luminous intensity

TheInfoList

OR:

In photometry, luminous intensity is a measure of the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adjac ...

-weighted power emitted by a
light source Light or visible light is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequency, fr ...
in a particular direction per unit
solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The poi ...

, based on the luminosity function, a standardized model of the sensitivity of the
human eye The human eye is a sensory organ (biology), organ, part of the sensory nervous system, that reacts to light, visible light and allows humans to use visual information for various purposes including Visual perception, seeing things, Balance (abil ...

. The unit of luminous intensity is the
candela The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...

(cd), an
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which a ...

.

# Measurement

Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the
visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
and has different sensitivities to
light Light or visible light is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequency, fr ...

of different wavelengths within the spectrum. When adapted for bright conditions (
photopic vision Photopic vision is the visual perception, vision of the human eye, eye under well-lit conditions (luminance levels from 10 to 108 candela per square metre, cd/m2). In humans and many other animals, photopic vision allows color vision, color ...
), the eye is most sensitive to yellow-green light at 555 nm. Light with the same radiant 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. This curve, denoted ''V''(λ) or $\textstyle \overline\left(\lambda\right)$, 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.

# Relationship to other measures

Luminous intensity should not be confused with another photometric unit, luminous flux, which is the total perceived power emitted in all directions. Luminous intensity is the perceived power ''per unit solid angle''. If a lamp has a 1 lumen bulb and the optics of the lamp are set up to focus the light evenly into a 1
steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians ...

beam, then the beam would have a luminous intensity of 1 candela. If the optics were changed to concentrate the beam into 1/2 steradian then the source would have a luminous intensity of 2 candela. The resulting beam is narrower and brighter, though its luminous flux remains unchanged. Luminous intensity is also not the same as the radiant intensity, the corresponding objective
physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
used in the measurement science of
radiometry Radiometry is a set of techniques for measuring electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentu ...
.

# Units

Like other SI base units, the candela has an
operational definition An operational definition specifies concrete, replicable procedures designed to represent a construct. In the words of American psychologist S.S. Stevens (1935), "An operation is the performance which we execute in order to make known a concept." F ...
—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 The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James W ...

s per
steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians ...

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 in a vacuum of 555 nm, which is near the peak of the eye's response to light. If the 1 candela source emitted uniformly in all directions, the total
radiant flux In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the Spec ...
would be about 18.40 mW, since there are 4π steradians in a sphere. Note that a typical modern
candle A candle is an ignitable candle wick, wick embedded in wax, or another flammable solid substance such as tallow, that provides light, and in some cases, a Aroma compound, fragrance. A candle can also provide heat or a method of keeping time. ...

produces very roughly one candela while releasing heat at roughly 80 W. Prior to the definition of the candela, a 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 standard: candlepower. One candlepower was the light produced by a pure
spermaceti Spermaceti is a waxy substance found in the head cavities of the sperm whale The sperm whale or cachalot (''Physeter macrocephalus'') is the largest of the toothed whales and the largest toothed predator. It is the only living member of ...

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. In 1881, Jules Violle 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

thumb , Photopic (black) and scotopic vision, scotopic (green) luminosity functions. The photopic includes the CIE 1931 standard (solid), the Judd–Vos 1978 modified data (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data (dotted). The horizontal axis is wavelength in Nanometre, nm. The luminous intensity for monochromatic light of a particular wavelength λ is given by $I_\mathrm = 683 \cdot \overline(\lambda) \cdot I_\mathrm,$ where *''I''v is the luminous intensity in candelas (cd), *''I''e is the radiant intensity in watts per steradian  (W/sr), *$\overline(\lambda)$ 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 A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a Continuum (measurement), continuum. The word was first used scientifically in optics to describ ...

of wavelengths present to get the luminous intensity: $I_\mathrm = 683 \int_0^\infty \overline(\lambda) \cdot \frac \, d\lambda.$