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 ) 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 )
so
a)
/
= ( 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
/
= ( 520 / 665 )⁴
/
= ( 0.781954887 )⁴
/
= 0.3739
= 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
b)
/
= ( 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
/
= ( 520 / 420 )⁴
/
= ( 1.238095 )⁴
/
= 2.3497
= 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