Question

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that $8^{th}$ bright fringe in the medium lies where $5^{th}$ dark fringe lies in air. The refractive index of the medium is nearly

• A. 1.59
• B. 1.69
• C. 1.78
• D. 1.25

Answer 1

The correct option is C 1.78

In medium ${\lambda }_{medium}=\frac{{\lambda }_{air}}{\mu }$
${\lambda }^{\prime }=\frac{\lambda }{\mu }$
For Air, $5^{th}$ dark,
$y_s=(2m-1)\frac{\lambda D}{2d}$
For $m=5$, $y_s=\frac{9\lambda D}{2d}$
For bright in medium ($n=8$)
$y^{\prime }=n\frac{{\lambda }^{\prime }D}{d}$, ${\lambda }^{\prime }=\frac{\lambda }{\mu }$
$\therefore y^{\prime }=\frac{8\lambda }{\mu }\frac{D}{d}$
$y^{\prime }=y$
$\frac{9\times D}{2d}=\frac{8\times D}{\mu d}$
$\therefore \mu =\frac{8\times 2}{9}$
$\mu =1.78$