Answer
The radiation pressure on the surface is equal to the energy density in the incident beam.
Work Step by Step
We can write an expression for the energy density of an electromagnetic wave:
$u = \frac{1}{2}~\epsilon_0~E^2$
We can show that $p_r = u$:
$p_r = \frac{I}{c}$
$p_r = \frac{\frac{E^2}{2c~\mu_0}}{c}$
$p_r = \frac{E^2}{2c^2~\mu_0}$
$p_r = \frac{E^2}{2(\frac{1}{\sqrt{\mu_0~\epsilon_0}})^2~\mu_0}$
$p_r = \frac{\mu_0~\epsilon_0~E^2}{2~\mu_0}$
$p_r = \frac{\epsilon_0~E^2}{2}$
$p_r = u$
The radiation pressure on the surface is equal to the energy density in the incident beam.
