Question

If the ratio of amounts of scattering of two light waves is $ 1 : 4 $ , the ratio of their wavelength is

• A. $ 1:2 $
• B. $ \sqrt{2}:1 $
• C. $ 1:\sqrt{2} $
• D. $ 1:1 $
• E. $ 2:1 $

Answer 1

Answer: (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} $