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A totally reflecting small plane mirror placed horizontally faces a parallel beam of light as hown in figure. The mass of mirror is $20\, gm$. Assume that there is no absorption in the lens and that $30\%$ of the light emitted by the source goes through the lens. Find the power of the source needed to support the weight of the mirror ............... $MW$ (take $g = 10\, m/s^2$) :-
$80$
$100$
$20$
$25$
Solution
For perfectly reflecting mirror, the force exerted by the light of power $P$ is
$\mathrm{F}=\frac{2(\text { power })}{\mathrm{c}}$
for equilibrium
$\mathrm{F}=\mathrm{mg}=\frac{2(\text { power })}{\mathrm{c}}$
Power $ = \frac{{mg \times c}}{2} = 30 \times {10^6}{\rm{\,W}}$
As only $30 \%$ of the power is given to the mirror
So, $\mathrm{P}^{\prime}=30 \times \frac{100}{30}=100 \mathrm{\,MW}$
