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Chapter 24
Wave Optics
Review – optical elements
General
Physics
Optical equations

Sign conventions
p (+) real on the side
light goes in
q (+) real on the side
light comes out
f (+) for focusing optics
R
check sign of f
M (+) for upright images
General
Physics
Interference
Sections 1 – 3
General
Physics
Wave Optics

The wave nature of light explains various
phenomena
 Interference
 Diffraction
 Polarization
General
Physics
Principle of Superposition
Two waves travelling in opposite directions
will pass straight through each other
 When the waves are on top of each other,
the two amplitudes add up to get the total
amplitude
 This is the cause of interference effects

General
Physics
Huygen’s Principle
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Christian Huygens (1629 – 1695) assumed that light is
a form of wave motion rather than a stream of particles
Huygens’ Principle is a geometric construction for
determining the position of a new wave at some point
based on the knowledge of the wave front that
preceded it
All points on a given wave front are taken as point
sources for the production of spherical secondary
waves, called wavelets, which propagate in the forward
direction with speeds characteristic of waves in that
medium

After some time has elapsed, the new position of the wave
front is the surface tangent to the wavelets
General
Physics
Huygens’ Construction for a Plane
Wave

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At t = 0, the wave front is
indicated by the plane AA’
The points are
representative sources for
the wavelets
After the wavelets have
moved a distance cΔt, a
new plane BB’ can be
drawn tangent to the
wavefronts
General
Physics
Huygens’ Construction for a
Spherical Wave

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The inner arc represents
part of the spherical wave
The points are
representative points
where wavelets are
propagated
The new wavefront is
tangent at each point to
the wavelet
General
Physics
Diffraction

Huygens’ principle
requires that the waves
spread out after they
pass through narrow slits

This spreading out of light
from its initial line of
travel is called diffraction

In general, diffraction
occurs when waves pass
through small openings,
around obstacles or by
sharp edges
General
Physics
Interference


Light waves interfere with
each other much like
water waves do
All interference associated
with light waves arises
when the electromagnetic
fields that constitute the
individual waves combine
General
Physics
Conditions for Interference

For sustained interference between two
sources of light to be observed, there are
two conditions which must be met
 The
sources must be
coherent
 They
must maintain a
constant phase with
respect to each other
 The
waves must have
identical wavelengths
General
Physics
Producing Coherent Sources

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Light from a monochromatic (single
wavelength) source is allowed to
pass through a narrow slit, So
The light from the single slit is
allowed to fall on a screen containing
two narrow slits, S1 and S2
The first slit is needed to insure the
light comes from a tiny region of the
source which is coherent
The waves emerging from the
second screen originate from the
same wave front and therefore are
always in phase
General
Physics
Producing Coherent Sources
Currently, it is common to use a laser as a
coherent source
 The laser produces an intense, coherent,
monochromatic beam over a width of
several millimeters
 The laser light can be used to illuminate
multiple slits directly

General
Physics
Young’s Double Slit Experiment
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Thomas Young first demonstrated interference
in light waves from two sources in 1801
The light from the two slits form a visible
pattern on a screen
The pattern consists of a series of bright and
dark parallel bands called fringes
Constructive interference occurs where a bright
fringe appears
Destructive interference results in a dark fringe
General
Physics
Resulting Interference Pattern
Active Figure: Young's Double-Slit Experiment
General
Physics
Interference Patterns

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Constructive
interference occurs at
the center point
The two waves travel
the same distance



Therefore, the waves
arrive in phase
A bright fringe occurs
Path difference is δ = 0
General
Physics
Interference Patterns, 2

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The upper wave travels onehalf of a wavelength farther
than the lower wave
The trough of the bottom
wave overlaps the crest of
the upper wave

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This is destructive
interference

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Therefore, the waves arrive
out of phase
A dark fringe occurs
Path difference is δ = 1/2λ
General
Physics
Interference Patterns, 3

The upper wave travels
one wavelength farther
than the lower wave


Again, constructive
interference results

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Therefore, the waves
arrive in phase
A bright fringe occurs
Path difference is δ = λ
General
Physics
Interference Equations

The path difference is
δ = r2 – r1

If L is much greater
than d (L » d)
The paths are
approximately parallel
 The path difference is
found from the
smaller triangle to be
 δ = r2 – r1 = d sin θ

General
Physics
Interference Equations, 2
For a bright fringe, produced by constructive
interference, the path difference must be either
zero or some integral multiple of the wavelength
 δ = d sin θbright = m λ
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m = 0, ±1, ±2, …
m is called the order number
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When m = 0, it is the zeroth order maximum
When m = ±1, it is called the first order maximum
etc.
General
Physics
Interference Equations, 3
For a dark fringe, produced by destructive
interference, the path difference must an odd
half wavelength
 δ = d sin θdark = (m + ½) λ


m = 0, ±1, ±2, …
General
Physics
Interference Equations, 4
The positions of the fringes can be measured
vertically from the zeroth order maximum
 y = L tan θ  L sin θ
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Assumptions
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for bright fringes sin θ = m λ / d
for dark fringes sin θ = (m + ½) λ / d
L>>d
d>>λ
Approximation

θ is small and therefore the approximation tan θ  sin θ
can be used
General
Physics
Interference Equations, final

For bright fringes
ybright 

L
d
m
m  0,  1,  2
For dark fringes
ydark
L 
1

m 

d 
2
m  0,  1,  2
General
Physics
Uses for Young’s Double Slit
Experiment
Young’s Double Slit Experiment provides a
method for measuring the wavelength of
the light
 This experiment gave the wave model of
light a great deal of credibility

 It
is inconceivable that particles of light could
cancel each other, as in the case of
destructive interference
General
Physics