Physics, 18.05.2021 19:30 AdiGirlBrainly

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

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Answer from: DIABLO3580

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)

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

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

Explanation:

Given the data in the question,

the visible spectrum (λ=520nm) =

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

∝ ( 1 / λ⁴ )

I_R / = ( λ / λ )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 is 665 nm

we substitute

I_R / = ( 520 / 665 )⁴

I_R / = ( 0.781954887 )⁴

I_R / = 0.3739

I_R = 0.3739 { in terms of }

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

I_V / = ( λ / λ )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 is 420 nm

we substitute

I_V / = ( 520 / 420 )⁴

I_V / = ( 1.238095 )⁴

I_V / = 2.3497

I_V = 2.3497 { in terms of }

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

Answer from: leleee10

Complete Question

(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.

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 $\lambda_v=420nm$

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)

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A beam of white light passes through a uniform thickness of air. If the intensity of the scattered l...