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

Options

A. `1.59`
B. `1.69`
C. `1.78`
D. `1.25`

Answer

C

Explanation

Positin of `8^(th)` bright fringe in medium,
`x=(8lambda_(m)D)/(d)`
Position of `5^(th)` dark fringe in air,
`x.=((5-(1)/(2))lambda_("air")D)/(d)=(4.5lambda_("air")D)/(d)`
Given `x=x.,:.(8lambda_(m)D)/(d)=(4.5lambda_("air")D)/(d)`
`mu_(m)=(lambda_("air"))/(lambda_(m))=(8)/(4.5)~~1.78`