\(I=I_{0} \cos ^{2} \frac{\phi}{2}\)

\(\frac{I_{0}}{2}=I_{0} \cos ^{2} \frac{\phi}{2}\)

\(\cos \frac{\phi}{2}=\frac{1}{\sqrt{2}}\)

\(\phi=\frac{\pi}{2}\)

The path difference is,

\(\Delta x=\frac{\lambda}{2 \pi} \times \frac{\pi}{2}\)

\(=\frac{\lambda}{4}\)

The distance of the point from the central maxima will be,

\(y=\frac{\Delta x D}{a}\)

\(=\frac{\lambda D}{4 a}\)

\(=\frac{500 \times 10^{-9} \times 2}{4 \times 2 \times 10^{-3}}\)

\(=125 \times 10^{-6} m\)

\(=125 \mu m\)