18. 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 ?

18. Young’s double slit experiment is 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 :

(a) 1.59 

(b) 1.69 

(c) 1.78 

(d) 1.25

Answer :  (c) 1.78 

\( {{x}_5}_{\text{air}} = {{x}_8}_{\text{medium}} \)

\( \frac{(2n-1)}{2} \cdot \lambda_{\text{air}} = n \lambda_{\text{medium}} \)

\( \frac{q}{2} \lambda_{\text{air}} = 8 \cdot \frac{\lambda_{\text{air}}}{\mu} \)

\( \mu = \frac{8 \times 2}{q} = \frac{16}{9} = 1.77 \)