Explanation

(b) From Rayleigh scattering concept
$I \propto \frac{1}{\lambda^{4}}or\frac{I_{1}}{I_{2}} = \left( \frac{\lambda_{2}}{\lambda_{1}} \right)^{4}$
$or\ \ \ \ \ \left( \frac{\lambda_{2}}{\lambda_{1}} \right)^{4} = \frac{1}{4}$
$or\ \ \frac{\lambda_{2}}{\lambda_{1}} = \left( \frac{1}{2} \right)^{1/2}$
$or\ \ \ \frac{\lambda_{1}}{\lambda_{2}} = \frac{\sqrt{2}}{1}$