Light emitted from a source or received by a surface is referred to as luminous flux, which is measured in Flux in Lumens (lm).

Luminous Intensity

Luminous intensity is a measure of how much flux is emitted within a small conical angle and is expressed in Candelas.

The inverse square law states that the illuminance E = l / d2, the intensity of the light source divided by the distance squared.

Inverse Square Law

If a source emits the same luminous flux in all directions, then the luminous intensity is the same in each direction, but for most sources, the flux emitted in each direction is not the same.

If a small light source has a luminous intensity of 1000 candelas and is positioned 2 metres directly above a surface, the illuminance measured in lux will be as shown in the diagram.

With such importance being placed on the illuminance required for different purposes, it is essential to have a method for calculating this quantity. This is called the inverse square law.

Illumination on a Surface

To understand the inverse square law, consider a cone-shaped beam of light coming from a small point source and falling onto a surface some distance away.

Suppose that the luminous flux within the cone is one lumen, and it strikes a surface 1 metre away, producing an illuminated area of 1 square metre. By dividing the luminous flux by the area we can find the illuminance, which will be 1 Lux.

If we now move the surface further away to a distance of 2 metres, then the luminous flux within the cone will stay the same, but the illuminated area will increase in size to 4 square metres. This will result in a illuminance of 1/4 lux.

Therefore, the area has increased in proportion to the square of the distance from the light source, and the illuminance has changed inversely with the square of the distance.

If we now move the surface still further away to a distance of 3 metres, we can see the inverse square law operating again. The area has increased in proportion to the distance squared and is now 9 square metres and the resultant illuminance falls inversely to 1/9th lux.

Cosine law of Illuminance

If the surface is turned so that rays strike at an angle, the illuminated area will increase in size and the illuminance will drop accordingly.

The ratio of the original illuminated area to the new area is equal to the cosine of the angel through which the surface has been moved. Therefore, the illuminance will fall by a factor of the cosine of the angle.

This is the cosine law of illuminance.

If a surface illuminated to 250 lux is twisted through an angle of 60 degrees, then the illuminance will fall to half or 125 lux because the cosine of 60 degrees is 1/2.

Inverse Square Law #2

This cosine law can be combined into one equation with the inverse square law.

If a small element of the surface receives 100 lumens and reflects 70 lumens, then the reflectance is 0.7, or it can be expressed as a percentage as 70%. The remaining 0.3 or 30% would be absorbed.

Diffuse Reflectance

Different surfaces also reflect light in different ways. For example, surfaces such as paper, emulsion paint, carpets and so on, exhibit what we call matt or diffuse reflection, that is, the light reflected from the surface is scattered in all directions.

Specular Reflection

At the other extreme is mirror or specular reflection exhibited by shiny metal surfaces such as chrome, silver or pure aluminium.

It is most important to realise that although specular reflections produce a clear image in the surface of the material, the actual amount of light reflected may be deceptively low.

A matt white painted surface, for instance, has a reflectance of 85% to 90% compared with only 60% specular reflectance from a polished stainless steel surface, while polished aluminium will be approximately 85%.

Mixed Reflection

Many surfaces such as gloss paint, wood, plastic and so on, exhibit a combination of these two types of reflection.

Gloss paint, for example scatters most of the light that it reflects, but also produces a specular reflection in the surface of the paint.

Measurement of Luminance

When measuring the reflected light from a surface it will depend upon a combination of the nature of the surface finish and its reflectance and will change with the viewing angle.

The brightness of the surface is measured in candelas per metre square (cd/m2) using a luminance meter as shown.