A stream of photons impinging normally on a completely absorbing screen in vacuum exerts a pressure $P$. If $I$ is the irradiance then,

The time rate of change of momentum equals force.

$\Rightarrow F=\frac{\Delta p}{\Delta t}$

Force per unit area is pressure

$\Rightarrow P=\frac{1}{A}\frac{\Delta p}{\Delta t}$

But for a photon $E=pc$, where

$p=$ momentum of photon

$E=$ energy of photon

$\therefore \Delta E=c\Delta p$

$\Rightarrow P=\frac{1}{Ac}\frac{\Delta E}{\Delta t}=\frac{1}{c}\left(\frac{\Delta E}{A\Delta t}\right)=\frac{1}{c}\left(I\right)$

Because irradiance $I$ is defined as energy per unit area per unit time.