Question

A regular hexagonal lamina of side a made up of perfectly absorbing material is kept in a region where a parallel beam of light with intensity I having a large aperture falls on it. If the normal to the surface of the hexagon makes an angle of ${30}^{\circ }$ with the beam then the force experienced by the hexagon will be

• A. $\frac{5a^{2}I}{4c}$
• B. $\frac{9a^{2}I}{4c}$
• C. $\frac{a^{2}I}{c}$
• D. $\frac{6a^{2}I}{c}$

Answer 1

The correct option is B

$\frac{9a^{2}I}{4c}$

Radiation pressure $=P=\frac{I}{c}$

Area of Hexagon = $(\frac{1}{s}a.\frac{a\sqrt{3}}{2})\times 6$

$F=PAcos\theta =\frac{I}{c}.\frac{3a^2\sqrt{3}}{2}.\frac{\sqrt{3}}{1}=\frac{9a^{2}I}{4c}$