A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of 24 W. [2023]

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Solution

Q.
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. [2023]

Ans.
(4)

$Force = \int P d A \cos θ$

$= \frac{2 I}{C} \int d A \cos θ = \frac{2 I}{C} π R^{2} = 2 \frac{p_{0}}{4 π R^{2}} \cdot \frac{π R^{2}}{C}$

$= \frac{p_{0}}{2 C} = \frac{24}{2 \times 3 \times 10^{8}} = 4 \times 10^{- 8} N$

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