Radiation pressure

Energy and momentum are related by the relativist equation $E^2 = (pc)^2 + (m_0 c^2)^2$ where $E$ is the total energy of the system, $p$ is its momentum, $c$ is the speed of light, and $m_0$ is the rest mass. Since electromagnetic waves have no mass, their energy is related to momentum by:

E = pc.

If a plane electromagnetic wave is completely absorbed by a surface, then the force it feels is $F=\frac{dp}{dt}$ . Using the energy-momentum relation above, $F=\frac1c \frac{dU}{dt}$ . Relating this to the intensity of radiation, $F=\frac1c I A$ . If a wave is completely reflected, then the force will be double (since the momentum of the wave needs to change by $2\times$ the amount).

The radiation pressure is defined as the force per area that a wave exerts on a surface. If the wave is fully absorbed:

\mathcal P_{\mathrm{rad} }^{\mathrm{abs} } = \frac FA = \frac{I}{c}

And if it is fully reflected:

\mathcal P_{\mathrm{rad} }^{\mathrm{ref} } = \frac{2F}{A} = \frac{2I}{c}