Irradiance and Illuminance

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Key learnings:
  • Irradiance Definition: Irradiance is defined as the radiant flux received by a detector area, measured in W/m².
  • Inverse Square Law: Irradiance follows the inverse square law, decreasing with the square of the distance from the light source.
  • Illuminance Definition: Illuminance is defined as the luminous flux received per unit area of the detector, measured in lux (lm/m²).
  • Illuminance vs Irradiance: Illuminance can be derived from irradiance using the conversion factor, highlighting the relationship between the two.
  • Luminous Flux and Angle: Illuminance on a surface depends on the angle of incidence of the light.

Irradiance is defined as the radiant flux received by a detector area, measured in watts per square meter (W/m²). It is denoted by Ee,λ,

φs represents the received radiant flux on the detector surface, while AD is the area of the detector.
Irradiance always follows the Inverse Square Law. Suppose from a point source the radiant flux is being received by two surfaces of A1 and A2 where they are equal surface area. They are placed at r1 and r2 distance.

Now the flux received by the surface

And the flux received by the surface
Where, Ie,λ radiant intensity and ω solid angle.

Again the radiant flux received per unit area for A1 and A2 are

Here A1 and A2 are equal.
Putting the φe,λ = Ie,λ ω in the equation we get

This is Inverse Square Law of irradiance.

If we convert this irradiance into Illuminance then we should follow the conversion equation i.e.

Where, Km is the constant which is called maximum spectral luminous efficacy and its value is 683 lm/W.
Illuminance is defined as the luminous flux received per unit area of the detector.
Its unit is Lux or Lumen per sq. meter (lm/sq. m).
It also follows the same inverse square law, i.e.

irradiance and illuminance
Ev is related to the surface dA where luminous flux is falling on this surface perpendicularly.
E’v relates to a surface dA’ that forms an angle θ with the base plane.
As per figure above,

This above equation can be written making it generalized,

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