Light carries momentum, even though photons have no rest mass. This is one of the key ideas behind radiation pressure, optical trapping, and concepts such as solar sails. When light falls on a surface, the photons transfer momentum to that surface. A steady stream of photons therefore exerts a force.
The momentum of a single photon is
\[
p=\frac{h}{\lambda},
\]
where \(h\) is Planck’s constant and \(\lambda\) is the wavelength. Shorter wavelengths correspond to larger photon momentum, while longer wavelengths correspond to smaller photon momentum.
For a beam of intensity \(I\), the power crossing an illuminated area \(A\) is
\[
P=IA.
\]
Since power is energy per unit time, this tells us how much photon energy arrives each second. If the surface perfectly absorbs the incoming light, then each photon gives the surface its incoming momentum \(p\). If the surface perfectly reflects the light straight back, then the photon reverses direction, so its momentum change is \(2p\). That is why reflection produces twice as much force as absorption in the simplest model.
From momentum flux, the radiation-pressure force becomes
\[
F=\frac{IA}{c}
\quad \text{for perfect absorption},
\]
and
\[
F=\frac{2IA}{c}
\quad \text{for perfect reflection}.
\]
Dividing by area gives the corresponding radiation pressure:
\[
P_{\text{rad}}=\frac{I}{c}
\quad \text{or} \quad
P_{\text{rad}}=\frac{2I}{c}.
\]
These formulas are extremely useful because they connect a macroscopic force directly to the beam intensity. They also show why the effect is usually small under everyday light levels: the speed of light \(c\) is very large, so the force for ordinary intensities is tiny.
For the sample case in the prompt,
\(I=1\,\text{W/m}^2\),
\(A=1\,\text{m}^2\),
and a perfect reflector,
the force is
\[
F=\frac{2IA}{c}=\frac{2}{2.9979\times10^8}\,\text{N}\approx 6.67\times10^{-9}\,\text{N}.
\]
This is about
\(6.67\,\text{nN}\),
which matches the sample output.
Another way to see the same result is to compute the photon flux. The energy of one photon is
\[
E_\gamma=\frac{hc}{\lambda}.
\]
So the number of photons arriving each second is
\[
\dot N_\gamma=\frac{IA}{E_\gamma}.
\]
Multiplying the photon rate by the momentum transfer per photon gives the force. For absorption that is
\(\dot N_\gamma p\),
and for perfect reflection it is
\(2\dot N_\gamma p\).
This agrees exactly with the intensity formulas above.
At a more advanced university level, one studies angled incidence, imperfect reflectivity, diffraction, beam profiles, optical cavities, and momentum carried by electromagnetic fields in media. These refinements matter in laser cooling, optical tweezers, cavity optomechanics, and spacecraft propulsion concepts. But the core physics is already visible in the basic formulas: light carries momentum, momentum flux creates pressure, and reflection doubles the transferred momentum compared with absorption.
\[
p=\frac{h}{\lambda},
\qquad
F=\frac{IA}{c},
\qquad
F=\frac{2IA}{c}.
\]
These relations explain why even a beam of light can push on matter and why highly reflective sails are attractive in radiation-pressure propulsion ideas.
