Candela

# Candela

Discussion

Encyclopedia
The candela is the SI base unit
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

of luminous intensity
Luminous intensity
In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye...

; that is, power emitted by a light source in a particular direction, weighted by the luminosity function
Luminosity function
The luminosity function or luminous efficiency function describes the average visual sensitivity of the human eye to light of different wavelengths. It should not be considered perfectly accurate in every case, but it is a very good representation of visual sensitivity of the human eye and it is...

(a standardized model of the sensitivity of the human eye to different wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

s, also known as the luminous efficiency function). A common candle
Candle
A candle is a solid block or cylinder of wax with an embedded wick, which is lit to provide light, and sometimes heat.Today, most candles are made from paraffin. Candles can also be made from beeswax, soy, other plant waxes, and tallow...

emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.

The word candela means candle in Latin, as well as in many modern languages.

## Definition

Like other SI base units, the candela has an operational definition
Operational definition
An operational definition defines something in terms of the specific process or set of validation tests used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman and is a part of...

—it is defined by a description of a physical process that will produce one candela of luminous intensity. Since the 16th General Conference on Weights and Measures
General Conference on Weights and Measures
The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...

(CGPM) in 1979, the candela has been defined as:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 hertz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

and that has a radiant intensity
In radiometry, radiant intensity is a measure of the intensity of electromagnetic radiation. It is defined as power per unit solid angle. The SI unit of radiant intensity is watts per steradian . Radiant intensity is distinct from irradiance and radiant exitance, which are often called intensity...

in that direction of  watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

The steradian is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane...

.

The definition describes how to produce a light source that (by definition) emits one candela. Such a source could then be used to calibrate instruments designed to measure luminous intensity.

The candela is sometimes still called by the old name candle, such as in foot-candle
Foot-candle
A foot-candle is a non-SI unit of illuminance or light intensity widely used in photography, film, television, conservation lighting, and the lighting industry...

and the modern definition of candlepower
Candlepower
Candlepower is a now-obsolete unit which was used to express levels of light intensity in terms of the light emitted by a candle of specific size and constituents...

.

## Explanation

The frequency chosen is in the visible spectrum near green
Green
Green is a color, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 520–570 nanometres. In the subtractive color system, it is not a primary color, but is created out of a mixture of yellow and blue, or yellow and cyan; it is considered...

, corresponding to a wavelength of about 555 nanometers. The human eye
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...

is most sensitive to this frequency, when adapted
In ocular physiology, adaptation is the ability of the eye to adjust to various levels of darkness and light.-Efficacy:The human eye can function from very dark to very bright levels of light; its sensing capabilities reach across nine orders of magnitude. This means that the brightest and the...

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

where Iv(λ) is the luminous intensity in candelas, Ie(λ) is the radiant intensity in W/sr and 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
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

of wavelengths present to get the total luminous intensity.

### Examples

A common candle emits light with roughly 1 cd luminous intensity. A 25 W compact fluorescent light bulb puts out around 1700 lumen
Lumen (unit)
The lumen is the SI derived unit of luminous flux, a measure of the total "amount" of visible light emitted by a source. Luminous flux differs from power in that luminous flux measurements reflect the varying sensitivity of the human eye to different wavelengths of light, while radiant flux...

s; if that light is radiated equally in all directions, it will have an intensity of around 135 cd. Focused into a 20° beam, it will have an intensity of around 18 000 cd.

The luminous intensity of light-emitting diode
Light-emitting diode
A light-emitting diode is a semiconductor light source. LEDs are used as indicator lamps in many devices and are increasingly used for other lighting...

s is measured in millicandela (mcd), or thousandths of a candela. Indicator LEDs are typically in the 50 mcd range; "ultra-bright" LEDs can reach 15 000 mcd, or higher.

## Origin

Prior to 1948, various standards for luminous intensity were in use in a number of 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 was the English
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...

standard of candlepower. One candlepower was the light produced by a pure spermaceti
Spermaceti
Spermaceti is a wax present in the head cavities of the sperm whale . Originally mistaken for the whales' sperm , spermaceti is created in the spermaceti organ inside the whale's head and connected to its nasal passage...

candle weighing one sixth of a pound and burning at a rate of 120 grains per hour. Germany, Austria and Scandinavia used the Hefnerkerze, a unit based on the output of a Hefner lamp
Hefner lamp
The Hefner lamp, or in German Hefnerkerze, is a flame lamp used in photometry that burns amyl acetate.The lamp was invented by Friedrich von Hefner-Alteneck in 1884 and he proposed its use as a standard flame for photometric purposes with a luminous intensity unit of the Hefnerkerze...

.

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
Black body
A black body is an idealized physical body that absorbs all incident electromagnetic radiation. Because of this perfect absorptivity at all wavelengths, a black body is also the best possible emitter of thermal radiation, which it radiates incandescently in a characteristic, continuous spectrum...

) at the temperature of freezing platinum
Platinum
Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...

. 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 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
In optics, radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which characterize the light's interaction with the human eye...

, the 16th CGPM 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 in terms of the second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

(an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition.

### Relationship between luminous intensity and luminous flux

If a source emits a known luminous intensity Iv (in candelas) in a well-defined cone, the total luminous flux
Luminous flux
In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of...

Φv in lumen
Lumen (unit)
The lumen is the SI derived unit of luminous flux, a measure of the total "amount" of visible light emitted by a source. Luminous flux differs from power in that luminous flux measurements reflect the varying sensitivity of the human eye to different wavelengths of light, while radiant flux...

s is given by
Φv = Iv ⋅ 2π ⋅ (1 - cos(A/2)),

where A is the radiation angle of the lamp—the full vertex angle of the emission cone. For example, a lamp that emits 590 cd with a radiation angle of 40° emits about 223 lumens. See MR16
MR16
MR16 and MR11 are standard formats for halogen multifaceted reflector light bulbs made by a variety of manufacturers. MR16-compatible LED lamps are also available...

for emission angles of some common lamps.

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.