Question

An electromagnetic wave of intensity $I$ falls on a surface kept in vacuum and exerts radiation pressure $P$ on it. Which of the following statement is not 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 real surfaces

Answer 1

Answer: (B)

Momentum per unit time per unit area
$=\frac{intensity}{speedofwave}=\frac{I}{c}$
Change in momentum per unit time per unit area $=\Delta I/c=$ radiation pressure $\left(P\right)$, 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 $\left(P\right)=$ 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 $\left(P\right)=\frac{I}{c}-\left(-\frac{I}{c}\right)=\frac{2I}{c}$
Here, $P$ lies between $\frac{I}{c}$ and $\frac{2I}{c}$.