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

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

The cange in momentum per unit time is given as:

$p=\frac{intensity}{speedofwave}=\frac{I}{c}$

When the wave is fully absorbed by the surface, the momentum of the reflected wave per unit time per unit area $=0$ .

So, Radiation pressure when wave is absorbed is:

$p$ = change in momentum per unit time per unit area i.e.

$\frac{\Delta I}{c}=\frac{I}{c}-0\Rightarrow \frac{I}{c}$

When the wave is totally reflected, then the momentum of the reflected wave per unit time per unit area $=-\frac{I}{C}$
So, Radiation pressure for case of reflected wave:

$p=\frac{I}{c}-(-\frac{I}{c})\Rightarrow \frac{2I}{c}$

The radiation pressure for a real surface lies between the perfectly absorbing and perfectly reflecting surface.

So, for real surface $p$ lies between $\frac{I}{c}$ and $\frac{2I}{c}$.

Option $\left(A\right),\left(C\right)$ and $\left(D\right)$ are correct.