Question

An EM wave of intensity $I$ falls on a surface kept in vacuum and exerts radiation pressure $p$ on it. Which of the followings are true?

• A. Radiation pressure is $I/c$ if the wave is totally absorbed
• B. Radiation pressure is $I/c$ if the wave is totally reflected
• C. Radiation pressure is $2I/c$ if the wave is totally reflected
• D. Radiation pressure is in the range $I/c<p<2I/c$ for the real surfaces

Answer 1

Answer: (A), (C), (D)

Radiation pressure $(p)$ is the force exerted by electromagnetic wave on unit area of the surface, i.e., rate of change of momentum per unit area of the surface.
Momentum per time per unit area $=\frac{\text{ intensity }}{\text{ speed of wave }}=\frac{I}{c}$
Change in momentum per unit time per unit area $=\Delta I/c=$ radiation pressure $(p)$, i.e., $p=\Delta I/c$.
Momentum of incident wave per unit time per unit area $I/c$.
When wave is fully absorbed by the surface, the momentum of the reflected wave per unit time per unit area $=0$.
Radiation pressure $(p)=$ change in momentum per unit time per unit area $=\frac{\Delta I}{c}=\frac{I}{c}-0=\frac{I}{c}$
When wave is totally reflected, then momentum of the reflected wave per unit time per unit area $=-I/c$.
Radiation pressure $(p)=\frac{I}{c}-\left(-\frac{I}{c}\right)=\frac{2I}{c}$
Here, $p$ lies between $I/c$.