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Chapter # 37 Wave Optics and
Chapter # 38 Diffraction
• 
Surface Wave Analogy
Waves on water surface
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Geometrical Optics versus
Physical Optics
• 
• 
• 
Geometrical Optics: λ << d0
Physical Optics:
λ ~ d0
There are two types of phenomena
which we can observe when λ ~ d0
1.  Interference
2.  Diffraction
Definitions
•  Interference is a phenomenon arising when
two beams of coherent light are
superimposed.
•  Waves always bend when they pass by a
barrier. This phenomenon is referred to as
diffraction.
•  Coherent?
What does it mean coherent?
•  Coherent beams of light maintain a constant
phase relationship during all experiment.
•  Usual choice is separation of one beam onto
two beams. Evidently that they must maintain
a constant phase relationship during all
experiment.
•  Sources whose relative phase vary randomly
with the time are said to be incoherent.
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Interference
•  Wave superposition: The displacement
caused by a combination of waves is the
algebraic sum of the displacements caused
by each wave individually.
•  If waves add to cause a larger displacement
we call it Constructive Interference.
•  If waves add to cause a smaller displacement
we call it Destructive Interference.
Constructive Interference versus
Destructive Interference.
•  In order to get
interference two
conditions must
be satisfied:
•  Light should be
monochromatic.
•  Sources must
be coherent.
Interference Conditions
•  Constructive at
P0 and P1 :
l2 − l1 = m λ
m = 0,± 1,±2,…
€
•  Destructive at
Q1 and Q2 :
1
l2 − l1 = (m − ) λ
2
m = 0,± 1,±2,…
€
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Two monochromatic sources
• 
CC questions 1, 3
•  When two light waves interfere destructively,
what happens to their energy?
•  If a radio station broadcasts its signal
through two different antennas
simultaneously, does this guarantee that the
signal you receive will be stronger?
Example 28-1
•  The radio signal is transmitted simultaneously by two
antennas and are picked up by two radios. Signal at
point P0 is strong but in point Q1 is very weak. What
is the wavelength if d=7.5 km, L=14 km, and y=1.88
km. Assume that Q1 is the point of first minimum.
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Two-Source
Interference of Light
Cylindrical wavefronts of coherent
waves
Young’s Experiment and
Huygens’s principle
•  If the light is a flux of
particles we will see only
two lines on the screen.
•  But light is a wave and
according to Huygens’s
principle:
•  Each point of wave front
becomes a new wave
source.
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Path difference
Δ l = d sin θ
•  Bright fringes:
d sin θ = m λ,
m = 0,± 1,± 2,…
€
•  Dark fringes:
€
1
d sin θ = (m − ) λ,
2
m = 0,± 1,± 2,…
€
Question
•  Two sources of waves are at A and B in
the figure. At point P, the path
difference for waves from these two
sources is:
•  A. x + y
•  B. (x + y)/2
•  C. x - y
•  D. (x - y)/2
Question
•  Two sources of waves are at A and B in
the Figure. Sources are emitting wave
of wavelength λ that are in phase with
each other. Constructive interference
will occur at point P if:
•  A. x = y
•  B. x + y = λ
•  C. x - y = λ
•  D. x - y = 5λ
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Exercise 28-1
•  Red light (λ = 752 nm)
passes through a pair
of slits with a
separation 6.2•10-5 m.
Find the angles
corresponding to (a)
the first bright fringe
and (b) the second
dark fringe above the
central bright fringe.
Example 28-2
•  Two slits with a
separation 8.5•10-5
m create an
interference pattern
on a screen 2.3 m
away. If the tenth
bright fringe above
the central fringe is
a linear distance of
12 cm from it, what
is the wavelength of
light?
Interference in Thin Films
•  Two glass
slides with a
narrow air
gap between
them
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Interference in Thin Films
• 
Slightly different geometry
•  Constrictive
interference
condition
•  2 t = m λ
m=0,1,2, …
Newton’s Rings
• 
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Inspection of a telescope objective
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Problem 37.3
•  Two radio antennas simultaneously
broadcast signals at the same wavelength.
What is the wavelength of the signal if it is a
second maximum at car’s position? How
much father must the car move to encounter
the next minimum?
Problem 28-4
•  A person driving at v = 18 m/s crosses the line
connecting two radio transmitters at right angles, as
shown in the Figure. The transmitters emit identical
signals in phase with each other, which the driver
receives on the car radio. When the car is at point A
the radio picks up a maximum net signal. What is the
longest possible wavelength of the radio waves?
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Problem 28-5
•  Two students in a dorm room listen to a pure
tone produced by two loudspeakers that are in
phase, and hear a maximum sound. What is
the lowest possible frequency of the
loudspeakers? (Take the speed of sound to be
343 m/s.)
Diffraction
•  Diffraction is a
deviation of light
from straight-line
path when the light
passes through an
aperture or around
an obstacle.
Waves on water surface
λ << d0
λ ~ d0
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Shadow produced with a sharp
edge
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Actual shadow of a razor blade
• 
Visible light pictures
• 
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Two examples more
• 
Why we observe such pictures?
•  According to Huygens’s principle:
•  Each point of
wave front
becomes a
new wave
source.
•  For points 1 and
1’ :
W
sin θ
2
€
Dark Fringes Conditions
•  Central fringe Constructive.
•  First minimum:
W
λ
sin θ = ⇒ W sin θ = λ
2
2
•  Second minimum:
€
W
λ
sin θ = 2 ⇒ W sin θ = 2 λ
2
2
W sin θ = mλ, m = ±1,±2,±3,…
€
€
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Bright Fringes Conditions
•  Bright Fringes are located
approximately halfway between
successive dark fringes.
Questions
•  Why can you easily hear sound around a
corner due to diffraction, while you cannot
see around the same corner?
•  The size of an atom is about 0.1 nm. Can a
light microscope make an image of an atom?
Explain.
Questions
•  You can readily block sunlight from reaching
your eyes. Why you can not block sound
from reaching your ears this way?
•  When you receive a chest x-ray at a
hospital, the rays pass through a series of
parallel ribs in your chest. Do these ribs
produce a diffraction effect for x-rays?
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Example 28-5
•  Light with a
wavelength of 511 nm
forms a diffraction
pattern after passing
through a single slit of
width 2.2•10-6 m. Find
the angle associated
with the first and the
second dark fringe
above the central
bright fringe.
Active example 28-2
•  Light passes through a single slit and
forms a diffraction pattern on a screen
2.31 m away. If the wavelength of light
is 632 nm, and the width of the slit is
4.2•10-5 m, find the linear distance on
the screen from the center of the
diffraction pattern to the first dark fringe.
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