Radiation pressure

Light carries not only energy but also momentum: striking a surface, it pushes it. The pressure exerted by an electromagnetic wave is:

Radiation pressure

$\ev{P_\text{rad} = \frac{|\vec{I}|}{c}}$

This formula holds for a surface that absorbs all the radiation. If instead the surface reflects it completely, the momentum changes sign rather than vanishing, and the pressure doubles: $P_\text{rad} = 2|\vec{I}|/c$. Microscopically: photons carry momentum $p = E/c$, and transferring it (or reversing it) generates a force on the surface.

Example — A solar sail

With $|\vec{I}| = 1{,}4\;\text{kW/m}^2$ (the solar irradiance at Earth’s orbit), the radiation pressure is $P_\text{rad} = \frac{1400}{3\cdot 10^8} \approx 4{,}7\cdot 10^{-6}\;\text{Pa}$ A sail of $100\;\text{m}^2$ receives a force of just $4{,}7\cdot 10^{-4}$ N: minuscule, but constant and requiring no fuel. The principle is used in real space missions such as the IKAROS probe (2010) and LightSail (2019).

The radiation pressure equals the energy density of the wave (for an absorber): a deep link between energy carried and thrust exerted. On an astronomical scale it is responsible for the tail of comets, always pointing away from the Sun.

Links

Topics: Electromagnetic waves Concepts: Radiation pressure · Poynting vector

Related exercises: Problem — Radiation pressure at Earth’s orbit · Problem — Dimensional analysis of the Poynting vector · Problem — Solar sail