Unit 4: Science and Materials in Construction and the Built Environment
Measurement of Lighting
Light is one form of energy and could be measured by the standard units
of energy. But the effect of light on the human environment also depends
upon the sensitivity of the eye, and a special set of units has therefore
been developed for the measurement of light and its effects.
13.1 Solid angle
As light can radiate in all three dimensions it is necessary to measure the
way in which the space around a point can be divided into “solid angles “.
The standard SI unit of solid angle is the steradian, illustrated in figure
13.1.

One steradian () is that solid angle at the centre of a sphere
which cuts an area on the surface of the sphere equal to the size of
the radius squared.
The size of a solid angle does not depend upon the radius of the sphere or
upon the shape of the solid angle. The total amount of solid angle
contained around a point at the centre of the sphere is equal to the
number of areas, each of size radius squared, which can fit on to the total
surface area of a sphere. That is
Therefore a complete sphere contains a total of 4 steradian.
Figure 13.1: The steradian
Chapter 13: Measurement of Lighting
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Unit 4: Science and Materials in Construction and the Built Environment
13.2 Luminous Intensity
The concept of luminous intensity is used to compare different light
sources and measure their ‘strength’.

Luminous intensity (I) is the power of a light source, or
illuminated surface, to emit light in a particular direction.
Unit: candela (cd)
The candela is one of the base units in the SI system. One candela is
defined as the luminous intensity in a given direction of a source that
emits monochromatic radiation of frequency 540 × 1012 Hz and of which
the radiant intensity in that direction is 1/683 W/.
The effect of one candela is still approximately the same as the original
idea of one candle power and the Mean Spherical Intensity (MSI) of a
100W light bulb, for example, is about 100 cd.
13.3 Luminous Flux
The rate of flow of any electromagnetic energy can be expressed in terms
of power, but light energy is also measured by luminous flux.

Luminous Flux (F) is the rate of flow of light energy.
Unit: Lumen (lm)
By definition, one lumen is the luminous flux emitted within one steradian
by a point source of light of one candela, as shown in figure 13.2. In
general, luminous flux and luminous intensity are related by the following
formula.
where
I = mean spherical intensity of the source (cd)
F = luminous flux emitted by the source (lm)
 = solid angle containing the flux (sterad)
Chapter 13: Measurement of Lighting
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Unit 4: Science and Materials in Construction and the Built Environment
Figure 13.2: Definition of the lumen
In the common case of a point source emitting flux in all directions, the
total solid angle around the point is 4 steradians.
Substituting the value of 4 and rearranging the formula
gives the following useful formula:
13.4 Illuminance
When luminous flux falls on a surface it illuminates that surface. The
lighting effect is termed illuminance.

Illuminance (E) is the density of luminous flux reaching a surface.
Unit: lux (lx) where 1 lux = 1 lumen/(metre)2
Common luminance levels range from 50 lux for low domestic lighting to
50 000 lux for bright daylight. Recommended lighting levels are specified
in terms of illuminance and examples of standards are given in the
section on lighting design.
If light is falling on a surface at right angles to the surface then the
illuminance is given by the following formula.
Chapter 13: Measurement of Lighting
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Unit 4: Science and Materials in Construction and the Built Environment
where
E = illuminance on surface (lx)
F = total flux reaching surface (lm)
A = area of the surface (m2)
Figure 13.3: Summary of lighting measurements
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Chapter 13: Measurement of Lighting
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Unit 4: Science and Materials in Construction and the Built Environment
Practical Example 1
A small source of light has a mean spherical intensity of 100 cd. One
quarter of the total flux emitted from the source falls at right angles onto
a surface measuring 3 m by 0.7 m. Calculate:
a) The total luminous flux given out by the source; and
b) The illuminance produced on the surface.
Answer
a) Know
where
I = 100 cd
 = 4
So
Total flux = 1256.64 lm
b) Know
where
F = 1256.64 × 0.25 = 314.16 lm
A = 3 × 0.7 = 2.1 m2
So
So illuminance = 150 lx
Chapter 13: Measurement of Lighting
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Unit 4: Science and Materials in Construction and the Built Environment
13.5 Inverse square law of illumination
As the luminous flux emitted by a point source of light travels away from
the source, the area over which the flux can spread increases. Therefore,
the luminous flux per unit area (i.e. the illuminance), must decrease. This
relationship is expressed by the inverse square law, as illustrated in figure
13.4.
13.5.1

Inverse square law
The illuminance produced by a point source of light decreases in
inverse proportion to the square of the distance from the source.
In SI units this law may be expressed mathematically by the following
formula.
where
E = illuminance on that surface (lx)
I = intensity of a point source (cd)
d = distance between source and surface (m)
An important consequence of the inverse square law is that changes in
the position of light sources produce relatively large changes in lighting
effect. For example, doubling the distance between a lamp and a surface
causes the illuminance on that surface to decrease to one quarter of its
original value.
Figure 13.4: Inverse square law of illumination
Chapter 13: Measurement of Lighting
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Unit 4: Science and Materials in Construction and the Built Environment
Practical Example 2
A lamp has a luminous intensity of 1200 cd and acts a point source.
Calculate the illuminance produced on surfaces at the following positions.
a) At 2 m distance from the lamp, and
b) At 6 m distance from the lamp.
Answer
Know
a) I = 1200 cd
d=2m
So
So illuminance at 2 m = 300 lx
b) I = 1200 cd
d=6m
So
So illuminance at 6 m = 33.33 lx
Chapter 13: Measurement of Lighting
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Unit 4: Science and Materials in Construction and the Built Environment
Exercise 13
1) A small lamp emits a total luminous flux of 1257 lm in all directions.
Calculate the luminous intensity of this light source.
2) A point source of light has an intensity of 410 cd and radiates
uniformly in all directions.
a) Calculate the quantity of flux flowing into a hemisphere.
b) Calculate the average illuminance produced on the inside surface of
this hemisphere if it has a radius of 1.5 m.
3) A small lamp has a mean luminous intensity of 80 cd. Calculate the
maximum direct illuminance the lamp produced on a surface under the
following conditions.
a) At a distance of 0.8 m from the lamp.
b) At a distance of 3.2 m from the lamp.
4) A street lamp has a uniform intensity of 1200 cd. It is positioned 7m
above the centre line of a road. Calculate the illuminance on the road
surface directly below the lamp.
Chapter 13: Measurement of Lighting
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