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Question #42224

Difficulty: 8/10 | 🟢 Free

The Question

A cylindrical container of height $H$ is filled with a liquid of density $\rho$ and optical absorption coefficient $\alpha$ . A uniform light beam of intensity $I_0$ is incident normally on the entire free surface of the liquid. Assuming the refractive index of the liquid is $n=1$ and the free surface does not reflect any light, what is the gauge pressure of the liquid at a depth $H$ ? (Here $c$ is the speed of light in vacuum, and assume the momentum of a photon is $E/c$ ).

Options

A.
$\rho g H + \frac{I_0}{c} (1 - e^{-\alpha H})$
B.
$\rho g H + \frac{I_0}{c}$
C.
$\rho g H + \frac{I_0}{c} e^{-\alpha H}$
D.
$\rho g H + \frac{\alpha I_0 H}{c}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Hydrostatic Paradox|Radiation Pressure|Principle of Superposition

Why This Question Is Tricky

Common Mistakes

This question tests the coupling of radiation pressure with fluid statics, specifically targeting the misconception that radiation pressure acts as a simple scalar boundary condition.

Students often incorrectly assume the gauge pressure is simply $\rho g H + I_0/c$ by treating the incident radiation as a surface pressure.

However, because the fluid is absorptive, the momentum transfer occurs continuously throughout the volume.

The trap lies in failing to recognize radiation pressure in an absorptive medium as a depth-dependent body force (derived from the gradient of the Poynting vector) that must be integrated over the optical path.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Mechanical Properties of Fluids - Class 11 Part 2
Concept	Hydrostatic Paradox
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free