Question

Show that the radiation pressure exerted by an EM wave of intensity I on a surface kept in vacuum is $\frac{I}{C}$.

Answer 1

Radiation pressure
$P=\frac{Force}{Area}=\frac{F}{A}$

$P=\frac{1}{A}\left(\frac{\Delta p}{\Delta t}\right)$ ...(i)

Energy imparted by wave I time $\Delta t,$
$\Delta U=c.\Delta p$

$P=\frac{1}{A}\left(\frac{\Delta U}{\Delta t}\right)\frac{1}{c}$
We know $I=\frac{Energy}{\text{per unit time per unit area}}$

$I=\frac{1}{A}\left(\frac{\Delta p}{\Delta t}\right)$

$P=\frac{I}{c}$

Final Answer:

$P=\frac{I}{c}$