Paragraph I: In a Young's double slit experiment, each of the two...

Paragraph I: In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of

0.8 \mathrm{~mm}

. The distance between the slits at time

t

is given by

d=(0.8+0.04 \sin \omega t) \mathrm{mm}

, where

\omega=0.08 \mathrm{rad} \mathrm{s}^{-1}

. The distance of the screen from the slits is

1 \mathrm{~m}

and the wavelength of the light used to illuminate the slits is

6000 Ã…

. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point

O

Paragraph I: In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are

The

8^{\text{th }}

bright fringe above the point

\mathrm{O}

oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer

(\mu \mathrm{m})

, is ___________ .

Correct answer

Step-by-step solution

\begin{aligned} & y=n \cdot\left(\frac{\lambda D}{d}\right) \\ & \text{\text{ for } } 8^{\text{th }} \text{ fringe } \\ & y=8 \frac{\lambda D}{d} \\ & y_{\max }=8 \frac{\lambda D}{d_{\min }} \\ & y_{\min }=8 \frac{\lambda D}{d_{\max }} \\ & y_{\max }-y_{\min }=8 \lambda D\left[\frac{1}{d_{\min }}-\frac{1}{d_{\max }}\right] \\ & \lambda=6000 Ã…\end{aligned}

\begin{aligned} & \mathrm{D}=1 \mathrm{ m} \\ & \mathrm{ d}_{\max }=0.34 \mathrm{ mm} \\ & \mathrm{ d}_{\text{min }}=0.76 \mathrm{ mm} \\ & y_{\max }-y_{\min }=8 \times 6000 \times 10^{-10} \times 1\left[\frac{1}{0.76 \times 10^{-3}}-\frac{1}{0.84 \times 10^{-3}}\right] \\ & =8 \times 6 \times 10^{-4} \times\left[\frac{0.08}{0.76 \times 0.84}\right]=601.5 \mu \mathrm{m} \\ & \end{aligned}

$ (answer range is from 598 to 602 )

Practice Wave Optics on Quantrex Academy →

More from Wave Optics

In the List-I, four optical effects are mentioned. The physical phenomena of light which… JEE Advanced 2026 In a single slit diffraction experiment, a slit of width (0.016 ± 0.002) mm is used to… JEE Advanced 2026 As shown in the figure, a ray AB of unpolarized light enters from water of refractive… JEE Advanced 2026 Some distant star is to be observed by some telescope of diameter of objective lens a… JEE Main 2026 In a Young double slit experiment, the wavelength of incident light is 6000 Å, the… JEE Main 2026 In interference experiment the path difference between two interfering waves at a point A… JEE Main 2026 An unpolarized light of intensity I_o passes through polarizer and then through a certain… JEE Main 2026 The maximum intensity in a Young's double slit experiment is I_0 . Distance between the… JEE Main 2026 Full Wave Optics list All JEE Advanced PYQs