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# Candela

The candela (symbol: cd) is the SI base unit of luminous intensity (that is, power emitted by a light source in a particular direction, weighted by the luminosity function, a standardized model of the sensitivity of the human eye to different wavelengths).

## Definition

Since the 16th General Conference on Weights and Measures in 1979, the candela has been defined as follows:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Note: The candela is sometimes still called by the old name candle [5], such as in foot-candle and the modern definition of candlepower.

## Explanation

The frequency chosen is in the visible spectrum near green, corresponding to a wavelength of about 555 nanometers. The human eye is most sensitive to this frequency, when adapted for bright conditions. At other frequencies, more radiant intensity is required to achieve the same luminous intensity, according to the frequency response of the human eye. The luminous intensity for light of a particular wavelength λ is given by

$I_v(\lambda)= 683.002\,\overline{y}(\lambda) I(\lambda)$

where Iv(λ) is the luminous intensity in candelas, I(λ) is the radiant intensity in W/sr and $\overline{y}(\lambda)$ is the standard luminosity function. If more than one wavelength is present (as is usually the case), one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity.

A common candle emits roughly 1 cd. A 100 W incandescent lightbulb emits about 120 cd.

## Origin

Prior to 1948, there existed a variety of standards for luminous intensity in use in various countries. These were typically based on the brightness of the flame from a "standard candle" of defined composition, or the brightness of an incandescent filament of specific design. One of the best-known of these standards was the candlepower.

It became clear that a better-defined unit was needed. The Commission internationale de l'éclairage (International Commission on Illumination) and the CIPM proposed a “new candle” based on the luminance of a Planck radiator (a black body) at the temperature of freezing platinum. The value of the new unit was chosen to make it similar to the earlier unit candlepower. The decision was promulgated by the CIPM in 1946:

The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre.

It was then ratified in 1948 by the 9th CGPM which adopted a new name for this unit, the candela. In 1967 the 13th CGPM (Resolution 5, CR, 104 and Metrologia, 1968, 4, 43-44) removed the term "new candle" and gave an amended version of the candela definition, specifying the atmospheric pressure applied to the freezing platinum:

The candela is the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons per square metre.

In 1979, because of the difficulties in realizing a Planck radiator at high temperatures, and the new possibilities offered by radiometry, 16th CGPM (1979, Resolution 3; CR, 100 and Metrologia, 1980, 16, 56) adopted the modern definition of the candela. The arbitrary (1/683) term was chosen so that the new definition would exactly match the old definition. Although the candela is now defined partly in terms of the watt, which is a derived SI unit of power, the candela remains a base unit of the SI system, by definition.[6]

## SI photometric light units

SI photometry units
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Quantity Symbol SI unit Abbr. Notes
Luminous energy Qv lumen second lm·s units are sometimes called talbots
Luminous flux F lumen (= cd·sr) lm also called luminous power
Luminous intensity Iv candela (= lm/sr) cd an SI base unit
Luminance Lv candela per square metre cd/m2 units are sometimes called nits
Illuminance Ev lux (= lm/m2) lx Used for light incident on a surface
Luminous emittance Mv lux (= lm/m2) lx Used for light emitted from a surface
Luminous efficacy   lumen per watt lm/W ratio of luminous flux to radiant flux; maximum possible is 683.002 lm/W
Units-interrelation diagram   (full page)

### Relationship between luminous intensity and luminous flux

If a source emits a known intensity (in candelas) in a well-defined cone, the total luminous flux in lumens can be calculated by taking the number of candelas, and dividing it by the number in the table below that corresponds to the "radiation angle" of the lamp (the full vertex angle of the emission cone). See MR16 for emission angles of some common lamps. Theory Formulas Online converter

• Example: A lamp that emits 590 cd with a radiation angle of 40°: 590/2.64 = approximately 223 lumens.
Radiation angle Divide by
167.22
10° 41.82
15° 18.50
20° 10.48
25° 6.71
30° 4.67
35° 3.44
40° 2.64
45° 2.09

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4π: a uniform 1 candela source emits 12.6 lumens.

## References

• The Unit of Luminous Intensity: Candela (cd). Retrieved on 2006-02-08.
• Base unit definitions: Candela. The NIST Reference on Constants, Units, and Uncertainty. Retrieved on 2006-02-08.