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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
Explanation
Fringe width in a medium is reduced by a factor $\mu$.
Detailed Solution
$X_1 = X_{5th\ dark} = (2\times5 - 1)\frac{\lambda D}{2d}$
$X_2 = X_{8th\ bright} = 8\frac{\lambda D}{\mu d}$
$X_1 = X_2 \Rightarrow \frac{9}{2}\frac{\lambda D}{d} = 8\frac{\lambda D}{\mu d}$
$\mu = \frac{16}{9} = 1.78$