$\frac{1}{\lambda }=R(\frac{1}{{{{{n}'}}^{2}}}-\frac{1}{n})\Rightarrow \left\{ \begin{matrix} \frac{1}{\lambda }=R(\frac{1}{{{1}^{2}}}-\frac{1}{{{4}^{2}}})\Rightarrow \lambda =\frac{16}{15R} \\ \frac{1}{{{\lambda }'}}=R(\frac{1}{{{1}^{2}}}-\frac{1}{{{{{n}'}}^{2}}})\Rightarrow {\lambda }'=\frac{{{{{n}'}}^{2}}}{({{{{n}'}}^{2}}-1)R} \\ \end{matrix} \right.$
$\frac{\lambda }{{{\lambda }'}}=\frac{\frac{16}{15R}}{\frac{{{{{n}'}}^{2}}}{({{{{n}'}}^{2}}-1)R}}=\frac{16({{{{n}'}}^{2}}-1)}{15{{{{n}'}}^{2}}}=\frac{4}{5}\Rightarrow \frac{{{{{n}'}}^{2}}-1}{{{{{n}'}}^{2}}}=\frac{3}{4}\Rightarrow 4{{{n}'}^{2}}-4=3{{{n}'}^{2}}\Rightarrow {n}'=2$