Question

A plane electromagnetic wave is incident on a plane surface of area A normally and is perfectly reflected. If energy E strikes the surface in time t then average pressure exerted on the surface is (c = speed of light):

• A. Zero
• B. $\frac{E}{Atc}$
• C. $\frac{2E}{Atc}$
• D. $\frac{E}{c}$

Answer 1

Answer: (C)

Electromagnetic waves strikes the surface at normal incidence and transports a total energy E to surface in a time, t.

Incident momentum, $p=Ec$

If the surface reflects all the incident energy, the total momentum transported to the surface has a magnitude, i.e., for perfectly reflecting surface with normal incidence

$\Delta p=2p=\frac{2E}{c}$

We know

$F=\frac{\Delta p}{\Delta t}=\frac{2E}{ct}$

Then, the pressure exerted on the surface by an electromagnetic wave is given by

$P=\frac{F}{A}$

Now substituting the corresponding values, we get

$P=\frac{\frac{2E}{ct}}{A}⟹P=\frac{2E}{Atc}$

is the average pressure exerted on the surface