Question

A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum (λ=520nm) is I, find the intensity (in terms of I) of scattered light

Answer 1

Complete Question

A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum (λ=520nm) is I, find the intensity (in terms of I) of scattered light  

(a)  

in the middle of the red part of the spectrum (λ=665nm)

Express your answer in terms of I.  

(b)  

in the middle of the violet part of the spectrum (λ=420nm)  

Express your answer in terms of I.

Answer:

  $l_r=0.374I$         (in terms of I)

  $I_v=2.35I$          (in terms of I)

Explanation:

From the question we are told that:

Intensity of the scattered light Green part  $\lambda_g=520nm$

Intensity of the scattered light Red part $\lambda_R=665nm$

Intensity of the scattered light  Violet part $\lambda_v=420nm$

a)

Generally the equation for intensity of scattered in the middle of the red part of the spectrum is mathematically given by

Since light scattered intensity is proportional to $1/\lambda^4$

   $\frac{I_r}{I}=(\frac{\lambda}{\lambda_r} )^4$

  $\frac{I_r}{I}=(\frac{520}{665} )^4$

  $\frac{I_r}{I}=0.374$

  $l_r=0.374I$(in terms of I)

Generally the equation for intensity of scattered in the middle of the red part of the spectrum is mathematically given by

   $\frac{I_v}{I}=(\frac{\lambda}{\lambda_v} )^4$

  $\frac{I_v}{I}=(\frac{520}{420} )^4$

  $\frac{I_v}{I}=2.35$

  $I_v=2.35I$ (in terms of I)

Answer 2

This question is incomplete, the complete question is;

A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum (λ=520nm) is I, find the intensity (in terms of I) of scattered light

a) In the middle of the red part of the spectrum (λ= 665 nm)

b) In the middle of the violet part of the spectrum (λ = 420 nm)

Answer:

a) the intensity of scattered light ( in terms of $I$ ) In the middle of the red part of the spectrum is 0.3739$I$

b) the intensity of scattered light ( in terms of $I$ ) In the middle of the violet part of the spectrum is 2.3497$I$  

Explanation:

Given the data in the question,

the visible spectrum (λ=520nm) = $I$

we know that; intensity of scattered light is proportional to 1 / λ⁴  

$I$ ∝ ( 1 / λ⁴ )

so

a)

$I_R$ / $I$ = ( λ / λ$_R$ )⁴

As the middle of the green part of the visible spectrum λ is 520nm and middle of the red part of the spectrum λ$_R$ is 665 nm

we substitute

$I_R$ / $I$ = ( 520 / 665 )⁴

$I_R$ / $I$ = ( 0.781954887 )⁴

$I_R$ / $I$ = 0.3739

$I_R$  =  0.3739$I$  { in terms of $I$  }

Therefore, the intensity of scattered light ( in terms of $I$ ) In the middle of the red part of the spectrum is 0.3739$I$

b)

$I_V$ / $I$ = ( λ / λ$_V$ )⁴

As the middle of the green part of the visible spectrum λ is 520nm and middle of the red part of the spectrum λ$_R$ is 420 nm

we substitute

$I_V$ / $I$ = ( 520 / 420 )⁴

$I_V$ / $I$ = ( 1.238095 )⁴

$I_V$ / $I$ = 2.3497

$I_V$ = 2.3497$I$  { in terms of $I$  }

Therefore, the intensity of scattered light ( in terms of $I$ ) In the middle of the violet part of the spectrum is 2.3497$I$