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Dual Nature of Radiation and Matter — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsDual Nature of Radiation and Matter3 Marks
Question
A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light, as shown in the figure. The mass of the mirror is $20g$. 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. Take $g = 10m/s^2.$​​​​​​​
✓

Answer

$m = 20g$
The weight of the mirror is balanced. Thus force exerted by the photons is equal to weight
$\text{p}=\frac{\text{h}}{\lambda}$
$\text{E}=\frac{\text{hc}}{\lambda}=\text{pc}$
$\Rightarrow\frac{\text{E}}{\text{t}}=\frac{\text{p}}{\text{t}}\text{c}$
$\Rightarrow $ Rate of change of momentum $=\frac{\text{power}}{\text{C}}$
$30\%$ of light passes through the lens.
Thus it exerts force. $70\%$ is reflected.
$\therefore$ Force exerted $= 2($rate of change of momentum$)$
$=2\times\frac{\text{power}}{\text{C}}$
$30\%\Big(\frac{2\times\text{power}}{\text{C}}\Big)=\text{mg}$
$\Rightarrow\text{power}=\frac{20\times10^{-3}\times10\times3\times10^{8}\times10}{2\times3}$
$=10\text{W}=100\text{MW.}$

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