Diffraction spread \(=\frac{\lambda}{\mathrm{a}} \times \mathrm{L}=\frac{\lambda \mathrm{L}}{\mathrm{a}}\)

The sum \(b=a+\frac{\lambda L}{a}\)

For \(b\) to be minimum \(\frac{{{\text{db}}}}{{{\text{da}}}} = 0\)                  \(\frac{{\text{d}}}{{{\text{da}}}}\left( {{\text{a}} + \frac{{\lambda {\text{L}}}}{{\text{a}}}} \right) = 0\)

\(a =\sqrt{\lambda L}\)

\(b\, \min =\sqrt{\lambda L}+\sqrt{\lambda L}=2 \sqrt{\lambda L}=\sqrt{4 \lambda L}\)