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Question #43110

Difficulty: 8/10 | 🟢 Free

The Question

A perfectly reflecting flat mirror moves with a constant velocity $v$ directly towards a stationary laser source in the laboratory frame. The laser emits a continuous, parallel beam of electromagnetic radiation with intensity $I$ and frequency $\nu$ , as measured in the laboratory frame. What is the radiation pressure $P$ exerted by the light beam on the mirror, measured in the laboratory frame? (Assume $c$ is the speed of light in vacuum)

Options

A.
$\frac{2I}{c} \left( \frac{c+v}{c-v} \right)$
B.
$\frac{2I}{c} \left( 1 + \frac{v}{c} \right)$
C.
$\frac{2I}{c} \left( \frac{c}{c-v} \right)$
D.
$\frac{2I}{c}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Spectrum Order and Frequency/Wavelength|Work-Energy Theorem Validity|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to synthesize the particle nature of light (momentum transfer) with relativistic kinematics (frame-dependent flux and Doppler shift).

A common lethal trap is blindly applying the static radiation pressure formula $P = 2I/c$ , ignoring the relative velocity entirely.

A more subtle trap occurs when students account for the increased photon collision rate (flux $\propto c+v$ ) but fail to account for the Doppler shift of the reflected photons, leading to the incorrect answer $\frac{2I}{c}(1 + v/c)$ .

The correct approach requires applying Momentum Conservation dynamically, recognizing that the moving mirror does work on the reflected photons, thereby increasing their energy and momentum by the exact relativistic Doppler factor.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Spectrum Order and Frequency/Wavelength
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free