in a given direction, the intensities of the scattered light by a scattering substance for two beams of light are in ratio of 256:81. What is the ratio of the amplitude of the first beam to the amplitude of the second beam?

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Solution

Dear student

Given the intensity ratio
$\frac{I_{1}}{I_{2}} = \frac{256}{81}$
The intensity of a beam of light is proportional to the square of the amplitude of the beam i.e.
$I \propto a^{2} \Rightarrow \frac{I_{1}}{I_{2}} = \frac{a_{1}^{2}}{a_{2}^{2}} \Rightarrow \frac{a_{1}^{2}}{a_{2}^{2}} = \frac{256}{81} \Rightarrow \frac{a_{1}}{a_{2}} = \sqrt{\frac{256}{81}} = \frac{16}{9} \Rightarrow \frac{a_{1}}{a_{2}} = \frac{16}{9}$

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