Luminous intensity

Luminous intensity is a physical quantity whose unit of measurement in the International System is the candela. The luminous intensity (I_{textrm{V}}) of a point source in a given direction in the unit solid angle is the luminous flux. It belongs, among other groupings of physical quantities, to the group of photometric quantities.

In other words, the luminous intensity is a part of the luminous flux that falls on the area of a certain volume and depends on the luminous flux of the light source, the angle of the beam and the distance of the measured area from the source. Luminous intensity can also be thought of as the number of photons passing through a unit section of a sample (which can also be a vacuum) in the unit of time.

Luminous flux is an important variable that we should pay attention to when choosing lighting. It indicates the light energy, radiated by the source in 1 second, so it is a form of power.

The luminous intensity for monochromatic light of a particular wavelength \(\lambda\) is given by:

\[I_{\mathrm{v}}=683\cdot {\overline{y}}(\lambda )\cdot I_{\mathrm{e}}\]

where:

  • Iv is the luminous intensity in candelas (cd),
  • Ie is the radiant intensity in watts per steradian  (W/sr),
  • \(\textstyle{\overline{y}}(\lambda )\) 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:

\[\displaystyle I_{\mathrm {v} }=683\int _{0}^{\infty }{\overline {y}}(\lambda )\cdot {\frac {dI_{\mathrm {e} }(\lambda )}{d\lambda }}\,d\lambda\]

The knowledge of the luminous intensity emitted by a source in different directions allows the construction of the photometric solid, which is that geometric figure delimited by a closed surface, formed by the place of the extreme points of segments whose length is proportional to the luminous intensity in that direction and center in the source. If the photometric solid of an artificial source is known, from it the value of the luminous intensity in the various directions can be traced, which is useful for design purposes.

Often the photometric solids present symmetries around one or more axes, in this case the solid is completely identifiable through one or more plane polar diagrams, obtained by intersecting the photometric surface with one or more planes passing through the axis of symmetry. Thus the photometric curves of the source under examination are obtained.

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