\(\Delta x =\left(\mu_2-\mu_1\right) t\)

\(=(1.55-1.51) 0.1\,mm\)

\(=0.04 \times 10^{-4}\)

\(\Delta x =4 \times 10^{-6}=4\,\mu m\)

\(y =\frac{\Delta xD }{ d }=4 \times 10^{-6} \frac{ D }{ d }\)

\(\{ y\) is the distance of central maxima from geometric center \(\}\)

fringe width \((\beta)=\frac{\lambda D}{d}=4 \times 10^{-6} m \frac{ D }{ d }=4\,\mu m \frac{ D }{ d }\)

Central bright fringe spot will shift by ' \(x\) '

Number of shift \(=\frac{y}{\beta}\)

\(=\frac{4 \times 10^{-6} D / d }{4 \times 10^{-7} D / d }=10\,Ans\)