Question 170: EM waves

Question

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of $$24 \mathrm{~W}$$. The radius of curvature of hemisphere is $$10 \mathrm{~cm}$$ and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is ____________ $$	imes~10^{-8} \mathrm{~N}$$.

Accepted Answer

$$
\begin{aligned}
& 	ext { Force }=\int P d A \cos 	heta \\
& =\frac{2 \mathrm{I}}{\mathrm{C}} \int \mathrm{dA} \cos 	heta=\frac{2 \mathrm{I}}{\mathrm{C}} \pi \mathrm{R}^2=2 \frac{\mathrm{p}_0}{4 \pi \mathrm{R}^2} \cdot \frac{\pi \mathrm{R}^2}{\mathrm{C}} \\
& =\frac{\mathrm{p}_0}{2 \mathrm{C}}=\frac{24}{2 	imes 3 	imes 10^8}=4 	imes 10^{-8} \mathrm{~N}
\end{aligned}
$$

EM waves

Integer / Numeric Answer Type