Question

A plane wave of intensity $I=0.70Wc{m}^{-2}$ illuminates a sphere with ideal mirror surface. The radius of sphere is $R=5.0cm$. From the standpoint of photon theory, find the force that light exerts on the sphere.

• A. $0.18\mu N$
• B. $0.12\mu N$
• C. $0.15\mu N$
• D. $1.2\mu N$

Answer 1

Answer: (A)

$0.18\mu N$

Given,

$I=0.7W{cm}^{-2}R=5.0cm$

Due to symmetry the force is exerted in the direction of light.

$F=\frac{2I}{c}{\int }_0^{\frac{\pi }{2}}{cos}^2\theta \times cos\theta \times 2\pi R^2\times sin\theta \times d\theta =\frac{2I}{c}\times \frac{2\pi R^2}{4}=\pi R^2\frac{I}{C}$

Substitute all value in above equation

$F=\pi {\times 5}^2\times {10}^{-4}\times \frac{0.7\times {10}^4}{3\times {10}^8}=18.31\times {10}^{-8}N=0.18\mu N$