Question

A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per second is 1.0 × 10¹⁹. Calculate the force exerted by the light beam on the mirror.

Answer 1

Here,
$$\begin{gathered} \mathrm{Wavelength}\mathrm{of}\mathrm{monochromatic}\mathrm{light},\lambda =663\times {10}^{-9}\mathrm{m} \\ \mathrm{Angle}\mathrm{of}\mathrm{incidence},\mathrm{\theta }=60° \\ \mathrm{Number}\mathrm{of}\mathrm{photons}\mathrm{per}\mathrm{second},n=1\times {10}^{19} \\ \mathrm{Momentum}\mathrm{of}\mathrm{photon}, \\ p=\frac{h}{\lambda }, \\ \text{w}\mathrm{here}h\mathrm{is}\text{P}\mathrm{lanck}\text{'}s\mathrm{constant}. \\ p=\frac{6.63\times {10}^{-34}}{663\times {10}^{-9}}={10}^{-27} \end{gathered}$$

Force exerted on the wall,
$$\begin{gathered} F=n\times \left[p\mathrm{cos\theta }-(-p\mathrm{cos\theta })\right]=2np\mathrm{cos\theta } \\ =2\times 1\times {10}^{19}\times {10}^{-27}\times \frac{1}{2} \\ =1.0\times {10}^{-8}\mathrm{N} \end{gathered}$$