33-3 Radiation Pressure#
Prompts
What is the difference between force and pressure? How are they related for a flat surface?
EM waves carry momentum. When radiation is totally absorbed by a surface, how is the momentum change \(\Delta p\) related to the energy \(\Delta U\) absorbed? What about total reflection back along the path?
For a uniform beam of intensity \(I\) perpendicular to area \(A\): derive the force for (a) total absorption and (b) total reflection. What is the radiation pressure \(p_r\) in each case?
Why don’t you feel a “punch” from a camera flash? When can radiation pressure become significant?
If radiation is partly absorbed and partly reflected, where does the force lie between the two extremes?
Lecture Notes#
Overview#
EM waves transport momentum as well as energy; when they strike a surface, they exert a force and thus a pressure.
Total absorption: momentum transfer \(\Delta p = \Delta U/c\); force \(F = IA/c\).
Total reflection (back along path): momentum transfer doubles; force \(F = 2IA/c\).
Radiation pressure \(p_r = F/A\) is typically small (e.g., camera flash) but can be significant for focused laser beams.
Momentum transfer#
Maxwell showed that when an object absorbs EM radiation, it gains both energy and linear momentum. For radiation totally absorbed:
where \(\Delta U\) is the energy absorbed and \(c\) is the speed of light. The momentum change is in the direction of the incident beam.
For radiation totally reflected back along its original path:
Elastic vs inelastic analogy
Reflection gives twice the momentum transfer—like a perfectly elastic ball bouncing off a wall versus a perfectly inelastic lump of putty sticking to it. The ball reverses momentum; the putty stops. If partly absorbed and partly reflected, \(\Delta p\) lies between \(\Delta U/c\) and \(2\Delta U/c\).
Force and pressure#
From \(F = \Delta p/\Delta t\) and intensity \(I = \text{power}/\text{area} = (\text{energy}/\text{time})/\text{area}\), the energy intercepted by area \(A\) in time \(\Delta t\) is \(\Delta U = IA\,\Delta t\).
Total absorption:
Total reflection (back along path):
The radiation pressure \(p_r = F/A\):
Case |
Radiation pressure |
|---|---|
Total absorption |
\(p_r = I/c\) |
Total reflection (back along path) |
\(p_r = 2I/c\) |
SI unit: Pa (N/m²), same as fluid pressure.
Use \(p_r\) for radiation pressure to avoid confusion with momentum \(p\).
Typical magnitudes#
Radiation pressure is usually very small. For example, sunlight at Earth has \(I \approx 1400\) W/m², so \(p_r \approx I/c \approx 5 \times 10^{-6}\) Pa—negligible compared to atmospheric pressure (\(\sim 10^5\) Pa).
Important
Laser beams can be focused to a tiny spot, delivering high intensity to a small area. Radiation pressure then becomes measurable and is used in optical tweezers, laser cooling, and related applications.
Summary#
EM waves exert force and pressure on surfaces by transferring momentum.
Total absorption: \(F = IA/c\), \(p_r = I/c\).
Total reflection (back along path): \(F = 2IA/c\), \(p_r = 2I/c\).
Partly absorbed, partly reflected: between these extremes.
Radiation pressure is small for ordinary light but significant for focused lasers.