I.Definition
Irradiance (denoted by $E$) is the radiant flux incident on a surface per unit area. Its SI unit is $W\cdot m^{-2}$
Mathematical Expression:
$$E = \frac{d\Phi}{d$}$$ where $\Phi$ is the radiant flux and $A$ is the surface area.

II.Irradiance from a point source
For an isotropic point source, the radiant intensity in a given direction is denoted by $I$ (unit:$W\cdot sr^{-1}$). Consider a differential surface element $dA$ located at a distance from the source and oriented perpendicular to the incident direction.

• The solid angle subtended by $dA$ at the source is:
  

$$d\Omega = \frac{dA}{r^2}$$

• The radiant flux emitted by the source into this solid angle is:

$$d\Phi = I \cdot d\Omega = I \cdot \frac{dA}{r^2}$$

• Substituting into the definition of irradiance:
  

$$E = \frac{d\Phi}{dA} = \frac{I \cdot \dfrac{dA}{r^2}}{dA} = \frac{I}{r^2}$$

Summary: Under normal incidence, the irradiance on a surface element due to a point source is proportional to the radiant intensity and inversely proportional to the square of the distance from the source. This relationship is known as the inverse square law of irradiance.