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.
The angle of reflection will be the same as angle of incidence, i.e θ
Linear momentum of incident light pi= -(h/λ)cosθ î + (h/λ)sinθ ĵ
Linear momentum of reflected light pr= (h/λ)cosθ î + (h/λ)sinθ ĵ
Change in linear momentum = pr – pi
= [(h/λ)cosθ î + (h/λ)sinθ ĵ] – [-(h/λ)cosθ î + (h/λ)sinθ ĵ]
= -2(h/λ)cosθ î + 0 ĵ
⇒ Change in linear momentum is in x-direction = 2hcosθ/λ