Question

A parallel beam of light is incident normally on a plane surface absorbing 50% of the light and reflecting the rest. If the incident beam carries $90\text{ W}$ of power, the force exerted by it on the surface is ( $\text{C} =$ velocity of light in air $= 3 \times 10^8\text{ m/s}$ )}

• A. $4.5 \times 10^{-7}\text{ N}$
• B. $1.5 \times 10^{-7}\text{ N}$
• C. $3 \times 10^{-7}\text{ N}$
• D. $9 \times 10^{-7}\text{ N}$

Hint:

Perfect absorber ($r=0$) $\rightarrow F=P/c$. Perfect reflector ($r=1$) $\rightarrow F=2P/c$. For anything in between, use the $(1+r)$ factor.

Answer 1

The Correct Option is A

Step 1: Concept
Force exerted by light is $F = \frac{P}{c}(1 + r)$, where $P$ is power and $r$ is the reflection coefficient.

Step 2: Meaning
Since 50% is reflected, $r = 0.5$.

Step 3: Analysis
$F = \frac{90}{3 \times 10^8} \times (1 + 0.5)$
$F = (30 \times 10^{-8}) \times 1.5 = 45 \times 10^{-8} \text{ N}$
$F = 4.5 \times 10^{-7} \text{ N}$.

Step 4: Conclusion
The force exerted is $4.5 \times 10^{-7}\text{ N}$. Final Answer: (A)