Question

Frequencies of light incident on a system of scattering particles are in the ratio of $1:2$. Then, the intensities of scattered light in a particular direction is in the ratio :

• A. $1:4$
• B. $1:2$
• C. $1:8$
• D. $1:16$

Answer 1

The correct option is D $1:16$

According to Rayleigh scattering,

$I\propto \frac{1}{{\lambda }^4}$

$\Rightarrow I\propto f^4[\because c=\lambda f]$

So,

$\frac{I_1}{I_2}=\frac{f_1^4}{f_2^4}={\left(\frac{f_1}{f_2}\right)}^4$

$\Rightarrow \frac{I_1}{I_2}={\left(\frac{1}{2}\right)}^4=1:16$

Hence, option $\left(D\right)$ is the correct answer.