Electromagnetic waves carry momentum as well as energy. In vacuum, the electromagnetic momentum density is related to the Poynting vector by

$$\boxed{\mathbf g=\frac{\mathbf S}{c^2}}.$$

For a plane wave, the energy density $u$ and momentum density magnitude $g$ satisfy

$$g=\frac{u}{c}.$$

A pulse carrying total electromagnetic energy $U$ therefore carries momentum magnitude

$$\boxed{p=\frac{U}{c}}.$$

The momentum points in the direction of energy propagation.

Radiation pressure from absorption

When a wave is absorbed by a surface, its momentum is transferred to the material. For normally incident light of intensity $I$, energy

$$\Delta U=IA\Delta t$$

reaches an area $A$ during time $\Delta t$.

The associated momentum is

$$\Delta p=\frac{\Delta U}{c} =\frac{IA\Delta t}{c}.$$

The average force is therefore

$$F=\frac{\Delta p}{\Delta t}=\frac{IA}{c}.$$

Dividing by area gives the radiation pressure

$$\boxed{P_{\rm rad}=\frac{I}{c}}$$

for ideal absorption at normal incidence.

Radiation pressure from reflection

For ideal specular reflection at normal incidence, the incoming momentum reverses direction. The momentum change is therefore twice as large as for absorption, giving

$$\boxed{P_{\rm rad}=\frac{2I}{c}}.$$

This factor of two is a direct consequence of momentum reversal.

Worked example

A perfectly absorbing surface is illuminated normally with intensity

$$I=1000,\mathrm{W/m^2}.$$

Using

$$c=3.00\times10^8,\mathrm{m/s},$$

the radiation pressure is

$$P_{\rm rad}=\frac{1000}{3.00\times10^8} \approx3.33\times10^{-6},\mathrm{Pa}.$$

For a perfect reflector under the same illumination,

$$P_{\rm rad}\approx6.67\times10^{-6},\mathrm{Pa}.$$

The pressure is tiny on everyday scales, but it is measurable and can become important when forces must be extremely precise or act for long periods.

Momentum conservation with fields

Radiation pressure is one example of a broader principle: momentum can reside in electromagnetic fields and flow through space before being transferred to matter. Forces on matter therefore obey momentum conservation only when field momentum is included along with mechanical momentum.

More general electromagnetic stress states can be described with the Maxwell stress tensor, but the plane-wave results above already capture the central Physics II idea: energy flux carries momentum flux, so absorbing or redirecting electromagnetic radiation exerts a force.