Question

Light in certain cases may be considered as a stream of particles called photons. Each photon has a linear momentum h/λ where h is the Planck's constant and λ is the wavelength of the light. A beam of light of wavelength λ is incident on a plane mirror at an angle of incidence θ. Calculate the change in the linear momentum of a photon as the beam is reflected by the mirror.

Answer 1

It is given that:
Wavelength of light = λ
Momentum of each photon = h/λ
Angle of incidence = θ



$$\begin{gathered} {\overrightarrow{\mathrm{P}}}_{Incidence}=\left(\frac{h}{\lambda }\right)\cos \mathrm{\theta }\hat{i}-\left(\frac{\mathrm{h}}{\mathrm{\lambda }}\right)\sin \mathrm{\theta }\hat{j} \\ {\overrightarrow{\mathrm{P}}}_{\mathrm{Reflected}}=-\left(\frac{h}{\mathrm{\lambda }}\right)\cos \mathrm{\theta }\hat{i}-\left(\frac{h}{\mathrm{\lambda }}\right)\sin \mathrm{\theta }\hat{j} \\ \mathrm{The}\mathrm{change}\mathrm{in}\mathrm{momentum}\mathrm{will}\mathrm{only}\mathrm{be}\mathrm{in}\mathrm{the}\mathrm{direction}\mathrm{of}\mathrm{x}-\mathrm{axi}si.e., \\ \left|\mathrm{\Delta P}\right|=\left(\frac{h}{\mathrm{\lambda }}\right)\cos \mathrm{\theta }-\left(-\frac{h}{\mathrm{\lambda }}\cos \mathrm{\theta }\right) \\ =\left(\frac{2h}{\mathrm{\lambda }}\right)\cos \mathrm{\theta } \end{gathered}$$