Respuesta :
Answer:
Explanation:
The problem is based on interference in thin films .
for constructive interference the condition is as follows
2μd = ( 2n+1 ) λ/2 , μ is refractive index of oil , t is thickness , λ is wavelength of light.
2 x 1.45 x 380 nm = ( 2n+1 ) λ/2
= 1102 nm = odd multiple of λ/2
if we take odd multiple as 3
λ = 734.66 nm which is the wavelength of red light .
So from above red light will be visible .
b )
when viewed from below , in the transmitted light , the condition for constructive interference is as follows
2μd = n λ
2 x 1.45 x 380 = n λ
1102 = n λ
when n = 2
λ = 501 nm
This is wavelength of green colour .
So from water side green colour will be visible.
A) The predominant wavelength seen at the point where oil is 380 nm thick is; 441 nm and the colour is Indigo
B) The visible wavelength that would
be enhanced when transmitted through the water is; 551 nm and colour is yellow.
We are given;
Refractive index of oil; η_oil = 1.45
Refractive index of sea water; η_sea = 1.35
Thickness of oil; t = 380 nm
A) To find the wavelength of the light, we will use the Formula for constructive interference which is;
2t = (m + ½)λ
Where;
t is thickness
m is order
λ is wavelength
λ = λ_light/η_oil
Thus;
2t = (m + ½)(λ_light/η_oil)
Making λ_light the subject;
λ_light = 2tη_oil/(m + ½)
Where m = 2;
Plugging in the relevant values;
λ_light = (2 × 380 × 1.45)/(2 + 1/2)
λ_light ≈ 441 nm
B) In this case, m = 2 but we will use formula for destructive interference;
2t = mλ
Where;
λ = λ_light/η_oil
Thus;
2t = m(λ_light/η_oil)
λ_light = (2t * η_oil)/m
λ_light = (2 × 380 × 1.45)/2
λ_light = 551 nm
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