Question

A perfectly reflecting mirror has an area of $1c{m}^2$. Light energy is allowed to fall on it for $1h$ at the rate of $10W/c{m}^2$. The force that acts on the mirror is:

• A. $3.35\times {10}^{-8}N$
• B. $6.7\times {10}^{-8}N$
• C. $1.34\times {10}^{-7}N$
• D. $2.4\times {10}^{-4}N$

Answer 1

The correct option is B $6.7\times {10}^{-8}N$

Light rays are quanta of energy called photons.
Let $E=$ Energy falling on the surface per second $=10J$
Momentum of photons
$p=\frac{h}{\lambda }=\frac{h}{\left(c/v\right)}=\frac{hv}{c}=\frac{E}{c}$
On reflection,
Change in momentum per second $=2p=\frac{2E}{c}$
We know that,
Change in momentum per second $=$ force
$F=\frac{2E}{c}=\frac{2\times 10}{3\times {10}^8}$
$=6.7\times {10}^{-8}N$
All photons emitted from a source, travel through space with the same speed (equal to the speed of light).