Q: Young’s double slit experiment is made in a liquid. The 10th bright fringe in liquid lies where 6th dark fringe lies in vacuum. The refractive index of the liquid is approximately
Sol: Fringe width β = λD/d, When the apparatus is immersed in a liquid, λ and hence β is reduced μ (refractive
index) times.
$\large 10\beta’ = \frac{2 \times 6 -1}{2}\times \beta = 5.5 \beta $
$\large 10 \times \frac{\lambda’ D}{d} = 5.5 \times \frac{\lambda D}{d} $
or, $\large \frac{\lambda}{\lambda’} = \frac{10}{5.5} $
$\large \mu = \frac{10}{5.5} = 1.8 $