\(F=\frac{f}{D}\)
For F/4 camera, F number is \(4,\)
\(4=\frac{f}{D_{1}}\)
For \(F/5.6\) camera, \(F\) number is \(5.6,\)
\(5.6=\frac{f}{D_{2}}\)
\(\frac{D_{2}}{D_{1}}=\frac{4}{5.6}\)
\(\frac{D_{2}}{D_{1}}=\frac{1}{1.412}\)
\(D_{2}=\frac{D_{1}}{\sqrt{2}}\)