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Question #43203

Difficulty: 8/10 | 🟢 Free

The Question

A point object is placed at $x = -40 \text{ cm}$ on the principal axis of a thin convex lens of focal length $f_1 = 30 \text{ cm}$ located at the origin ( $x = 0$ ). A concave mirror of focal length $f_2 = 30 \text{ cm}$ is placed at $x = 180 \text{ cm}$ , facing the lens. A solid glass slab of thickness $t = 60 \text{ cm}$ and refractive index $\mu = 1.5$ is placed such that its faces are perpendicular to the principal axis, occupying the region from $x = 60 \text{ cm}$ to $x = 120 \text{ cm}$ . Find the x-coordinate of the final image formed after the light rays pass through the lens, travel through the slab, reflect from the mirror, pass back through the slab, and finally emerge through the lens.

Options

A.
$-120 \text{ cm}$
B.
$-60 \text{ cm}$
C.
$-48 \text{ cm}$
D.
$-40 \text{ cm}$

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

Lateral Shift in Slab|Virtual Object Trap|Refractive Index Relativity

Why This Question Is Tricky

Common Mistakes

This problem tests the principle of optical path shifting by a dielectric slab and its superposition with spherical mirrors and lenses.

The primary trap is the 'Virtual Object Trap' combined with directional dependence.

Students often memorize the shift formula $\Delta x = t(1 - 1/\mu)$ but fail to apply it as a vector quantity dependent on the direction of light propagation.

Common mistakes include: (1) Ignoring the slab on the return journey (yielding $-60 \text{ cm}$ ), (2) Applying the return shift in the $+x$ direction instead of $-x$ (yielding $-48 \text{ cm}$ ), or (3) Forgetting the slab entirely for both passes (yielding $-40 \text{ cm}$ ).

By forcing the beam to converge exactly at the slab boundaries, it also tests confidence in applying the shift formula to boundary-case virtual objects.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Lateral Shift in Slab
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free