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

`y_(8) = y_(5)`
`(n lambda_(1)D)/(d) = ((2n-1))(lambda D)/(2)`
`(8D)/(d) lambda_(1) = ((2 xx 5-1))/(2) (lambda D)/(d)`
`8 lambda_(1) = (9)/(2)lambda`
`lambda_(1) = (9)/(16)lambda`
`(lambda)/(mu) = (9)/(16)lambda [lambda_(1) = (lambda_("air"))/(mu)]`
`mu = (16)/(9)`
`mu = 1.78`