Question

When the $YDSE$ apparatus is immersed in a liquid, the fringe width decreases by $20\%$. The refractive index of the liquid is

• A. $0.75$
• B. $1.25$
• C. $2$
• D. $1.75$

Answer 1

The correct option is B $1.25$

Let the initial fringe width be $\beta$ and the new fringe width when the entire apparatus is immersed in liquid $={\beta }^{\prime }$

Given, ${\beta }^{\prime }=\frac{80\beta }{100}=\frac{4\beta }{5}...\left(1\right)$

As, $\beta =\frac{\lambda D}{d}$

And, ${\beta }^{\prime }=\frac{{\lambda }^{\prime }D}{d}=\frac{\lambda }{\mu }\frac{D}{d}...\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,

$\Rightarrow \frac{\lambda }{\mu }\frac{D}{d}=\frac{4}{5}\beta =\frac{4}{5}\frac{\lambda D}{d}$

$\Rightarrow \frac{1}{\mu }=\frac{4}{5}$

$\therefore \mu =\frac{5}{4}=1.25$

Hence, option $\left(\text{B}\right)$ is correct.