Question

Find the force exerted by a light beam of intensity I, incident on a cylinder (height h and base radius R) placed on a smooth surface as shown in figure if surface of cylinder is having reflection coefficient 0.8. (assume no transmission)

• A. $\frac{38}{15}\frac{Irh}{c}$
• B. $\frac{23}{15}\frac{Irh}{c}$
• C. $\frac{70}{15}\frac{Irh}{c}$
• D. $\frac{58}{15}\frac{Irh}{c}$

Answer 1

The correct option is A

$\frac{38}{15}\frac{Irh}{c}$

Force due to absorption of light is $F_1=\frac{0.4IrL}{C}$

Considering energy of each photon is E. change in momentum due to reflection is $\frac{nE}{c}cos\theta$

Number of photos striking the elementary area is n= $\frac{0.8I\times Rcos\theta \times d\theta \times h}{E}$

So $dF=\frac{1.6IRh}{C}cos2\theta .d\theta$

Force due to reflection is ${\int }_{-\pi /2}^{\pi /2}dFcos\theta =\frac{4}{3\times \frac{1.6IRh}{C}}$

$\therefore Fnet=(1.6\times \frac{4}{3}+0.4)\frac{Irh}{C}=\frac{38}{15}\frac{Irh}{c}$