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 

\[\vec{P}_{Incidence} = \left( \frac{h}{\lambda} \right) \cos \theta  \hat {i}- \left( \frac{h}{\lambda} \right) \sin \theta \hat j \]
\[ \vec{P}_{Reflected} = - \left( \frac{h}{\lambda} \right) \cos \theta \hat i - \left( \frac{h}{\lambda} \right) \sin \theta \hat j \]
\[\text{ The change in momentum will only be in the direction of x - axis i . e . , }\]
\[\left| \Delta P \right| = \left( \frac{h}{\lambda} \right) \cos \theta - \left( - \frac{h}{\lambda} \cos \theta \right)\]
\[ = \left( \frac{2h}{\lambda} \right) \cos \theta\]