Q173 / 180 · KCET 2010 · Physics

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
    $64: 27$
  • Correct answer
    D
    None of these

Solution

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.

Hence, the correct answer is option: 'D'.

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