Question

Young's double-slit experiment is made in a liquid. The $10^{th}$ bright fringe in liquid lies where $6^{th}$ dark fringe lies in vacuum the refractive index of the liquid is approximately-

• A. $1.8$
• B. $1.54$
• C. $1.67$
• D. $1.2$

Answer 1

Answer: (A)

Fringe width $\beta =\frac{\lambda D}{d}$
When the apparatus is immersed in a liquid
Then ${\lambda }^{\prime }=\frac{\lambda }{\mu }$
Given that $10^{th}$ bright fringe in liquid $=6^{th}$ dark fringe in air
$\Rightarrow 10\frac{{\lambda }^{\prime }D}{d}=\left(2\times 6-1\right)\frac{\lambda D}{2d}$
$\Rightarrow 10{\lambda }^{\prime }=\frac{11}{2}\lambda$
$\Rightarrow \frac{{\lambda }^{\prime }}{\lambda }=\frac{11}{20}$
$\Rightarrow \frac{1}{\mu }=\frac{11}{20}$
$\Rightarrow \mu =\frac{20}{11}=1.8$