Question

In a double slit experiment the angular width of a fringe is found to be $0.2^{o}$ , find the angular width of the fringe if entire experimental apparatus is immersed in a liquid with refractive index $\frac{4}{3}$ .

• A. $0.15^{o}$
• B. $1^{o}$
• C. $2^{o}$
• D. $0.3^{o}$

Answer 1

Answer: (A)

Since a fringe of width $\beta $ is formed on the screen.
At distance $D$ from the slits, so the angular fringe width
$\theta =\frac{\beta }{D}=\frac{D \lambda / d}{D}=\frac{\lambda }{d} \, \left[\therefore \beta = \frac{D \lambda }{d}\right]$
$\Longrightarrow d=\frac{\lambda }{\theta }$
If the wavelength in water be $\lambda '$ and the angular fringe
Width be $\theta ^{'},$ then
$d=\frac{\lambda '}{\theta ^{'}}$ or $\frac{\lambda }{\theta }=\frac{\lambda '}{\theta '}$ or $\theta ^{'}=\frac{\lambda '}{\lambda }. \, \theta ^{'}=\frac{\lambda / \mu }{\lambda }.\theta \, \left[\therefore \, \lambda ^{'} = \frac{\lambda }{\mu }\right]$
$\therefore \, \theta ^{'}=\frac{0.2^{o}}{4 / 3}=0.15^{o}$