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(C) The position of the $n^{th}$ bright fringe in a medium with refractive index $\mu$ is given by $x_b = \frac{n \lambda_m D}{d}$,where $\lambda_m =

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$1.78$

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(C) The position of the $n^{th}$ bright fringe in a medium with refractive index $\mu$ is given by $x_b = \frac{n \lambda_m D}{d}$,where $\lambda_m = \frac{\lambda_{air}}{\mu}$.So,the position of the $8^{th}$ bright fringe in the medium is $x = \frac{8 \lambda_{air} D}{\mu d}$.The position of the $n^{th}$ dark fringe in air is given by $x_d = \frac{(n - 0.5) \lambda_{air} D}{d}$.So,the position of the $5^{th}$ dark fringe in air is $x' = \frac{(5 - 0.5) \lambda_{air} D}{d} = \frac{4.5 \lambda_{air} D}{d}$.Given that the positions are the same,$x = x'$,we have:$\frac{8 \lambda_{air} D}{\mu d} = \frac{4.5 \lambda_{air} D}{d}$.Canceling common terms $\lambda_{air}, D,$ and $d$ from both sides:$\frac{8}{\mu} = 4.5$.$\mu = \frac{8}{4.5} = \frac{80}{45} = \frac{16}{9} \approx 1.78$.

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

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