Question

Young's double slit experiment is performed in a liquid medium. The ${10}^{\text{th}}$ bright fringe in liquid lies where $6^{\text{th}}$ 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

The correct option is A $1.8$

Fringe width, $\beta =\frac{\lambda D}{d}$

When the apparatus is immersed in a liquid, $\lambda$ and hence $\beta$ is reduced, $\mu$ (refractive index) times,

$(\beta {)}_{10,b}=(\beta {)}_{6,d}$
or, $\frac{n{\lambda }^{\prime }D}{d}=\frac{(2n-1)\lambda D}{2d}$
$\Rightarrow 10{\lambda }^{\prime }\left(\frac{D}{d}\right)=\left(5.5\right)\frac{\lambda D}{d}$
$\Rightarrow \frac{\lambda }{{\lambda }^{\prime }}=\frac{10}{5.5}=\mu$
$\Rightarrow \mu \approx 1.8$

Hence, $\left(A\right)$ is the correct answer.