of luminaires for optimal brightness distribution
- Photography: Determine aperture and exposure time based on light conditions
- Occupational safety: Set minimum brightness requirements for different types of work
- Astronomy: Determine apparent brightness of celestial objects
- Sensor technology: Calibrate light sensors and cameras
- Energy efficiency: Optimize lighting systems to reduce energy consumption
Note: Validity Range
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