A plane wave of intensity `I=0.70W cm^(-2)` illuminates a sphere with ideal mirror surface. The radius of sphere is `R=5.0cm`. From the standpoint of photon theory, find the force that light exerts on the sphere.

Options

A. `0.8muN`
B. `0.2muN`
C. `0.5muN`
D. `1.2muN`

Answer

A

Explanation

Imagine the sphere to be made of thin curcular rings of radius r, thickness `ds=R dq` and subtending an angle of `theta` at the center.
Momentum per second of incident photons,
`((dP)/(dt))_(incident)=(I)/(c )cos^2theta`
Since surface of mirror is considered to be ideal, i.e., reflection coeffiecient is unity, photons suffer momentum change is normal direction only.
`((dP)/(dt))_(photon)=(2I)/(c )dAcos^2theta`
`dF_n=((dP)/(dt))_(ball)=+(2I)/(c )dAcos^2theta`
This force may be resolved into horizontal and vertical components. The vertical component `dF_n sintheta` is cancelled because every element on the upper half has a symmetrically placed element in the lower half. So, resultant force on the ball,
`F=intdF_ncostheta=int(2I)/(c)dAcos^3theta`
`dA=(2piRsintheta)Rd theta`
`F=int_0^((pi)/(2))R^2cos^3thetasinthetad theta`
`=(4piR^2I)/(c)int_0^((pi)/(2))cos^3thetasinthetad theta=(piR^2I)/(c)`