Luminous flux

The luminous flux is a measure of the perceived light power. It differs from radiant flux, the measure of the total power emitted, in that it is adjusted to reflect the sensitivity of the human eye to different wavelengths.

Its unit of measurement in the International System of Units is the lumen (lm) and is defined from the basic SI unit, the candela (cd), as:

lm=cd⋅ ⋅ sr{displaystyle {rm {lm=cdcdot sr}}}}

The luminous flux is obtained by weighting the power for each wavelength with the function of luminosity, which represents the sensitivity of the eye according to the wavelength. The luminous flux is therefore the weighted sum of power in all the wavelengths of the visible spectrum. Radiation outside the visible spectrum does not contribute to the luminous flux. So, for any point of light, if F{displaystyle scriptstyle {F}} represents the luminous flux, ≈ ≈ (λ λ ){displaystyle scriptstyle {Philambda}} symbolizes the spectral radiant power of the point of light in question and V(λ λ ){displaystyle scriptstyle {V(lambda)}} the luminous sensitivity function, then:

F=683,002∫ ∫ λ λ visible≈ ≈ (λ λ )V(λ λ )dλ λ {displaystyle F=683{,}002int _{lambda _{mathrm {visible}}}}}{ }Phi (lambda)V(lambda),dlambda }

Under photopic conditions a monochromatic light of 555 nm (green colour) with a radiant flow of 1 W, generates a luminous flux of 683,002 lm, which corresponds to the maximum response of the human eye. On the other hand, the same radiation flow located in another wavelength different from that of the peak would generate a smaller luminous flux, according to the curve V(λ λ ){displaystyle scriptstyle {V(lambda)}}.

Relationship with luminous intensity

Luminous flux (in lumens) is a measure of the total light output emitted by a lamp (perceived quantity). Luminous intensity (in candelas) is a measure of how bright the beam is in a particular direction. Considering the formula:

lm=cd⋅ ⋅ sr{displaystyle {rm {lm=cdcdot sr}}}}

If a lamp has a light source of 1 lumen and the optics of the lamp are set to focus all light evenly within 1 steradian, the beam would have a luminous intensity of 1 candela. If the optics are changed to focus the beam by half a steradian then the source would have a luminous intensity of 2 candelas, ie the resulting beam is narrower and brighter, however the luminous flux remains the same.