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Photoelectric Effect and WaveParticle Duality — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsPhotoelectric Effect and WaveParticle Duality3 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/s2.

✓

Answer

m = 20g

The weight of the mirror is balanced. Thus force exerted by the photons is equal to weight

$\text{p}=\frac{\text{h}}{\lambda}$

$\text{E}=\frac{\text{hc}}{\lambda}=\text{pc}$

$\Rightarrow\frac{\text{E}}{\text{t}}=\frac{\text{p}}{\text{t}}\text{c}$

⇒ 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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