KAHIBARO
Table of Contents
Light Can Push
Radiation pressure is the pressure exerted by electromagnetic radiation when it transfers momentum to a surface. Light is often introduced as a wave, but it also carries momentum. When light is absorbed, reflected, or emitted, momentum is exchanged, and this produces a force.
This idea may seem surprising because light has no rest mass, yet it still carries energy and momentum. Because momentum transfer per unit time is force, and force per unit area is pressure, light can produce a measurable pressure on matter.
Momentum Carried by Radiation
Electromagnetic waves carry energy, and with that energy they also carry momentum. For radiation in free space, the momentum $p$ associated with energy $E$ is
$$
p = \frac{E}{c}
$$
where $c$ is the speed of light.
If a beam of light strikes a surface, the change in momentum of the light gives a force on the surface. A larger energy flow means a larger momentum flow, and therefore a larger pressure.
The energy flow per unit area per unit time is the intensity $I$. Since intensity tells us how much energy arrives each second on each square meter, it also tells us how much momentum arrives.
Important relation between energy and momentum for radiation:
$$
p = \frac{E}{c}
$$
This is the key reason light can exert a force and pressure.
Pressure on an Absorbing Surface
Consider light of intensity $I$ falling perpendicularly on a surface. In time $\Delta t$, the energy arriving on area $A$ is
$$
E = I A \Delta t
$$
The momentum carried by that radiation is
$$
p = \frac{E}{c} = \frac{I A \Delta t}{c}
$$
If the surface absorbs all the light, that momentum is transferred to the surface. The force is
$$
F = \frac{\Delta p}{\Delta t} = \frac{I A}{c}
$$
So the radiation pressure $P$ is
$$
P = \frac{F}{A} = \frac{I}{c}
$$
This is the pressure for complete absorption.
For a perfectly absorbing surface at normal incidence:
$$
P = \frac{I}{c}
$$
Pressure on a Reflecting Surface
If the surface reflects the light back, the momentum change is larger. Before reflection, the light has momentum toward the surface. After reflection, it has momentum away from the surface. The total change in momentum is therefore twice as large as in absorption.
So for perfect reflection,
$$
P = \frac{2I}{c}
$$
A perfectly reflecting surface experiences twice the radiation pressure of a perfectly absorbing one, for the same intensity.
For a perfectly reflecting surface at normal incidence:
$$
P = \frac{2I}{c}
$$
Reflection doubles the momentum change and therefore doubles the pressure.
Comparison of Cases
The main results can be summarized clearly.
| Surface type | Momentum change of light | Radiation pressure |
|---|---|---|
| Perfect absorber | $\Delta p = p$ | $P = \frac{I}{c}$ |
| Perfect reflector | $\Delta p = 2p$ | $P = \frac{2I}{c}$ |
Real materials are often between these two limits. Some light is absorbed and some is reflected, so the actual pressure lies between $\frac{I}{c}$ and $\frac{2I}{c}$.
Force from Radiation Pressure
If the pressure is known, the force on a surface of area $A$ is
$$
F = PA
$$
So for a perfectly absorbing surface,
$$
F = \frac{IA}{c}
$$
and for a perfectly reflecting surface,
$$
F = \frac{2IA}{c}
$$
These forces are usually very small in everyday situations, because $c$ is very large. But with intense light, or over very large areas, the effect becomes important.
Radiation force is found from pressure just like ordinary pressure:
$$
F = PA
$$
Physical Interpretation
Radiation pressure is a direct consequence of momentum transport by electromagnetic waves. A beam of light does not just bring energy, it also brings directed momentum. When that directed momentum is reduced, stopped, or reversed by a surface, the surface feels a push.
This is similar in spirit to wind pressure, but with a different mechanism. Air pressure comes from collisions of particles with mass. Radiation pressure comes from momentum carried by electromagnetic fields.
Relation to Electromagnetic Waves
In electromagnetic theory, the intensity of a wave is related to the rate at which energy flows through space. Since energy flow is tied to momentum flow, a stronger electromagnetic wave produces greater radiation pressure.
A more advanced description uses the Poynting vector to describe energy flow. Here, the important point is simple: more intensity means more pressure.
Everyday and Scientific Examples
Radiation pressure is small for ordinary sunlight, but it is real and measurable. It plays a role in several important situations. Sunlight exerts pressure on dust particles in space. It also acts on spacecraft surfaces. Very powerful lasers can produce noticeable forces on small objects. A solar sail is a large reflective sheet that uses sunlight itself to provide thrust in space.
Solar Sail Idea
A solar sail works best when it reflects light, because reflection gives a larger pressure than absorption. The force is tiny, but in space there is very little friction, so even a small continuous force can gradually change the motion of a spacecraft.
Units
Pressure is measured in pascals, where
$$
1 \ \mathrm{Pa} = 1 \ \mathrm{N/m^2}
$$
Intensity is measured in
$$
\mathrm{W/m^2}
$$
Since
$$
1 \ \mathrm{W} = 1 \ \mathrm{J/s}
$$
the formula $P = I/c$ has the correct units of pressure.
Final Core Formulas
The essential formulas of radiation pressure are the following.
Radiation pressure at normal incidence:
For absorption,
$$
P = \frac{I}{c}
$$
For perfect reflection,
$$
P = \frac{2I}{c}
$$
Force on area $A$:
$$
F = PA
$$
These relations show that light does more than illuminate objects. It can also push them.