Question

A sphere of radius $1.00cm$ is placed in the path of a parallel beam of light of large aperture. The intensity of the light is $0.50W{cm}^{-2}$. If the sphere completely absorbs the radiation falling on it, find the force exerted by the light beam on the sphere

Answer 1

Sphere of radius $R=100cm$

Intensity of light$=0.50Wc{m}^{-2}$

Find F

Radiation force exerted by the light beam on the sphere$=\frac{P}{A}=\frac{E/T}{A}I=\frac{Force\times displacement}{times\times Area}$

$Intensity=\frac{Force\times displacement}{times\times Area}0.5W/c{m}^2=\frac{F\times displacement}{time\times Area}=\frac{F\times R}{times\times 4\pi R^2}=\frac{F}{times\times 4\pi R}$

Now, $F=0.5W/c{m}^2\times times\times 4\pi R=0.5\times 4\pi \times 1.00\times time\frac{F}{t}=\frac{1}{2}\times 4\pi =2\times \frac{22}{7}=\frac{44}{7}=6.28N$