Frequencies of light incident on a system of | vedclass

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Question

(A) According to Rayleigh's law of scattering, the intensity of scattered light $(I)$ is inversely proportional to the fourth power of its wavelength

Vedclass · Accepted Answer

$1: 16$

Vedclass · Answer

(A) According to Rayleigh's law of scattering, the intensity of scattered light $(I)$ is inversely proportional to the fourth power of its wavelength $(\lambda)$: $I \propto \frac{1}{\lambda^{4}}$.Since the frequency $(f)$ is inversely proportional to the wavelength $(\lambda = \frac{c}{f})$, we can express the intensity in terms of frequency as $I \propto f^{4}$.Given the ratio of frequencies $f_{1} : f_{2} = 1 : 2$, the ratio of intensities of scattered light is $\frac{I_{1}}{I_{2}} = \left(\frac{f_{1}}{f_{2}}\right)^{4}$.Substituting the values, we get $\frac{I_{1}}{I_{2}} = \left(\frac{1}{2}\right)^{4} = \frac{1}{16}$.Therefore, the ratio of the intensity of scattered light is $1: 16$.

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

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