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Question #91081

Difficulty: 5/10 | 🟢 Free

The Question

In a Young's Double Slit Experiment, the slit separation is $d$ and the distance to the screen is $D$ ( $D \gg d$ ). The coherent light source has wavelength $\lambda$ . A small point-like light detector is embedded in the screen at the central maximum ( $y=0$ ). At $t=0$ , the screen begins to move transversely (parallel to the plane of the slits) with a constant acceleration $a$ . The detector has a finite response time $\tau$ , meaning it can only resolve intensity variations whose instantaneous frequency $f$ satisfies $f \le 1/\tau$ . For $f > 1/\tau$ , it records a constant time-averaged blurred intensity. At what time $t_c$ does the detector stop resolving individual fringes and start recording a blurred intensity?

Options

A.
$\frac{\lambda D}{a d \tau}$
B.
$\frac{2 \lambda D}{a d \tau}$
C.
$\sqrt{\frac{\lambda D}{a d}}$
D.
$\frac{\lambda D \tau}{a d}$

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

Intensity Distribution in YDSE|Non-Uniform Acceleration Constraint

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 concept of dynamic superposition and instantaneous frequency in a non-inertial setup.

The primary trap lies in calculating the frequency of intensity variations.

Students often incorrectly assume the frequency is $f = \phi(t)/(2\pi t)$ by simply dividing the total phase by time, leading to a missing factor of 2 (Option B).

The correct physical principle requires differentiating the time-dependent phase $\phi(t)$ to find the instantaneous angular frequency $\omega = d\phi/dt$ .

Additionally, the problem serves as a dimensional analysis filter; Option D has dimensions of $[T^3]$ , punishing students who blindly manipulate variables without checking units.

Finally, Option C traps students who calculate the time to reach the first interference minimum instead of applying the detector's bandwidth constraint.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Wave Optics - Class 12
Concept	Intensity Distribution in YDSE
Difficulty	5
Cognitive Load	6
Target Solve Time	140 sec
Access	Free