Question

Given that the amplitude A of scattered light is:

(i) Directly proportional to the amplitude (A0) of incident light.

(ii) Directly proportional to the volume (V) of the scattering particle

(iii) Inversely proportional to the distance (r) from the scattered particle

(iv) Depend upon the wavelength (λ) of the scattered light.


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Answer 1

Complete question :

Given that the amplitude A of scattered light is:

(i) Directly proportional to the amplitude (A0) of incident light.

(ii) Directly proportional to the volume (V) of the scattering particle

(iii) Inversely proportional to the distance (r) from the scattered particle

(iv) Depend upon the wavelength (λ) of the scattered light.

Show that the intensity of scattered light varies as  $\frac{1}{{\lambda}^4}$.

Answer:

As per the information given in the question,

we can write it as,

$A=k A_0^aV^br^c\lambda^d$

According to the statements, it is clear that

$a=1\\b=1\\c=-1\\\\A=A_0Vr^{-1}\lambda^d$

On writing dimensions of both sides, and equating powers of M, L, T, we get,

$[L]=[L][L^3][L^{-1}][L^d]\\\\= \ [L^{3+d}]$

$\implies 1=3+d\\\\\implies d=-2$

Hence, $A\propto\frac{1}{\lambda^2}$

We know that,

$Intensity (I)\propto amplitude^2(A)$

So, $I\propto \lambda^4$

Hence proved.

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Answer 2

The amplitude A of scattered light is , $I \propto \lambda^{4}$.

What is amplitude with example?

• The definition of amplitude refers to the length and width of waves, such as sound waves, as they move or vibrate.
• How much a radio wave moves back and forth is an example of its amplitude.

According to the question:

As per the information given in the question,

we can write it as,

$A=k A_{0}^{a} V^{b} r^{c} \lambda^{d}$

According to the statements, it is clear that

$a=1 b=1\\ c=-1\\ A=A_{0} V r^{-1} \lambda^{d}$

On writing dimensions of both sides, and equating powers of M, L, T, we get,

${[L]=[L]\left[L^{3}\right]\left[L^{-1}\right]\left[L^{d}\right] }$

$=\left[L^{3+d}\right]$

$\Longrightarrow 1=3+d$

$\Longrightarrow d=-2$

Hence, $A \propto \frac{1}{\lambda^{2}}$

We know that,

Intensity $(I) \propto amplitude ^{2}(A)$

So, $I \propto \lambda^{4}$

Learn more about amplitude here,

https://brainly.in/question/1180321?msp_poc_exp=5

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