# Irradiance and Illuminance

Published on 24/2/2012 & updated on Wednesday 27th of June 2018 at 07:37:02 PMHOME / ILLUMINATION ENGINEERING / THEORY OF LIGHT

**Irradiance**is the radiant flux received by the detector area. The unit of

**irradiance**is W/m

^{2}.

**Irradiance**is denoted by E

_{e,λ}, φ

_{s}is the received radiant flux on the detector surface and A

_{D}is the detector area or surface. Irradiance always follows the Inverse Square Law. Suppose from a point source the radiant flux is being received by two surfaces of A

_{1}and A

_{2}where they are equal surface area. They are placed at r

_{1}and r

_{2}distance.

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Now the flux received by the surface
And the flux received by the surface
Where, I_{e,λ} radiant intensity and ω solid angle.

Again the radiant flux received per unit area for A_{1} and A_{2} are
Here A_{1} and A_{2} are equal.
Putting the φ_{e,λ} = I_{e,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, K_{m} is the constant which is called maximum spectral luminous efficacy and its value is 683 lm/W.
By definition the luminous flux received by unit area of the detector is called **Illuminance**.
Its unit is Lux or Lumen per sq. meter (lm/sq. m).
It also follows the same inverse square law, i.e.
E_{v} is related to the surface dA where luminous flux is falling on this surface perpendicularly.
E'_{v} is related to the surface dA' where this surface creates an angle Ɵ to the base plane.
As per figure above,
This above equation can be written making it generalized,

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