Question

A beam of light with intensity \( 10^5 \, \text{Nm}^{-2} \) and cross-sectional area \( 20 \, \text{cm}^2 \) is incident on a fully reflective surface at an angle of \( 45^\circ \). Find the force exerted by the beam on the surface.

• A. \( 2.3 \times 10^{-15} \, \text{N} \)
• B. \( 1.33 \times 10^{-14} \, \text{N} \)
• C. \( 6.67 \times 10^{-15} \, \text{N} \)
• D. \( 9.4 \times 10^{-15} \, \text{N} \)

Hint:

For reflective surfaces: \( F = \frac{2IA \cos^2 \theta}{c} \), where \( \theta \) is the angle of incidence.

Answer 1

The Correct Option is D

Force on a reflective surface: \[ F = \frac{2I \cdot A \cdot \cos^2 \theta}{c}, \quad I = 10^5, \, A = 20 \times 10^{-4}, \, \theta = 45^\circ, \, c = 3 \times 10^8 \] \[ F = \frac{2 \cdot 10^5 \cdot 20 \times 10^{-4} \cdot \left( \frac{1}{\sqrt{2}} \right)^2}{3 \times 10^8} = \frac{2 \cdot 10^5 \cdot 20 \times 10^{-4} \cdot \frac{1}{2}}{3 \times 10^8} = \frac{200 \cdot 10^{-4}}{3 \times 10^8} = 9.4 \times 10^{-15} \, \text{N} \]