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Q.

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

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a

1.59

b

1.69

c

1.78

d

1.25

answer is C.

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Detailed Solution

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The distance of n^th dark band in air from centre of screen is $y = (n - \frac{1}{2}) β \dots (1)$
The distance of n^th bright band in medium:
$y^{'} = n^{'} \cdot β^{'}$
where $β^{'} = \frac{β}{μ} .$
But y=y''
$\begin{array}{l} (n - \frac{1}{2}) β = n^{'} \cdot β^{'} \Rightarrow (5 - \frac{1}{2}) β = 8 \cdot \frac{β}{μ} \\ \Rightarrow μ = \frac{16}{9} = 1.78 . \end{array}$

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