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…

Question

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 $6000 Å$. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point $O$. The $8^{	ext {th }}$ 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 ___________ .

Aicharya · Accepted Answer

$\begin{aligned} & y=n \cdot\left(\frac{\lambda D}{d}ight) \ & 	ext { for } 8^{	ext {th }} 	ext { fringe } \ & y=8 \frac{\lambda D}{d} \ & y_{\max }=8 \frac{\lambda D}{d_{\min }} \ & y_{\min }=8 \frac{\lambda D}{d_{\max }} \ & y_{\max }-y_{\min }=8 \lambda D\left[\frac{1}{d_{\min }}-\frac{1}{d_{\max }}ight] \ & \lambda=6000 Å\end{aligned}$ $\begin{aligned} & \mathrm{D}=1 \mathrm{~m} \ & \mathrm{~d}_{\max }=0.34 \mathrm{~mm} \ & \mathrm{~d}_{	ext {min }}=0.76 \mathrm{~mm} \ & y_{\max }-y_{\min }=8 	imes 6000 	imes 10^{-10} 	imes 1\left[\frac{1}{0.76 	imes 10^{-3}}-\frac{1}{0.84 	imes 10^{-3}}ight] \ & =8 	imes 6 	imes 10^{-4} 	imes\left[\frac{0.08}{0.76 	imes 0.84}ight]=601.5 \mu \mathrm{m} \ & \end{aligned}$ (answer range is from 598 to 602 ) `

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

Solution