A totally reflecting small plane mirror placed horizontally faces… - Vidyadip

MCQ

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 $g = 10\, m/s^2$) :-

A
$80$
✓
$100$
C
$20$
D
$25$

✓

Answer

Correct option: B.

$100$

b
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, $\mathrm{P}^{\prime}=30 \times \frac{100}{30}=100 \mathrm{\,MW}$

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