Discussion Forum



1)

Let  $S_{1}$  be the amount of Rayleigh scattered light of wavelength  $\lambda_{1}$ and $S_{2}$ that of light of wavelength $\lambda_{2}$  from a particle  of size a. Which of the following statement is true?


A) $\frac{S_{1}}{S_{2}}=\left(\frac{\lambda_{2}}{\lambda_{1}}\right)^{4}, if \lambda_{1},\lambda_{2}>> a$

B) $\frac{S_{1}}{S_{2}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right)^{4}, if \lambda_{1},\lambda_{2}>> a$

C) $\frac{S_{1}}{S_{2}}=\left(\frac{\lambda_{2}}{\lambda_{1}}\right)^{4}, if \lambda_{1},\lambda_{2} << a$

D) $\frac{S_{1}}{S_{2}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right)^{4}, if \lambda_{1},\lambda_{2} <<a$

Answer:

Option A

Explanation:

 Condition for scattering is 

   $\lambda$  >> a

 and according to Rayleigh , intensity (or amount ) of  scattered wavelength  is inversely proportional to fourth power of the wavelength  of incident wave, 

 i.e,

    $s \propto\frac{1}{\lambda^{4}}\Rightarrow \frac{S_{1}}{S_{2}}=\left(\frac{\lambda_{2}}{\lambda_{1}}\right)^{4}$ and $\lambda>>a$