Question

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

• A. $\frac{4h}{\lambda }sin\theta$
• B. $\frac{2h}{\lambda }sin\theta$
• C. $\frac{4h}{\lambda }cos\theta$
• D. $\frac{2h}{\lambda }cos\theta$

Answer 1

The correct option is D

$\frac{2h}{\lambda }cos\theta$

The situation is depicted as shown in figure.

Clearly, $\overrightarrow{P_t}=\frac{h}{\lambda }sin\theta \hat{i}-\frac{h}{\lambda }cos\theta \hat{j}$
$\overrightarrow{P_f}=\frac{h}{\lambda }sin\theta \hat{i}+\frac{h}{\lambda }cos\theta \hat{j}$
$\overrightarrow{\Delta P}=\overrightarrow{P_f}-\overrightarrow{P_t}$
$\overrightarrow{\Delta P}=\frac{2h}{\lambda }cos\theta \hat{j}$
$\overrightarrow{\Delta P}=\frac{2h}{\lambda }cos\theta$