Find the force exerted by a light beam of intensity I, indicated on a cylinder of height h and base radius R placed on a smooth surface as shown in figure if surface of cylinder is perfectly reflecting

Options

A. `(2IhR)/c`
B. `(4IhR)/(3c)`
C. `(8IhR)/(3c)`
D. `(4IhR)/c`

Answer

C

Explanation

Top view of cylinder.

Change in momentum of one photon
`=(2h)/lambda cos theta`
No.of photons striking per second on small area `=N(Rd theta cos theta) xx h`
`rArr` Total change in momentum per second striking small area.
`=(N Rd theta costheta xx h) (2h)/lambda cos theta`
`=N(2h)/lambda Rh(cos^(2)theta d theta)`
`int dF = N(2I)/C Rh int cos^(3) theta d theta`
`=(8IhR)/(3C)`