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 Page 1
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 10 12 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. 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 Page 2
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) 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 Page 3
E = illuminance on surface (lx) F = total flux reaching surface (lm) A = area of the surface (m 2 ) Figure 13.3: Summary of lighting measurements F I π E F A Chapter 13: Measurement of Lighting Page 4
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 I = 100 cd = 4 So Total flux = 1256.64 lm b) Know F = 1256.64 0.25 = 314.16 lm A = 3 0.7 = 2.1 m 2 So So illuminance = 150 lx Chapter 13: Measurement of Lighting Page 5
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. 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 Page 6
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 = 2 m So So illuminance at 2 m = 300 lx b) I = 1200 cd d = 6 m So So illuminance at 6 m = 33.33 lx Chapter 13: Measurement of Lighting Page 7
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 Page 8