Light of intensity I falls along the axis on a perfectly refleccting right circular cone having semi-vertical angle `theta` and base radius R. If E is the energy of one photon and c is the speed oh light, then find
Q. the number of photons hitting the cone per second

Options

A. `(piR^2I)/(2E)`
B. `(2piR^2I)/(E)`
C. `(piR^2I)/(4E)`
D. `(piR^2I)/(E)`

Answer

D

Explanation

Power of light received by the cone `=(piR^2)`
Let number of photons hitting the cone per second is n.
Then, `nE=IpiR^2impliesn=(piR^2I)/(E)`
By symmetry, the net force on the cone will be vertically downward.
Force due to one photon:
`f=2(h)/(lamda)sintheta`
This force is perpendicular to the surface of cone. Hence, net force on the cone will be
`F=nfsintheta=n(2(h)/(lamda)sintheta)sintheta`
`=(piR^2I)/(c)(1-cos2theta)`