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 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

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ANSWER::

P₁(incidence) = (h/λ) cos Ф i - (h/λ) sin Ф j

P₂(reflected) = -(h/λ) cos Ф i - (h/λ) sin Ф j

Change in momentum will be in x-axis direction ::

ΔP = (h/λ) cos Ф - [(h/λ) cos Ф] = (2h/λ) cos Ф

Hope it helps!

Answer 2

The change in the linear momentum of a photon as the beam is reflected by the mirror $\Delta P=\frac{2 h \cos \Phi}{\lambda}$

Explanation:

To find: The change in the linear momentum of a photon

Step 1:

Light can be perceived as a stream of particles termed photons in certain circumstances. The photon consists of a linear momentum     in which h is the constant of the Planck and p is the light's wavelength.  

A wavelength light beam is occurring at an incidence angle on the plane mirror.

$\begin{aligned}&P_{1}(\text { incidence })=\frac{h}{\lambda} \cos \Phi \mathrm{i}-\frac{h}{\lambda} \sin \Phi \mathrm{j}\\&P_{2}(\text { reflected })=-\frac{h}{\lambda} \cos \Phi i-\frac{h}{\lambda} \sin \Phi j\end{aligned}$

Step 2:

Change of momentum in the direction of the x-axis

$\begin{aligned}&\mu P=\frac{h}{\lambda} \cos \Phi \mathrm{i}-\frac{h}{\lambda} \cos \Phi \mathrm{j}\\&\Delta P=\frac{h \cos \Phi i-h \cos \Phi j}{\lambda}\end{aligned}$

$\Delta P=\frac{2 h \cos \Phi}{\lambda}$