Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
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Page 653: Lesson Check

Exercise 23
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Light is a wave so it undergoes a similar phase change when it reflects. When light encounters a medium with a lower index of refraction, it is reflected with no phase change. In contrast, when a light encounters a medium with a higher index of refraction, it is reflected with a phase change of half a wavelength.
Result
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Light is a wave so it undergoes a similar phase change when it reflects. When light encounters a medium with a lower index of refraction, it is reflected with no phase change.
Exercise 24
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It does because for different thickness different colors are “removes” from the reflected spectrum due to destructive interference and different colors are amplified due to constructive interference in the spectrum of reflected light from both planes of the film.
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Exercise 25
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The phase of a reflected wave changes for $180^circ$ in respect to the one that is incident only when the reflection occurs on a medium (medium 2 on the figure) that has higher index of refraction than the medium in which both the incident and the reflected wave travel (medium 1 on the figure) so here we conclude that the index of medium 2 has to be higher than $1.35$.
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Exercise 26
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Ray 1 reflects on the material with lower index of refraction than that of the material it travels in so there is no phase change. Ray 2 reflects on the material that has higher index of refraction than that of the medium it travels in so it changes its’ phase for $180^circ$ meaning that the phase shift of ray 1 due to reflection is less than that of the ray 2.
Result
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Exercise 27
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Here the light reflecting on the upper surface (glass-air boundary) experiences no phase shift while the light reflecting on the lower surface (air-glass boundary) experiences a shift of $180^circ$ so here the condition for constructive interference reads

$$
2n_{air}t = left(m+frac{1}{2}right)lambda.
$$
Putting $n_{air} = 1$ and $m=250$ we get

$$
2t=250.5lambdaRightarrow lambda = frac{2t}{250.5} = frac{2times5.1times10^{-5}text{ m}}{250.5} = 407text{ nm}.
$$

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Exercise 28
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Here we have to apply the condition for destructive interference which reads

$$
2nt = mlambda.
$$

Putting $m=1$ we have

$$
2nt=lambdaRightarrow n=frac{lambda}{2t} = frac{523text{ nm}}{2times 195text{ nm}} =1.34.
$$

Result
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Exercise 29
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The green light is absent from the reflection because it interferes destructively. We can write the condition for destructive interference

$$
2n_{oil}t = mlambda
$$
yielding for the thickness

$$
t=frac{mlambda}{2n_{oil}}.
$$
We see that the thickness is minimal when we put $m=1$ so finally we obtain
$$
t=frac{lambda}{2n_{oil}} = frac{521text{ nm}}{2times1.38} = 189text{ nm}.
$$

Result
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