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 20 g. 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.
Figure

Answer 1

The power of the source needed to support the weight of the mirror is $100 \mathrm{MW}$

Explanation:

Incident power projection beam , P = 10 watt

Wavelength (λ) to momentum (p) ratio:

where h is constant of Planck

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

We get on separating the two sides by t:

$\frac{p}{t}=\frac{h}{\lambda t} \ldots(1)$

Energy is ,

$\begin{aligned}&E=\frac{h c}{\lambda}\\&\frac{E}{t}=\frac{h c}{\lambda t}\end{aligned}$

Let the power be P.Then,  

$P=\frac{E}{t}=\frac{h c}{\lambda t}$

$P=\frac{p c}{\varepsilon}[\text {Utilisation of equation }(1)]$

$\frac{P}{c}=\frac{p}{t}$

Force is given by  $F=\frac{p}{t}=\frac{P}{c} \quad(\text { since } F=\text {Momentum} \text { Time })$

Thus, momentum change rate is given by  = $\frac{Power}{c}$

As the light is reflecting normally,

Force = 2 (momentum change rate)

          = 2 × $\frac{Power}{c}$

$30 \% \text { of }\left(\frac{2 \times P_{\text {ower }}}{c}\right)=m g$

$\text { Power }=\frac{20 \times 10^{-3} \times 10 \times 3 \times 10^{8} \times 10}{2 \times 3}$

           $=100 \mathrm{MW}$