Question

Consider normal incidence of a monochromatic beam of photons of power $P$ on a flat surface. Of the incident beam, 10% gets absorbed, 10% gets transmitted, and the rest is reflected by the flat surface. If $c$ is the speed of light, what is the force exerted on the flat surface by the beam?

• A. $1.7 \frac{P}{c}$
• B. $1.8 \frac{P}{c}$
• C. $1.6 \frac{P}{c}$
• D. $0.9 \frac{P}{c}$

Hint:

For radiation pressure force calculations, use the formula $F = (1 + R - T)\frac{P}{c}$, where $R$ is the reflection coefficient, and $T$ is the transmission coefficient.
Here, $R=0.8$ and $T=0.1$, so $F = (1 + 0.8 - 0.1)\frac{P}{c} = 1.7\frac{P}{c}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Force is defined as the rate of change of momentum. A beam of power P carries momentum per second equal to \( P/c \).

Step 2: Detailed Explanation:
1. Momentum per second (\( p_{s} \)): \( P/c \).
2. Individual Contributions:
$\bullet$ Absorbed (10%): Force \( F_{a} = 0.1 \times \frac{P}{c} \) (photon stops, transfers all momentum).
$\bullet$ Transmitted (10%): Force \( F_{t} = 0 \) (photon passes through with no momentum change).
$\bullet$ Reflected (80%): Force \( F_{r} = 0.8 \times \left( \frac{2P}{c} \right) = 1.6 \frac{P}{c} \) (photon bounces back, transfer is \( p - (-p) = 2p \)).
3. Total Force:
\[ F_{\text{total}} = 0.1\frac{P}{c} + 0 + 1.6\frac{P}{c} = 1.7\frac{P}{c} \]

Step 3: Final Answer:
The total force is \( 1.7 P/c \).