Radiation Pressure

Radiation Pressure

Electromagnetic waves carry linear momentum as well as energy. Under normal incidence with irradiance I on a flat surface of area A characterized by absorbance a, reflectance r, and transmittance t (where a + r + t = 1), absorbed photons transfer their momentum p = h/λ while reflected photons reverse direction and transfer 2h/λ. The resulting radiation pressure is P = I(a + 2r)/c and the net mechanical force is F = PA.

Worked Example

Calculate the radiation pressure, force, power, photon momentum, and photon arrival rate on a perfectly absorbing surface under normal incidence:

1. Inputs: Surface = Absorber (a = 1, r = 0, t = 0), Irradiance I = 300 W/m², Area A = 2 cm² = 2 × 10⁻⁴ m², Wavelength λ = 600 nm = 600 × 10⁻⁹ m.
2. Radiation Pressure: P = I(a + 2r)/c = 300 × 1 / 299792458 ≈ 1.0006922855945 × 10⁻⁶ Pa = 1.0006922855945 μPa.
3. Force: F = P × A = 1.0006922855945 × 10⁻⁶ Pa × 2 × 10⁻⁴ m² ≈ 0.20013845711889 nN.
4. Incident and Absorbed Power: P_inc = P_abs = I × A = 300 × 2 × 10⁻⁴ = 0.06 W.
5. Per-Photon Momentum and Rate: p = h/λ = 6.62607015 × 10⁻³⁴ / (600 × 10⁻⁹) = 1.104345025 × 10⁻²⁷ kg·m/s, and photon rate N = P_inc / (hc/λ) ≈ 181.22819643154 × 10¹⁵ s⁻¹.

Experiment

Explore how surface optical properties, irradiance, area, and wavelength affect photon momentum transfer in the Radiation Pressure module:

1. Compare Surface set to Absorber versus Mirror at I = 300 W/m² and A = 2 cm². Notice that pressure and force double for the mirror (from 0.200138457119 nN to 0.400276914238 nN) while absorbed power drops to 0 W.
2. Change Wavelength nm between 400, 600, and 800 at fixed irradiance. Observe that macroscopic pressure and force remain invariant because the change in per-photon momentum is exactly compensated by the inverse change in photon arrival rate.
3. Select Transparent to verify that transmitted photons continuing in the same direction exert zero radiation pressure and zero force.

Limitations

This model assumes strictly normal incidence of monochromatic plane waves on a flat macroscopic target in vacuum. It neglects oblique incidence angles, diffuse scattering from rough surfaces, refractive momentum changes inside dielectric media, and asymmetric thermal re-emission recoil (such as the Yarkovsky effect).

References

The electromagnetic momentum density, Poynting flux, and radiation pressure relations for absorbing and reflecting surfaces are covered in:

• OpenStax University Physics Volume 2, Section 16.4: Momentum and Radiation Pressure