Young’s double slit experiment in 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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1.59

1.78

1.25

1.69

answer is A.

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Detailed Solution

In Young's double slit experiment, the position of bright and dark fringes depends on the wavelength of light and the medium through which it travels. When light passes through a medium other than air, its speed changes due to the change in the refractive index, which also affects the fringe positions.

In air, the fringe positions are determined by the wavelength of light in air ( $\lambda_{\text{air}}$ $λ$ $air$ $$ ), and the formula for the position of the $m$ $m$ -th bright fringe is:

${y_1} = {y_2} \Rightarrow \frac{{(\Delta {x_1})D}}{d} = \frac{{(\Delta {x_2})D}}{d}\$

$\Rightarrow {\eta _1}{\lambda _m} = \frac{{(2{n_2} - 1){\lambda _a}}}{2}\$ $;\,8{\lambda _m} = \frac{{(2 \times 5 - 1){\lambda _a}}}{2}\,;\$

$\frac{8}{{4.5}} = \frac{{{\lambda _a}}}{{{\lambda _m}}} = \mu \,\,;$ $\mu = \frac{{16}}{9} = 1.77\$

By using the relationship between the positions of the fringes, we can derive the refractive index $n$ $n$ . Since the positions of the fringes are directly proportional to the wavelength, we can conclude that the refractive index of the medium is $n = 1.78$ n=1.78, which is the correct answer. This means the light slows down in the medium, reducing the fringe separation compared to air

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