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Question #43737

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The Question

A plane wavefront of wavelength $\lambda = 600 \text{ nm}$ is incident normally on a converging lens $L_1$ of focal length $f_1 = 30 \text{ cm}$ . A single slit of width $a = 0.3 \text{ mm}$ is placed at a distance of $10 \text{ cm}$ behind $L_1$ . A diverging lens $L_2$ of focal length $f_2 = -20 \text{ cm}$ is placed at a distance of $10 \text{ cm}$ behind the slit. A screen is placed behind $L_2$ such that a sharp Fraunhofer diffraction pattern of the slit is observed on it. Find the distance $D$ of the screen from $L_2$ and the linear width $W$ of the central maximum of the diffraction pattern.

Options

A.
$D = 20 \text{ cm}, W = 1.6 \text{ mm}$
B.
$D = 20 \text{ cm}, W = 0.8 \text{ mm}$
C.
$D = 20 \text{ cm}, W = 1.2 \text{ mm}$
D.
$D = 30 \text{ cm}, W = 1.6 \text{ mm}$

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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

Single Slit Diffraction Minima|Virtual Object Trap|Ray Optics

Why This Question Is Tricky

Common Mistakes

This question tests the advanced wave-optics concept of Fraunhofer diffraction formed by converging beams and the subsequent imaging of these diffraction patterns.

A common misconception is that the Fraunhofer pattern is always formed at infinity or at the focal plane of the nearest lens, leading students to incorrectly use $D = f_2$ or calculate the width using the physical distance from the slit to the screen ( $W = 2\lambda(d+D)/a$ ).

The trap lies in failing to recognize that the original convergence point acts as a virtual object for the second lens.

The true Fraunhofer plane shifts to the geometric image of this virtual object, and the diffraction pattern's width scales exactly by the lateral magnification of this imaging process, forcing a shift from standard textbook formulas to fundamental Fourier optics propagation logic.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Wave Optics - Class 12
Concept	Single Slit Diffraction Minima
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free