Respuesta :
Answer:
a) 473.33 nm
b) 568 nm and 406 nm
c) bluish green and blue
Explanation:
a) As the light traverses the layer of oil it first reflects at the front surface of the oil. Here the index of refraction increases from that of air to that of the oil , so a phase change occurs. The light then reflects from the rear surface of oil. The index of refraction increases from that of the oil to that of the glass , so again a phase change occurs. Thus two phase changes occur.
In thin-film interference with 0 or 2 phase changes, condition for constructive interference is:
2t=mλ/n
So:
λ= 2tn/m
For m=1
λ=1420 nm
For m=2
λ=710 nm
For m=3
λ=473.33 nm
For m=4
λ=355 nm
Thus the only wavelength in the visible spectrum (400 - 700 nm) that will give constructive interference is 473.33 nm
b)
In thin-film interference with 0 or 2 phase changes, condition for destructive interference is:
2t=(m+1/2)λ/n=(2m+1)*λ/2n
so;
λ=4tn/(2m+1)
For m=1
λ=946.667 nm
For m=2
λ=568 nm
For m=3
λ=405.33 nm
For m=4
λ=315.56 nm
Thus the wavelengths in the visible spectrum (400 to 700 nm) that will give destructive interference are 568 nm and 406 nm
c) The color of reflected light is bluish green since the wavelength is 473.3 nm . We know that the colors of reflected and transmitted light are complimentary to each other.Thus the color of transmitted light is blue (due to the combination of wavelengths 568 nm (green) and 406 nm (deep violet).
The color of reflected light will be "Blue" and color of transmitted light will be "Yellow and Violet".
Waves and Light
According to the question,
(a) We know that,
→ 2nt = kλ
λ = [tex]\frac{2nt}{k}[/tex]
By substituting the values, we get
= [tex]\frac{2\times 1.42\times 500}{k}[/tex]
= [tex]\frac{1420}{k}[/tex] nm
Now, the wavelength for different k will be:
k = 1, λ = 1420 nm
k = 2, λ = 710 nm
k = 3, λ = 473 nm
The range will be:
= 390 - 700
We can say that k = 1 and 2 not lies in visible light range.
(b) We know that,
→ 2nt = (k + [tex]\frac{1}{2}[/tex]) λ
or,
λ = [tex]\frac{2nt}{k+\frac{1}{2} }[/tex]
By substituting the values,
= [tex]\frac{2\times 1.42\times 500}{k+0.5 }[/tex]
= [tex]\frac{1420}{k+0.5}[/tex] nm
When,
k = 2, λ = 568 nm
k = 3, λ = 406 nm
Thus the responses above are correct.
Find out more information about wavelength here:
https://brainly.com/question/10750459
