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Question #43054

Difficulty: 8/10 | 🟢 Free

The Question

In a Young's Double Slit Experiment, light of wavelength $\lambda$ illuminates two slits separated by an initial distance $d_0$ . The interference pattern is recorded on a photographic plate placed at a distance $D$ ( $D \gg d_0$ ). During the exposure time $T$ , the plane containing the slits is uniformly heated such that the slit separation increases linearly with time, reaching a final separation of $d_0 + \Delta d$ . The plate records the time-averaged intensity $\langle I(y) \rangle = \frac{1}{T} \int_0^T I(y,t) dt$ , where $y$ is the distance from the central maximum. What is the minimum non-zero distance $y$ where the fringe contrast completely vanishes?

Options

A.
$\frac{\lambda D}{\Delta d}$
B.
$\frac{\lambda D}{2 \Delta d}$
C.
$\frac{\lambda D}{d_0 + \Delta d/2}$
D.
$\frac{\lambda D}{d_0}$

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

Optical Path Difference|Fringe Width Invariance|Linear Expansion

Why This Question Is Tricky

Common Mistakes

This question tests the distinction between discrete superposition and continuous time-averaging in wave optics.

A common trap is assuming that a spatial shift corresponding to half a fringe width (a phase shift of $\pi$ ) causes complete blurring, as it does when superimposing two discrete static patterns.

Consequently, students incorrectly set $\Delta \phi = \pi$ , leading to the trap answer $\lambda D / (2 \Delta d)$ .

However, for a continuously expanding slit separation, a phase sweep of $\pi$ only reduces the contrast (yielding an amplitude factor of $2/\pi$ ).

Complete vanishing of the fringe contrast requires the time-average integral to cover exactly one full period of the cosine function, meaning the phase must sweep through $2\pi$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Wave Optics - Class 12
Concept	Optical Path Difference
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free