$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ is:

• A
  $\frac{\sqrt{2}-1}{\sqrt{2}+1}$
• B
  $\frac{1+\sqrt{5}}{\sqrt{5}-1}$
• C
  $\frac{1+\sqrt{5}}{\sqrt{2}-1}$
• D
  $\frac{\sqrt{3}+1}{\sqrt{2}-1}$