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Question #43732

Difficulty: 8/10 | 🟢 Free

The Question

A monochromatic point source $S$ emitting light of proper wavelength $\lambda$ is placed on the principal axis of a Young's Double Slit apparatus having two identical slits. The source is at a large distance from the slits. At $t=0$ , the source starts accelerating towards the slits with a time-dependent acceleration $a(t) = \alpha t$ , where $\alpha$ is a positive constant. A small detector is fixed on the screen at a point $P$ which initially coincides with the $n$ -th order bright fringe ( $n \gg 1$ ). Assuming the speed of the source remains much less than the speed of light $c$ during the observation, and ignoring the light travel time, at what time $t$ will the detector record a zero intensity for the first time?

Options

A.
$\sqrt{\frac{c}{n \alpha}}$
B.
$\sqrt{\frac{2c}{n \alpha}}$
C.
$\sqrt{\frac{c}{2 n \alpha}}$
D.
$\sqrt{\frac{c}{\alpha}}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Diffraction vs Interference|Young's Double Slit Geometry|Non-Uniform Acceleration Constraint|Approximation (Binomial)

Why This Question Is Tricky

Common Mistakes

This question tests the coupling of kinematics with wave optics and the Doppler effect.

A common trap is misapplying the phase difference condition by assuming a full $2\pi$ phase shift is needed for zero intensity (leading to option B), or incorrectly integrating the non-uniform acceleration as $v = \alpha t^2$ without the factor of $1/2$ (leading to option C).

Furthermore, students often incorrectly expand the time-dependent phase difference $\Delta \phi(t) = 2\pi n (1 - v/c)^{-1}$ by dropping the fringe order $n$ in the variable term (leading to option D).

The problem requires a rigorous transition from a static geometric path difference to a dynamic, time-dependent phase analysis using the binomial approximation.

Quick Facts About This Question

Question Information

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