c
\( \text { For } n^{\text {th }} \text { minima } \)

\( b \sin \theta=n \lambda \)

\( (\lambda \text { is } \operatorname{small} \text { so } \sin \theta \text { is small, hence } \sin \theta \simeq \tan \theta) \)

\( b \tan \theta=n \lambda \)

\( b \frac{y}{D}=n \lambda \)

\( \Rightarrow y_n=\frac{n \lambda D}{b} \text { (Position of } n^{\text {th }} \text { minima) }\)

\( \mathrm{B} \rightarrow 1^{\mathrm{st}} \text { minima, } \mathrm{A} \rightarrow 3^{\mathrm{rc}} \text { minima } \)

\( \mathrm{y}_3=\frac{3 \lambda \mathrm{D}}{\mathrm{b}}, \mathrm{y}_1=\frac{\lambda \mathrm{D}}{\mathrm{b}} \)

\( \Delta \mathrm{y}=\mathrm{y}_3-\mathrm{y}_1=\frac{2 \lambda \mathrm{D}}{\mathrm{b}} \)

\( 3 \times 10^{-3}=\frac{2 \times 6000 \times 10^{-10} \times 0.5}{\mathrm{~b}} \)

\( \mathrm{~b}=\frac{2 \times 6000 \times 10^{-10} \times 0.5}{3 \times 10^{-3}} \)

\( \mathrm{~b}=2 \times 10^{-4} \mathrm{~m} \)

\( x=2\)