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

(N/A) The radiation pressure $P$ is defined as the force per unit area,$P = \frac{F}{A}$.
According to Newton's second law,force is the rate of change of momentum,$F = \frac{dp}{dt}$.
For an electromagnetic wave,the relationship between energy $U$ and momentum $p$ is given by $p = \frac{U}{c}$.
Substituting this into the force equation,we get $F = \frac{d}{dt} \left( \frac{U}{c} \right) = \frac{1}{c} \frac{dU}{dt}$.
Intensity $I$ is defined as the energy incident per unit area per unit time,$I = \frac{1}{A} \frac{dU}{dt}$,which implies $\frac{dU}{dt} = I \cdot A$.
Substituting this into the expression for force,$F = \frac{1}{c} (I \cdot A)$.
Finally,the pressure $P = \frac{F}{A} = \frac{I \cdot A}{A \cdot c} = \frac{I}{c}$.