Question

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

Answer 1

$ \text { Force }=\int PdA \cos \theta$
$ =\frac{2 I }{ C } \int dA \cos \theta=\frac{2 I }{ C } \pi R ^2=2 \frac{ p _0}{4 \pi R ^2} \cdot \frac{\pi R ^2}{ C } $
$ =\frac{ p _0}{2 C }=\frac{24}{2 \times 3 \times 10^8}=4 \times 10^{-8} N$