Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Optical Distance Law

Geometric dilution of light vs. distance.

Optical distance law

The illumination intensity on a surface is inversely proportional to the square of its distance from the light source and can be expressed as

E = Φ / d2(1)


E = light intensity, illumination (lux, lumen/m2)

Φ = the quantity of light emitted by a lamp or a light source - luminous flux (lumen, lm)

d = distance from light source (m)


E1 d12= E2d2 2 = constant (2)

(2) can be modified to

E1 / E2= d2 2 / d12(2b)

Example - Illumination Intensity from a Lamp at distance

The illumination intensity from lamp with luminance 10000 lumens at distance 2 m can be calculated with (1) as

E1 = (10000 lumens) / (2 m)2

= 2500 lux

The illumination intensity at distance 5 m can be calculated by modifying (2b) to

E2= E1 d12/ d2 2

= (2500 lux) (2 m)2/ (5 m)2

= 400 lux

Light intensity vs. distance from source

Cosine law of Illumination

E = Φ / d2cos θ                 (3)


θ = angle between light source vertical line and sight line

Related Topics

  • Basics

    Basic engineering data. SI-system, unit converters, physical constants, drawing scales and more.
  • Mathematics

    Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

Related Documents


Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .


This page can be cited as

  • The Engineering ToolBox (2003). Optical Distance Law. [online] Available at: [Accessed Day Month Year].

Modify the access date according your visit.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter