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 $\frac{{\lambda }_1}{{\lambda }_2}=\frac{\sqrt{2}}{1}$