KCET · Physics · Waves and Sound
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
- A \(64: 127\)
- B \(1: 2\)
- C \(64: 27\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
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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