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What is Luminous Intensity?

light from a desk lamp

Luminous intensity is a measure of power emitted by a light source in a certain direction per unit of solid angle, adjusted to a wavelength weight that is determined by a luminosity function. Because luminous intensity is a measure of how humans react to light of a given power, the luminosity function is weighted according to a standardized model of how the human eye reacts to light of given wavelengths. The SI unit for luminous intensity is the candela, which also has units of watts per steradian. One candela of luminous intensity is equal to 1/683 watts per Steradian.

The notion of the solid angle can be confusing to some. One has to think of it as a three dimensional angle that defines the cone of light coming from a particular source that will eventually hit the human eye. Depending on one’s distance from the source, the solid angle can change, which can have an effect on one’s perception of the luminosity of the source of light. A standard steradian is the cone of light that would illuminate a single square meter of a sphere with a one meter radius around its source. One can calculate the luminous intensity of a source of light for a given steradian value, either big or small, and then multiply this value or divide in order to get to the standard value for one steradian.

Because of natural selection, the human eye has two ways it can see light. In photopic vision, the human eye is the most sensitive to green and yellow light at a wavelength of 555 nanometers. Photopic vision is the visual system adapted for bright conditions. Scotopic vision, on the other hand, is the system that works best in very low-light conditions, and it has its own associated wavelength of high sensitivity. In scotopic vision, this wavelength is somewhere around 500 nanometers. Our eyes are generally much less sensitive to light that ranges in the violet and red to infrared ranges. Both the photopic and scotopic vision curves reflect this fact.

A light source can have the same radiant intensity, but have different values for luminous intensity at different wavelengths depending on the luminosity function. Radiant intensity is a measure of the power of a light source that is not weighted to a luminosity function that is dependent on how the human eye perceives light. It can be thought of as the intensity of the light as it is in the objective world, having nothing to do with the sensitivity of the human eye. For example, a source of light could have a very high radiant intensity but if it falls outside of the range of visible light then, according to the luminosity function that source of light will have a zero-valued luminous intensity. The luminosity function for scotopic vision ranges between the wavelengths of 400 nanometers to 625 nanometers. Any light source outside of that range is necessarily zero-valued.

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