JEE Main 2021 — Physics Optics

2021mcqhard

In the Young's double slit experiment, the distance between the slits varies in time as $d(t)={d}_{0}+{a}_{0}\mathrm{sin}\omega t$ ; where ${d}_{0},\omega$ and ${a}_{0}$ are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as:

Official previous-year question

Held on 25 Jul 2021 · Verified 6 Jul 2026.

Options

A
$\frac{2\lambda D({d}_{0})}{({d}_{0}^{2}-{a}_{0}^{2})}$
B
$\frac{2\lambda D{a}_{0}}{({d}_{0}^{2}-{a}_{0}^{2})}$
C
$\frac{\lambda D}{{d}_{0}^{2}}{a}_{0}$
D
$\frac{\lambda D}{{d}_{0}+{a}_{0}}$

Did you get this right?

Solution

Fringe width,

$\beta =\frac{\lambda D}{d}$

${\beta }_{\mathrm{max}}\Rightarrow {d}_{\mathrm{min}}$ and ${\beta }_{\mathrm{min}}\Rightarrow {d}_{\mathrm{max}}$

$d={d}_{0}+{a}_{0}\mathrm{sin}\omega t$

${d}_{\mathrm{max}}={d}_{0}+{a}_{0}$ and ${d}_{\mathrm{min}}={d}_{0}-{a}_{0}$

$\therefore {\beta }_{\mathrm{min}}=\frac{\lambda D}{{d}_{0}+{a}_{0}}$ and $\therefore {\beta }_{\mathrm{max}}=\frac{\lambda D}{{d}_{0}-{a}_{0}}$

${\beta }_{\mathrm{max}}-{\beta }_{\mathrm{min}}=\frac{\lambda D}{{d}_{0}-{a}_{0}}-\frac{\lambda D}{{d}_{0}+{a}_{0}}=\frac{2\lambda D{a}_{0}}{{d}_{0}^{2}-{a}_{0}^{2}}$

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Options

$\frac{2\lambda D({d}_{0})}{({d}_{0}^{2}-{a}_{0}^{2})}$

$\frac{2\lambda D{a}_{0}}{({d}_{0}^{2}-{a}_{0}^{2})}$

$\frac{\lambda D}{{d}_{0}^{2}}{a}_{0}$

$\frac{\lambda D}{{d}_{0}+{a}_{0}}$

Solution

Fringe width,

$\beta =\frac{\lambda D}{d}$

${\beta }_{\mathrm{max}}\Rightarrow {d}_{\mathrm{min}}$ and ${\beta }_{\mathrm{min}}\Rightarrow {d}_{\mathrm{max}}$

$d={d}_{0}+{a}_{0}\mathrm{sin}\omega t$

${d}_{\mathrm{max}}={d}_{0}+{a}_{0}$ and ${d}_{\mathrm{min}}={d}_{0}-{a}_{0}$

$\therefore {\beta }_{\mathrm{min}}=\frac{\lambda D}{{d}_{0}+{a}_{0}}$ and $\therefore {\beta }_{\mathrm{max}}=\frac{\lambda D}{{d}_{0}-{a}_{0}}$

${\beta }_{\mathrm{max}}-{\beta }_{\mathrm{min}}=\frac{\lambda D}{{d}_{0}-{a}_{0}}-\frac{\lambda D}{{d}_{0}+{a}_{0}}=\frac{2\lambda D{a}_{0}}{{d}_{0}^{2}-{a}_{0}^{2}}$

JEE Main 2021 — Physics Optics

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JEE Main 2021 — Physics Optics

Options

Did you get this right?

Solution

Your note

JEE Main Optics in other years

More JEE Main Optics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Thermodynamics

Waves & Oscillations

Keep practicing Optics