# Light output

Physical size
Surname Light output
Formula symbol ${\ displaystyle \ eta, \, \ eta _ {\ mathrm {v}} \,}$
Size and
unit system
unit dimension
SI lm · W −1 M −1 · L −2 · T 3 · J

The light output of a lamp is the quotient of the luminous flux emitted by the lamp and the power consumed by it . Your SI unit is lumen by Watt . ${\ displaystyle \ eta _ {\ mathrm {v}}}$ ${\ displaystyle \ Phi _ {\ mathrm {v}}}$ ${\ displaystyle P}$

${\ displaystyle \ eta _ {\ mathrm {v}} \, = \, {\ frac {\ Phi _ {\ mathrm {v}}} {P}}}$

The greater its value, the greater the luminous flux that can be used by the eye for a given power consumption of the lamp.

## definition

The light output of a lamp is made up of two factors: the radiation output of the lamp (proportion of the power consumed that is emitted as radiation) and the photometric radiation equivalent of the radiation emitted (sensitivity of the eye to this radiation): ${\ displaystyle \ eta _ {\ mathrm {e}}}$ ${\ displaystyle K}$

${\ displaystyle \ eta _ {\ mathrm {v}} \, = \, \ eta _ {\ mathrm {e}} \ cdot K = \, {\ frac {\ Phi _ {\ mathrm {e}}} { P}} \ cdot {\ frac {\ Phi _ {\ mathrm {v}}} {\ Phi _ {\ mathrm {e}}}}}$.

The English term luminous efficacy can denote (luminous efficacy of radiation) or (overall luminous efficacy) depending on the context . ${\ displaystyle K}$ ${\ displaystyle \ eta _ {\ mathrm {v}}}$

The radiation output ( English radiant efficiency is) of a light source of the quotient of the emitted from the light source radiation power and the recorded (usually electric) power : ${\ displaystyle \ eta _ {\ mathrm {e}}}$ ${\ displaystyle \ Phi _ {\ mathrm {e}}}$${\ displaystyle P}$

${\ displaystyle \ eta _ {\ mathrm {e}} \, = \, {\ frac {\ Phi _ {\ mathrm {e}}} {P}}}$

The greater this number, the greater the proportion of the power consumed that is emitted as electromagnetic radiation. Usually only part of the emitted radiation power is in the visible spectral range and can therefore be used as "light" by the eye.

The human eye is differently sensitive depending on the wavelength of the light. In order to describe the extent to which electromagnetic radiation can be used as visible light, the radiation power measured in watts is multiplied by a factor that describes the sensitivity of the eye and is strongly dependent on the wavelength . This factor is the photometric radiation equivalent. The result is the luminous flux , which is specified in the SI unit of lumen : ${\ textstyle \ Phi _ {\ mathrm {e}}}$${\ textstyle K}$${\ textstyle \ lambda}$ ${\ displaystyle \ Phi _ {\ mathrm {v}}}$

${\ displaystyle \ Phi _ {\ mathrm {v}} = K \ cdot \ Phi _ {\ mathrm {e}} \, \,}$.

The greater K , the greater the luminous flux that can be used by the eye for a given radiant power of a light source. The eye is most sensitive to green light with a wavelength of 555 nm; For monochromatic light of this wavelength, K has its maximum possible value of 683 lm / W. Usually, however, light is a mixture of electromagnetic radiation of different wavelengths. K is then the weighted mean (“average”) of the photometric radiation equivalent of the individual wavelengths.

## Light output of some light sources

Radiation power of a Planck radiator at different temperatures. A large part of the radiation emitted lies outside the visible spectral range

Glow wire temperature (upper curve) and relative luminous efficacy (lower curve) of an incandescent lamp 12V / 60W depending on the operating voltage. The light output is roughly doubled with a 20 percent increase in the operating voltage, but the service life is drastically reduced.

Since most of the radiation emitted lies outside the visible spectral range, thermal emitters generally have only a low photometric radiation equivalent and, despite the high radiation yield, only achieve a low light yield. The light output can be increased through higher temperatures, but for this advantage you have to accept other disadvantages. In the case of incandescent lamps, for example, an increase in the operating voltage by 1% leads to an increase in output by 1.5 to 1.6% and the luminous flux by 3.4 to 4% (i.e. a better light yield), but also to a reduction in service life by 12 to 16%. An overvoltage of around 10% reduces the service life to around 50%.

In the case of some incandescent lamps that are operated briefly, a significantly shorter service life is accepted in order to achieve the highest possible light output. While a normal general-purpose incandescent lamp (100 W) achieves around 14 lm / W with a service life of 1000 hours, cinema projection lamps achieve 27 lm / W, but only have a service life of 100 hours. Narrow film lamps achieve 27.7 lm / W, but their service life is limited to 25 hours. The upper limit of the light output that can be achieved with incandescent lamps is around 40 lm / W.

Light sources such as fluorescent lamps or LED lamps achieve significantly lower radiation yields because of the lossy ballast electronics required, as well as the light generation, conversion and internal absorption losses. However, they emit a large part of the radiation generated in the visible range and therefore achieve significantly better light yields than incandescent lamps. The highest known luminous efficacy is achieved with 200 lm / W from light-emitting diodes and low-pressure sodium vapor lamps . The disadvantage of the latter, however, is their poor color rendering.

The energy efficiency class of the EU energy label provides information on the respective luminous efficacy of incandescent lamps, fluorescent lamps and halogen lamps for orientation when buying light sources . The energy efficiency class A stands for products with high luminous efficiency.

Lamp type Light output Power consumption for 700 lumens
Lightbulb 10 to 030 lm / W 60 W
Energy saving lamp 50 to 080 lm / W 12 W.
Led lamp 60 to 160 lm / W 08 W.

There is an extensive table with the light output in the article Light source # examples .

## Remarks

1. At very low brightness the eye has a different sensitivity curve. The photometric radiation equivalent for night vision is denoted by K ' .
2. The arbitrarily determined numerical value 683 lm / W results from the definition of the unit "lumen" from 1979. It was chosen so that the photometric units of measurement corresponded as closely as possible to their definition valid until 1979.