Irradiance

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.

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

Variable Key

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

I_{1} {d_{1}}^{2} = I_{2} {d_{2}}^{2}

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.