Young's double slit experiment is made in a liquid. The tenth bright fringe in liquid lies in screen where 6th dark fringe lies in vacuum. The refractive index of the liquid is approximately

Options

A. 1.52
B. 1.62
C. 1.82
D. 1.22

Answer

C

Explanation

When light travels in a liquid of refractive index n, its velocity and wavelength decrease and since the fringe width `Xproplamda`, the fringe width also decreases.
`lamda` becomes `lamda/n` and the fringe width becomes `X/n`
thus `X'=(X)/(n)=(lamdaD)/(nd)" "(because X=(lamdaD)/(d))`
IN the liquid, the distance of the 10th bright band from the centre `=10X'=10*(lamdaD)/(nd) `
and in air, the distance of the 6th dark band from the centre
`=(5.5)X=(11)/(2)X=(11)/(2)(lamdaD)/(d)`
and it is given that,
`10X'=(11)/(2)X or 10(lamdaD)/(nd)=(11)/(2)(lamdaD)/(d)" "therefore (10)/(n)=(11)/(2)`
`therefore 11n=20" "therefore n=(20)/(11)=1.82`