$\frac{1}{\lambda }=R(\frac{1}{{{{{n}'}}^{2}}}-\frac{1}{{{n}^{2}}})\Rightarrow \left\{ \begin{matrix}    \frac{1}{{{\lambda }_{1}}}=R(\frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}})=\frac{5R}{36}\Rightarrow {{\lambda }_{1}}=\frac{36}{5R}  \\    \frac{1}{{{\lambda }_{2}}}=R(\frac{1}{{{2}^{2}}}- frac{1}{{{4}^{2}}})=\frac{3R}{16}\Rightarrow {{\lambda }_{1}}=\frac{16}{3R}  \\ \end{matrix} \right.$  

$\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{\frac{36}{5R}}{\frac{16}{3R}}=\frac{27}{20}\Rightarrow \frac{6561}{{{\lambda }_{2}}}=\frac{27}{20}\Rightarrow {{\lambda }_{2}}=4860\overset{{}^\circ }{\mathop{A}}\,$