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'Luminous efficacy' is a property of light sources, which indicates what portion of the emitted electromagnetic radiation is usable for human vision. It is the ratio of emitted luminous flux to radiant flux. Luminous efficacy is related to the overall efficiency of a light source for illumination, but the overall 'lighting efficiency' also depends on how much of the input energy is converted into electromagnetic waves (whether visible or not).

Contents

Explanation

Efficacy and efficiency

Mathematical definition

Examples

Lighting efficiency

Examples

SI photometry units

See also

References

External links

Explanation

Wavelengths of light outside of the visible spectrum are not useful for illumination because they cannot be seen by the human eye. Furthermore, the eye responds more to some wavelengths of light than others, even within the visible spectrum. This response of the eye is represented by the luminosity function. This is a standardized function which represents the response of a "typical" eye under bright conditions (Photopic vision). One can also define a similar curve for dim conditions (Scotopic vision). When not specified, photopic conditions are generally assumed.
Luminous efficacy measures the fraction of electromagnetic power which is useful for lighting. It is obtained by dividing the luminous flux by the radiant flux. Light with wavelengths outside the visible spectrum does not contribute to the efficacy at all, because the luminous flux of such light is zero. Wavelengths near the peak of the eye's response contribute more strongly than those near the edges.
In SI, luminous efficacy has units of lumens per watt (lm/W). Photopic luminous efficacy has a maximum possible value of 683 lm/W, for the case of monochromatic light at a wavelength of 555 nm (green). Scotopic luminous efficacy reaches a maximum of 1700 lm/W for narrowband light of wavelength 507 nm.

Efficacy and efficiency

In some other systems of units, luminous flux has the same units as radiant flux. The luminous efficacy is then dimensionless. In this case, it is often instead called the 'luminous efficiency' or 'luminous coefficient' and may be expressed as a percentage. For example, it is common to express the luminous efficiency in units where the maximum possible efficacy, 683 lm/W, corresponds to an efficiency of 100%. The distinction between ''efficacy'' and ''efficiency'' is not always carefully maintained in published sources, so it is not uncommon to see "efficiencies" expressed in lumens per watt, or "efficacies" expressed as a percentage.

Mathematical definition

The dimensionless luminous efficiency measures the integrated fraction of the radiant power that contributes to its luminous properties as evaluated by means of the standard luminosity function.^[1] The luminous coefficient is
:
where
:''y''_λ is the standard luminosity function,
:''J''_λ is the spectral power distribution of the radiant intensity.
The luminous coefficient is unity for a narrow band of wavelengths at 555 nanometres.

Examples

Type	Luminous efficacy (lm/W)	Luminous efficiency[2]
Class M star (Antares, Betelgeuse), 3000 K	30	4%
ideal black-body radiator at 4000 K	47.5 [3]	7.0%
Class G star (Sun, Capella), 5800 K	80	12%
natural sunlight	93	14%
ideal black-body radiator at 7000 K	95	14%
ideal white light source	242.5 [4]	35.5%
ideal monochromatic 555 nm source	683 [5]	100%

Lighting efficiency

Artificial light sources are usually evaluated in terms of a related quantity, the '''overall'' luminous efficacy'. This is the ratio between the total luminous flux emitted by a device and the total amount of input power (electrical, etc.) it consumes. This is often simply called “luminous efficacy”, which can be confusing as it also has units of lm/W. It is also sometimes referred to as the 'wall-plug luminous efficacy' or simply 'wall-plug efficacy'. The overall luminous efficacy is a measure of the efficiency of the device with the output adjusted to account for the spectral response curve (the “luminosity function”). When expressed in dimensionless form (for example, as a fraction of the maximum possible luminous efficacy), this value may be called 'overall luminous efficiency', 'wall-plug luminous efficiency', or simply the 'lighting efficiency'.
The main difference between the regular and “overall” efficacies is that the latter account for input energy that is lost as heat or otherwise exits the source as something other than electromagnetic radiation. True luminous efficacy is a property of the radiation emitted by a source. ''Overall'' luminous efficacy is a property of the source as a whole.

Examples

The following table lists overall luminous efficacy and efficiency for various light sources:

Category	Type	Overall luminous efficacy (lm/W)	Overall luminous efficiency[2]
Combustion	candle	0.3 [7]	0.04%
Incandescent	5 W tungsten incandescent	5	0.7%
	40 W tungsten incandescent	12.6 [8]	1.9%
	100 W tungsten incandescent	17.5	2.6%
	glass halogen	16	2.3%
	quartz halogen	24	3.5%
	high-temperature incandescent	35 [4]	5.1%
Fluorescent	5–24 W compact fluorescent	45–60 [10]	6.6%–8.8%
	34 W fluorescent tube (T12)	50	7%
	32 W fluorescent tube (T8)	60	9%
	36 W fluorescent tube (T8)	up to 93	up to 14%
	28 W fluorescent tube (T5)	104	15.2%
Light-emitting diode	white LED	26–70 [11][12]	3.8%–10.2%
	white LED (prototypes)	up to 150 [13][14][15]	up to 22%
Arc lamp	xenon arc lamp	30–50	4.4%–7.3%
	mercury-xenon arc lamp	50–55	7.3%–8.0%
Gas discharge	high pressure sodium lamp	150 [16]	22%
	low pressure sodium lamp	183 up to 200 [17]	27%
	1400 W sulfur lamp	100	15%
Theoretical maximum (monochromatic 540x1012 Hz, approx. 555 nm, green)		683.002	100%

Sources that depend on thermal emission from a solid filament, such as incandescent light bulbs, tend to have low overall efficacy compared to an ideal blackbody source because, as explained by Donald L. Klipstein, “An ideal thermal radiator produces visible light most efficiently at temperatures around 6300°C (6600 K or 11,500°F). Even at this high temperature, a lot of the radiation is either infrared or ultraviolet, and the theoretical luminous efficiency [sic] is 95 lumens per watt. Of course, nothing known to any humans is solid and usable as a light bulb filament at temperatures anywhere close to this. The surface of the sun is not quite that hot.” At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared.

SI photometry units

See also

★ Luminous coefficient

★ Photometry

★ Light pollution

References

1. Van Nostrand's Scientific Encyclopedia, 3rd Edition, , , , D. Van Nostrand Company, Inc., January 1958,
2. Defined such that the maximum value possible is 100%.
3.
4. The Great Internet Light Bulb Book, Part I Klipstein, Donald L.
5. See luminosity function.
6. Defined such that the maximum value possible is 100%.
7. 1 candela
★ 4π steradians/40 W
8. http://physics.ccri.cc.ri.us/keefe/light.htm ''Referenced page is no longer available''.
9. The Great Internet Light Bulb Book, Part I Klipstein, Donald L.
10. China energy saving lamp
11. The Brightest and Most Efficient LEDs and where to get them Klipstein, Donald L.
12. Cree launches the new XLamp 7090 XR-E Series Power LED, the first 160-lumen LED!
13. Improving White LED Efficiency Through Scattered Photon Extraction
14. Cree Demonstrates 131 Lumens per Watt White LED
15. Nichia Corp. claims white LED delivering 150 lumens/Watt efficiency
16. LED or Neon? A scientific comparison
17. Why is lightning coloured? (gas excitations)

External links

★ Hyperphysics has these graphs of efficacy that do not quite comply with the standard definition

★ Energy Efficient Light Bulbs

★ Other Power

★ CIPCO Energy Library