$\frac{1}{\lambda} = Rz^2(\frac{1}{1^2} - \frac{1}{2^2})$

$\Rightarrow \lambda = \frac{4}{3Rz^2}$

$\Rightarrow \lambda_1 = \frac{4}{3R}$

$\Rightarrow \lambda_2 = \frac{4}{3R}$

$\Rightarrow \lambda_3 = \frac{4}{12R}$

$\Rightarrow \lambda_4 = \frac{4}{27R}$

$\Rightarrow \lambda_1 = \lambda_2 = 4\lambda_3 = 9\lambda_4$