Transcript Chapter 35

Chapter 37
Interference of Light Waves
(Cont.)
PHY 1371
Dr. Jie Zou
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Outline
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Change of phase due to reflection
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Lloyd’s mirror
Phase change due to reflection
Interference in thin films
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Interference in a wedge-shaped film
Newton’s rings
PHY 1371
Dr. Jie Zou
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Lloyd’s Mirror
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Lloyd’s mirror: Another
simple, yet ingenious,
arrangement for producing
an interference pattern with
a single light source.
Observation:
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Lloyd’s Mirror
PHY 1371
An interference pattern is
observed on the viewing
screen.
However, the positions of the
dark and bright fringes are
reversed relative to the
pattern created by Young’s
experiment.
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Change of phase due to
reflection
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PHY 1371
Explanation for the previous
observation: The coherent light
sources at points S and S’ differ in
phase by 180° (or  rad), a phase
change produced by reflection.
In general, an electromagnetic
wave undergoes a phase change of
180° upon reflection from a
medium that has a higher index of
refraction than the one in which the
wave is traveling.
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An analogy
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The general rules:
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An electromagnetic wave undergoes a 180° phase change when
reflected from a boundary leading to an optically denser (larger n)
medium.
No phase change occurs when the electromagnetic wave is reflected
from a boundary leading to a less optically dense (smaller n) medium.
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Observation of interference
effects in thin films
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PHY 1371
Examples of thin films in everyday
life: thin layers of oil on water or
the thin surface of a soap bubble.
Observation: varied colors are
observed when white light is
incident on such thin films.
Explanation for the
observation: The varied colors
result from the interference of
waves reflected from the two
surfaces of the film.
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Interference in thin films
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Two factors should be considered:
1.
2.
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The difference in path length for the two
rays.
The 180° phase change upon reflection.
Assumption: Normal incidence.
Condition for constructive
interference: 2nt = (m+1/2), m =0,
1, 2…
Condition for destructive
interference: 2nt = m, m = 0, 1, 2…
Note: These conditions are true only
when n1<n>n2 or n1>n<n2,, when a net
phase change of 180° due to reflection
occurs.
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Example 37.5: Interference in
a wedge-shaped film
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A thin, wedge-shaped
film of refractive
index n is illuminated
with monochromatic
light of wavelength .
Describe the
interference pattern
observed for this
case.
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Example 37.4 Nonreflective
coatings for solar cells
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PHY 1371
Suppose that a silicon (si) solar
cell (n = 3.5) is coated with a
thin film of silicon monoxide
(SiO, n= 1.45) in order to
minimize reflective losses from
the surface. Find the minimum
film thickness that produces
the least reflection at a
wavelength of 550 nm, near
the center of the visible
spectrum.
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Newton’s rings
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Set up: A plano-convex lens
on top of a flat glass surface.
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The air film between the glass
surfaces varies in thickness.
Observation: A pattern of
light and dark rings when
observed from above using
light of a single wavelength.
Derivation for the radii of
the dark rings (Problem
#67): rm  (mR/nfilm)1/2, m
=0, 1, 2…
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Homework
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Ch. 37, P. 1200, Problems: #32, 33,
39, 62.
PHY 1371
Dr. Jie Zou
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