Question

An isotropic point source having radiation power P is located on the axis of an ideal mirror plate. The distance between the source and the plate centre is n times the radius of the plate. In terms of photon theory find the force that light exerts on the plate.(c denotes speed of light) ?

• A. $\frac{P}{2C}\left[\frac{1}{1+n^2}\right]$
• B. $\frac{P}{C}\left[\frac{1}{1+n^2}\right]$
• C. $\frac{P}{2C}\left[\frac{1}{1+2n^2}\right]$
• D. $\frac{P}{C}\left[\frac{1}{1+2n}\right]$

Answer 1

The correct option is A $\frac{P}{2C}\left[\frac{1}{1+n^2}\right]$


$df=\frac{2I\left(2\pi rdr\right)co{s}^3\theta }{C}\because I=\frac{P}{4\pi (r^2+l^2{)}^{\prime }}cos\theta =\frac{1}{\sqrt{l^2+r^2}}\therefore df=\frac{Prco{s}^3\theta dr}{r^2+l^2}$
On integrating we get total force $f=\int df=\frac{P}{2c}\left[\frac{1}{1+n^2}\right]$