\(d=1\,mm\,=\,1 \times 10^{-3}\,mm\),  \(D=1 \mathrm{m}\),  \(\lambda=500 \times 10^{-9} \mathrm{m}\)

Fringe width \(\beta=\frac{D \lambda}{d}\)

Width of central maxima in a single slit As per question, width of central maxima of single slit pattem \(=\) width of \(10\) maxima of double slit pattern

\(\frac{{2\lambda D}}{a} = 10\left( {\frac{{\lambda D}}{d}} \right)\)

\(a = \frac{{2d}}{{10}} = \frac{{2 \times {{10}^{ - 3}}}}{{10}}\) \( = 0.2 \times {10^{ - 3}}{\text{m}} = 0.2\,{\text{mm}}\)