### Definition

Irradiance is the power of light per unit area.

Irradiance follows an inverse-square law: irradiance is directly proportional to the inverse square of the distance from the source.

### Formulae

$I=\frac{P}{A}=\frac{k}{{d}^{2}}$
Variable Key

• $I$ is the irradiance of a surface, in watts per square metre (${\text{W m}}^{-2}$).
• $P$ is the power received by the surface, in watts ($\text{W}$).
• $A$ is the surface area, in square metres (${\text{m}}^{2}$).
• $d$ is the distance of the surface from the light source, in metres ($\text{m}$).
• $k$ is a constant, which ensures direct proportionality.

Warning

This formula only works if the direction of the light source is normal to the surface!

Since $I=\frac{k}{{d}^{2}}$, we know that $I{d}^{2}=k$ where $k$ is constant. Therefore, we get:

Variable Key

• ${I}_{1}$ is the irradiance of a surface at a distance of ${d}_{1}$ from the light source.
• ${d}_{1}$ is a distance from the light source.
• ${I}_{2}$ is the irradiance of a surface at a distance of ${d}_{2}$ from the light source.
• ${d}_{2}$ is another distance from the light source.