If the ratio of amount of scattering of two light waves is 1:4, then the ratio of their wavelengths is

We know that, from Rayleigh’s scattering,
Amount of scattering $\propto \frac{1}{{\mathrm{\lambda }}^4}$
$\begin{array}{l}\Rightarrow \frac{( Amount\mathrm{of}\mathrm{scattering} {)}_1}{( Amount\mathrm{of}\mathrm{scattering} {)}_2}=\frac{{\lambda }_2^4}{{\lambda }_1^4}\\ \Rightarrow \frac{1}{4}={\left(\frac{{\lambda }_2}{{\lambda }_1}\right)}^4\\ \therefore {\lambda }_1:{\lambda }_2=\sqrt{2}:1\end{array}$