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. 1.25
B. 1.59
C. 1.69
D. 1.78

Answer

D

Explanation

`X_(1)=X_("5th dark")=(2xx5-1)(lambdaD)/(2d)`
`X_(2)=X_("8th bright")=8(lambdaD)/(mud)`
`X_(1)=X_(2)`
`(9)/(2)(cancel(lambda)cancel(D))/(cancel(d))=8(cancel(lambda)cancel(D))/(mucancel(d))`
`mu=(16)/(9)=1.78`