# Luminous intensity

## Overview

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.

Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions (photopic vision), the eye is most sensitive to greenish-yellow 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 $V(\lambda)$ or $\overline{y}(\lambda)$, 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, 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, the corresponding objective physical quantity used in the measurement science of radiometry.

## Units

Like other SI base units, the candela has an operational definition—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 540 THz light, and that has a radiant intensity of 1/683 watts per steradian in a given direction, that light source will emit one candela in the specified direction.[1]

The 540 THz frequency used in the definition corresponds to a wavelength of about 555 nm, which is green light near the peak of the eye's response. Since there are about 12.6 steradians in a sphere, the total radiant flux would be about 18.40 mW, if the source emitted uniformly in all directions. A typical candle produces very roughly one candela of luminous intensity.

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. It was superseded by the candela in 1946.

## Usage

The luminous intensity for monochromatic light of a particular wavelength $\lambda$ is given by

$I_v= 683I\,\overline{y}(\lambda),$

where

$I_v$ is the luminous intensity in candelas,
$I$ is the radiant intensity in W/sr,
$\overline{y}(\lambda)$ 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 luminous intensity:

$I_v= 683 \int^\infin_0 I(\lambda)\,\overline{y}(\lambda) d\lambda.$