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In a given direction, the intensities of the scattered light by a scattering substance for two beams of light are in the ratio of $256: 81$. The ratio of the frequency of the first beam to the frequency of the second beam is
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1643 Upvotes
Verified Answer
The correct answer is:
None of these
According to Rayleigh scattering formula Intensity of scattered light $I \propto \frac{1}{(\lambda)^{4}} \propto \mathrm{f}^{4}$ $\therefore$
$$
\begin{aligned}
\frac{f_{1}}{f_{2}} &=\left[\frac{I_{1}}{I_{2}}\right]^{1 / 4} \\
&=\left[\frac{256}{81}\right]^{1 / 4} \\
&=\frac{4}{3}
\end{aligned}
$$
Hence, option (d) is correct.
$$
\begin{aligned}
\frac{f_{1}}{f_{2}} &=\left[\frac{I_{1}}{I_{2}}\right]^{1 / 4} \\
&=\left[\frac{256}{81}\right]^{1 / 4} \\
&=\frac{4}{3}
\end{aligned}
$$
Hence, option (d) is correct.
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