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Question #43561

Difficulty: 8/10 | 🟢 Free

The Question

A thin biconvex lens made of an isotropic, highly compressible transparent polymer has a focal length $f_0 = 20 \text{ cm}$ when placed in a liquid at a reference hydrostatic pressure $P_0 = 6 \times 10^7 \text{ Pa}$ . The lens is then moved deeper into the same liquid to a region where the absolute hydrostatic pressure is $P = 10^8 \text{ Pa}$ . A converging beam of light traveling through the liquid is incident on the lens. In the absence of the lens, the beam would focus at a point $90 \text{ cm}$ behind the optical centre of the lens. Given that the bulk modulus of the lens material is $B = \frac{4}{3} \times 10^8 \text{ Pa}$ , find the transverse magnification of the image formed by the lens at this new depth. (Assume the refractive indices of the lens material and the liquid remain constant, and the lens remains thin and geometrically similar to its original shape).

Options

A.
$+\frac{1}{6}$
B.
$+\frac{1}{7}$
C.
$+\frac{2}{11}$
D.
$-\frac{1}{4}$

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

Virtual Object Trap|Optical Instrument Magnification|Atmospheric Pressure Reference|Binomial Approximation

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of elasticity and ray optics, specifically targeting two major traps.

First, the 'Atmospheric Pressure Reference' trap: students often blindly use the absolute pressure $P$ instead of the gauge pressure difference $\Delta P = P - P_0$ when calculating volumetric strain, leading to an incorrect focal length of $15 \text{ cm}$ and a magnification of $+1/7$ (Option B).

Second, the 'Virtual Object' trap: students frequently misassign the sign convention for a converging incident beam, treating it as a real object ( $u = -90 \text{ cm}$ ) rather than a virtual object ( $u = +90 \text{ cm}$ ), which drastically alters the magnification to $-1/4$ (Option D).

Option C catches those who ignore the pressure-induced deformation entirely.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Virtual Object Trap
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free