A point source of radiation power `P` is placed on the axis of an ideal plane mirror. The distance between the source and the mirror is `n` times the radius of the mirror. The force that light exerts on the mirror is `(P)/(xc(n^(2)+y))`

Options

A. `x-y=3`
B. `x+y=3`
C. `xy=3`
D. `x//y=3`

Answer

B

Explanation

Consider a ring of radius `x` and of width of `dx`. Power indicent on the ring.
`dP=(P)/(4pi[(nr)^(2)+x^(2)])2pidx.costheta=(Pxdx.nr)/(2[(nr)^(2)+x^(2)]^(3//2))`
No. of photons falling (per unit time) on the area`=(dP.lambda)/(hC)` momentum given by one photon `=2(h)/(lambda)costheta`. force on the ring `d F` (in the downward direction)
`=(dp.lambda)/(hC).(2h)/(lambda)costheta=(2dPcostheta)/(C)`
`F=int_(0)^(r)2.(Pxdxnr)/(2[(nr)^(2)+x^(2)]^(3//2))*(costheta)/(C)`
`=(Pn^(2)r^(2))/(C)int_(0)^(r)(x dx)/((n^(2)r^(2)+x^(2))^(2))`
`=(Pn^(2)r^(2))/(2C)*(1)/(n^(2)r^(2)(n^(2)+1))=(P)/(2C(n^(2)+1))`