Luminous intensity

# Luminous intensity

Discussion

Encyclopedia
In photometry
Photometry (optics)
Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy in terms of absolute power; rather, in photometry, the radiant power at each wavelength is weighted by...

, luminous intensity is a measure of the 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...

-weighted power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

emitted by a light source in a particular direction per unit solid angle
Solid angle
The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large that object appears to an observer looking from that point...

, based on 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
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...

. The SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

unit of luminous intensity is the candela
Candela
The candela 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 common candle emits light with a luminous intensity of roughly one candela...

(cd), an 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...

.

Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the visible spectrum
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...

and has different sensitivities to light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

of different wavelengths within the spectrum. When adapted for bright conditions (photopic vision
Photopic vision
Photopic vision is the vision of the eye under well-lit conditions. In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher visual acuity and temporal resolution than available with scotopic vision.The human eye uses three types...

), the eye is most sensitive to greenish-yellow light at 555 nm. Light with the same 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...

at other wavelengths has a lower luminous intensity. The curve which measures the response of the human eye to light is a defined standard, known as 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...

. This curve, denoted V(λ) or , is based on an average of widely differing experimental data from scientists using different measurement techniques. For instance, the measured responses of the eye to violet light varied by a factor of ten.

Luminous intensity should not be confused with another photometric unit, 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...

, which is the total perceived power emitted in all directions. Luminous intensity is the perceived power per unit solid angle.
Luminous intensity is also not the same as the 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...

, the corresponding objective physical quantity
Physical quantity
A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...

used in the measurement science of 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...

.

## Units

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 the description of a physical process that will produce one candela of luminous intensity. By definition, if one constructs a light source that emits monochromatic green light with a frequency of 540 THz, and that has a radiant intensity of 1/683 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...

in a given direction, that light source will emit one candela in the specified direction.

The frequency of light used in the definition corresponds to a wavelength of 555 nm, which is near the peak of the eye's response to light. If the source emitted uniformly in all directions, the total radiant flux

would be about 18.40 mW, since there are 4π steradians in a sphere. A typical candle produces very roughly one candela of luminous intensity.

Prior to the definition of the candela, variety of units for luminous intensity were used 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 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: 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...

. 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...

. In 1881, Jules Violle
Jules Violle
Jules Louis Gabriel Violle was a French physicist and inventor.He is notable for having determined the solar constant at Mont Blanc in 1875, and, in 1881, for proposing a standard for luminous intensity, called the Violle, equal to the light emitted by 1 cm² of platinum at its melting point...

proposed the Violle as a unit of luminous intensity, and it was notable as the first unit of light intensity that did not depend on the properties of a particular lamp. All of these units were superseded by the definition of the candela.

## Usage

The luminous intensity for monochromatic light of a particular wavelength λ is given by

where
Iv is the luminous intensity in candelas (cd),
Ie is the radiant intensity in watts per steradian (W/sr), is the standard 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...

.

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 luminous intensity: