c
Position of \(8^{\text {th }}\) bright fringe in medium,

\(x=\frac{8 \lambda_{m} D}{d}\)

Position of \(5^{\text {th }}\) dark fringe in air,

\({x^{\prime}=\frac{\left(5-\frac{1}{2}\right) \lambda_{\operatorname{air}} D}{d}}\)

\({x^{\prime}=\frac{4.5 \lambda_{\operatorname{air}} D}{d}}\)

Given \(x=x^{\prime}\)

\(\therefore \,\,\frac{{8{\lambda _m}D}}{d} = \frac{{4.5{\lambda _{{\text{air}}}}D}}{d}\)

\({\mu _m} = \frac{{{\lambda _{{\text{air}}}}}}{{{\lambda _m}}} = \frac{8}{{4.5}} = 1.78\)