Question

Light with an energy flux of $25\times {{10}^{4}}w{{m}^{-2}}$ falls on a perfectly reflecting surface at normal incidence. If the surface area is$15c{{m}^{2}}$, then the average force exerted on the surface is
$\begin{align}
  & A.1.25\times {{10}^{-6}}N \\
 & B.2.50\times {{10}^{-6}}N \\
 & C.1.20\times {{10}^{-6}}N \\
 & D.3.0\times {{10}^{-6}}N \\
\end{align}$

Answer 1

- Hint: First of all we have to notice that the surface is perfectly reflecting at normal incidence. Therefore find the momentum relation with energy flux keeping this in mind. After that substitute the momentum equation in the equation for force.

Complete step-by-step solution
Energy flux is defined as the rate of transfer of energy through a surface. The quantity is explained in two different ways, depending on the idea of total rate of energy transfer or specific rate of energy transfer.
In this case, it is mentioned in the question that the surface is given as perfectly reflecting and also the incidence is normal to the surface. Therefore the reflection will also be in the exact same direction. As the momentum can be written as,
$P=\dfrac{E}{C}$
Where $E$ the energy is and $C$ is velocity of light.
Therefore the change in momentum can be written as,
\[\Delta P=P-\left( -P \right)=2P\]
Now let us know that,
Force is given by the equation,
\[F=\dfrac{\Delta P}{\Delta t}\]
Substituting the equation of change in momentum in this equation of force will give,
\[F=\dfrac{2P}{t}\]
And also we know that
$P=\dfrac{E}{C}$
\[E=IA\]

Where \[I\]the energy flux is and \[A\]is the area of the surface.
 Therefore, by substituting this in the equation of force, we can write that,
 \[F=\dfrac{2P}{t}=\dfrac{2IA}{C}\]
Substituting the values in the equation will give,
\[\begin{align}
  & F=\dfrac{2IA}{C}=\dfrac{2\times 25\times {{10}^{4}}\times 15}{3\times {{10}^{8}}} \\
 & F=2.56\times {{10}^{-6}}N \\
\end{align}\]
Therefore the correct answer is option B.

Note: The term flux explains something that constantly varies. It is the effect that happens to pass or travel through a surface or a substance. A flux is an idea in applied mathematics and vector calculus which is having many applications in physics.