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The lumen (symbol: lm) is the unit of luminous flux, a measure of the perceived power of visible light emitted by a source, in the International System of Units (SI). Luminous flux differs from power ( radiant flux ), which encompasses all electromagnetic waves emitted, including non-visible ones such as thermal radiation ( infrared ).
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 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.
Luminous flux (in lumens) is a measure of the total amount of light a lamp puts out. The luminous intensity (in candelas) is a measure of how bright the beam in a particular direction is. 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 beam, then the beam would have a luminous ...
Radiant intensity, a radiometric quantity measured in watts per steradian (W/sr) Luminous intensity, a photometric quantity measured in lumens per steradian (lm/sr), or candela (cd) Irradiance, a radiometric quantity, measured in watts per square meter (W/m 2) Intensity (physics), the name for irradiance used in other branches of physics (W/m 2)
Therefore, the absolute magnitude can be calculated from a luminosity in watts: = + where L 0 is the zero point luminosity 3.0128 × 10 28 W and the luminosity in watts can be calculated from an absolute magnitude (although absolute magnitudes are often not measured relative to an absolute flux): L ∗ = L 0 × 10 − 0.4 M b o l ...
Φ v is the luminous flux, in lumens; Φ e,λ is the spectral radiant flux, in watts per nanometre; y (λ), also known as V(λ), is the luminosity function, dimensionless; λ is the wavelength, in nanometres. Formally, the integral is the inner product of the luminosity function with the spectral power distribution. [2]
The relation between watts and lumens is not just a simple scaling factor. We know this already, because the 60 watt incandescent bulb and the 15 watt compact fluorescent can both provide 900 lumens. The definition tells us that 1 watt of pure green 555 nm light is "worth" 683 lumens. It does not say anything about other wavelengths.
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write: =where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m 2 = kg·m −1 ·s −3); Φ is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m 2); and λ is the wavelength (SI unit: meter, m).