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Question #43723

Difficulty: 8/10 | 🟢 Free

The Question

A broad beam of monochromatic light is incident normally from a vacuum onto a transparent liquid layer of thickness $d$ . The liquid has a refractive index $n$ in its rest frame. The liquid flows uniformly with a velocity $v$ ( $v \ll c$ ) parallel to its surfaces. Assume the boundaries of the liquid layer remain flat and stationary in the laboratory frame. Due to the Fresnel drag effect, the direction of energy flow (ray direction) in the liquid is deflected. Find the lateral displacement $\Delta x$ of the emergent beam relative to the incident beam to the first order in $v/c$ . (Here $c$ is the speed of light in vacuum).

Options

A.
$d \frac{v}{c} \left(n - \frac{1}{n}\right)$
B.
$d \frac{v n}{c}$
C.
$d \frac{v}{c} \left(1 - \frac{1}{n^2}\right)$
D.
$d \frac{v}{c n}$

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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

Optical Path Difference|Snell’s Law Vector Form|Drift Velocity Mechanism

Why This Question Is Tricky

Common Mistakes

Students often assume that normal incidence implies zero refraction and zero lateral shift, ignoring the convective effect of the moving medium.

Alternatively, if they do consider the medium's velocity, they might incorrectly apply a simple Galilean velocity addition ( $\vec{v}_g = \frac{c}{n}\hat{z} + v\hat{x}$ ), leading to the incorrect shift $\Delta x = d \frac{vn}{c}$ .

The core misconception is failing to recognize that the medium acts as a flow that drags the light according to the Fresnel drag coefficient $v(1 - 1/n^2)$ , and that the ray direction (energy flow) diverges from the wave vector direction (which remains normal to the boundary due to phase matching).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Wave Optics - Class 12
Concept	Optical Path Difference
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free