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Question #83483

Difficulty: 5/10 | 🟢 Free

The Question

In a Young's double slit experiment, the distance between the two slits is $d$ and the width of each slit is $a = \frac{d}{3}$ . The slits are illuminated by a coherent monochromatic light of wavelength $\lambda$ . A screen is placed at a distance $D$ ( $D \gg d$ ) from the slits. Initially, the maximum intensity on the screen is $I_0$ . A transparent glass plate of refractive index $\mu$ and thickness $t = \frac{\lambda}{2(\mu-1)}$ is then placed directly in front of one of the slits. What is the intensity of the central interference maximum (the point on the screen where the net phase difference between the waves from the two slits is zero) after the glass plate is inserted?

Options

A.
$\frac{9I_0}{\pi^2}$
B.
$I_0$
C.
$\frac{3I_0}{\pi}$
D.
$\frac{4I_0}{\pi^2}$

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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

Phase Constant (Epoch)|Diffraction vs Interference|Fringe Width Invariance

Why This Question Is Tricky

Examiner Levers

Dimensional Analysis

Tests if the student verifies units/dimensions before selecting.

Difficulty Boost : +2

Common Mistakes

This question tests the student's understanding of the convolution of interference and diffraction in a Young's Double Slit Experiment.

A common trap is assuming that a phase plate shifts the entire intensity pattern uniformly, leading students to incorrectly conclude the central interference maximum retains its original peak intensity $I_0$ .

However, the phase plate only introduces a phase difference between the two slits (shifting the interference fringes) but does not create a phase gradient across an individual slit.

Thus, the diffraction envelope remains stationary.

Students must realize that the shifted interference maxima are now modulated by the lower-intensity regions of the stationary diffraction envelope.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Waves - Class 11 Part 2
Concept	Phase Constant (Epoch)
Difficulty	5
Cognitive Load	6
Target Solve Time	140 sec
Access	Free