Transcript Physics 2 chap 20


Waves vs. particles

Some properties of waves:
Huygens’ principle
Superposition — “adding” waves
Coherence

Some observed experimental effects:
Interference
experiments
Diffraction
— double-slit
— single-slit experiments
Phys 2: Chap. 24, Pg 1
Light: Waves or Particles?

Light carries energy. But how?
As a stream of particles travelling in the direction of
the light ray?
As a wave that spreads outward from the source?

We observe in nature:
Interference
These are wave phenomena!!
Diffraction
Polarization

In future chapters we will see light acting as a particle.
Wave-particle duality
Phys 2: Chap. 24, Pg 2
Question: Suppose light falls onto a screen with two slits.
What would you see on the wall behind the screen?
You might expect to see two bright lines on the wall:
But instead you would see many lines on the wall:
To understand this, we must understand these principles
Huygens’ Principle
Superposition of waves
Coherence
Phys 2: Chap. 24, Pg 3
Recall that a point source of …and that far from the source,
light emits a spherical wave
the wave is a plane wave
Huygens’ Principle
All points on a wave front serve as point sources of spherical waves
Apply Huygens’ Principle
to a spherical wave...
This also works for plane
waves...
Phys 2: Chap. 24, Pg 4
So What?
Waves can bend around corners!
This is a characteristic of all waves:
EM waves
sound waves
water waves
Phys 2: Chap. 24, Pg 5
Superposition
What happens when two particles are
in the same place at the same time?
They collide!
They “superpose”!
What happens when two waves are in Their amplitudes add
the same place at the same time?
to give one new wave!
Amplitude = 1
Amplitude = 1
+
+
Amplitude = 1
Constructive
Interference
=
Amplitude = 2
Destructive
Interference
Amplitude = 1
=
Amplitude = 0
Phys 2: Chap. 24, Pg 6
ConcepTest 1(Post) Interference

If waves A and B are
superposed (that is, their
amplitudes are added)
the resultant wave is
(1)
(2)
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Phys 2: Chap. 24, Pg 7
ConcepTest 1(ans) Interference

If waves A and B are
superposed (that is, their
amplitudes are added)
the resultant wave is
(1)
(2)
(3)
(4)
The amplitudes of waves
A and B have to be
added at each point!
Phys 2: Chap. 24, Pg 8
Phase
Phase refers to the relative position
of the wave crests of the two waves
Phase difference
180o or ½
“Out of phase”
Phase difference
0o
“In phase”
Phys 2: Chap. 24, Pg 9
constructive interference
destructive interference
waves are in phase
waves are out of phase
Phys 2: Chap. 24, Pg 10
Coherence
How is light produced?
Oscillating electrons!
In a light bulb, billions of electrons are oscillating.
Is the phase difference between the light from each electron
always the same?
In general, NO!
Two sources of light are said to be
 coherent if the phase difference between the
waves emitted is always the same
 incoherent if the phase difference between the
waves emitted is always changing
Everyday light sources are not coherent
Lasers DO produce coherent light
For future reference: no interference patterns appear for incoherent light.
Phys 2: Chap. 24, Pg 11
ConcepTest 2(Post) Phase

The two waves shown are
(1) out of phase by 180o
(2) out of phase by 90o
(3) out of phase by 45o
(4) in phase
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Phys 2: Chap. 24, Pg 12
ConcepTest 2(dis) Phase
¼

The two waves shown are
(1) out of phase by 180o
(2) out of phase by 90o
(3) out of phase by 45o
(4) in phase
The two waves are out of phase
by 1/4 wavelength (as seen in
the figure) , which corresponds
to a phase difference of 90o.
Phys 2: Chap. 24, Pg 13
ConcepTest 3(post) Phase

Two light sources emit waves of
 = 1 m which are in phase. The
two waves from these sources
meet at a distant point. Wave 1
traveled 2 m to reach the point,
and wave 2 traveled 3 m. When
the waves meet, they are
(1) out of phase by 180o
(2) out of phase, but not
by 180o
(3) in phase
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Phys 2: Chap. 24, Pg 14
ConcepTest 3(ans) Phase

Two light sources emit waves of
 = 1 m which are in phase. The
two waves from these sources
meet at a distant point. Wave 1
traveled 2 m to reach the point,
and wave 2 traveled 3 m. When
the waves meet, they are
(1) out of phase by 180o
(2) out of phase, but not
by 180o
(3) in phase
Since  = 1 m, wave 1 has traveled twice this
wavelength while wave 2 has traveled three
times this wavelength. Thus, their phase
difference is one full wavelength which
means they are still in phase.
Phys 2: Chap. 24, Pg 15
Interference of Sound Waves

Consider two sound waves that are in phase:
shift source by 2 wavelengths (constructive
interference)
2
Phys 2: Chap. 24, Pg 16
Interference of Sound Waves

Now what if the shifted wave is out of phase:
shift source by 3/2 wavelengths (destructive interference)
3/2 
Phys 2: Chap. 24, Pg 17
Question: Suppose light falls onto a screen with two slits.
What would you see on the wall behind the screen?
You might expect to see two bright lines on the wall:
But instead you would see many lines on the wall:
Phys 2: Chap. 24, Pg 18
Explanation of the double-slit observations

Where are the dark and bright spots and how
are they related to the light’s wavelength?
If both waves travel the same distance:
constructive interference
Phys 2: Chap. 24, Pg 19
Explanation of the double-slit Observations
We can explain the pattern of bright and dark fringes by
1. bending (diffraction / Huygens’ Principle)
and 2. superposition (adding of amplitudes)
of
3. coherent light waves!

1/
2

Bottom wave travels 1 whole Bottom wave travels ½ extra
extra wavelength. When waves wavelength. When waves
meet, they are in phase:
meet, they are out of phase:
constructive interference
destructive interference
Phys 2: Chap. 24, Pg 20
constructive
destructive
Phys 2: Chap. 24, Pg 21
Double-Slit Interference: The Math

r1
Path difference  between
waves determines phase
difference:
 = r2 - r1 = d sin 
y
r2

d

L
For Destructive Interference
For Constructive Interference
 = 1/2, 3/2, 5/2, 7/2, …
= (m + 1/2) 
 = 1, 2, 3, 4, …
=m
d sin  = (m + 1/2) 
d sin  = m 
m is an integer: m = 0, ± 1, ± 2, ...
Phys 2: Chap. 24, Pg 22
Intensity of Fringes
Constructive
Interference
m= 3
2
1
0
1
2
3
Light
Intensity
Destructive
Interference
m= 3
2
1
0
0
1
2
3
Phys 2: Chap. 24, Pg 23
ConcepTest 4(Post) Interference

In a double-slit experiment,
when the wavelength of the
light is increased, the
interference pattern
(1) spreads out
(2) stays the same
(3) shrinks together
(4) disappears
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Phys 2: Chap. 24, Pg 24
ConcepTest 4(Ans) Interference

In a double-slit experiment,
when the wavelength of the
light is increased, the
interference pattern
(1) spreads out
(2) stays the same
(3) shrinks together
(4) disappears
d sin  = m 
If  is increased and d does
not change, then  must
increase, so the pattern
spreads out.
Phys 2: Chap. 24, Pg 25
ConcepTest 5(Post) Interference

If instead the slits are
moved farther apart
(without changing the
wavelength), the
interference pattern
(1) spreads out
(2) stays the same
(3) shrinks together
(4) disappears
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Phys 2: Chap. 24, Pg 26
ConcepTest 5(Ans) Interference

If instead the slits are
moved farther apart
(without changing the
wavelength), the
interference pattern
(1) spreads out
(2) stays the same
(3) shrinks together
(4) disappears
d sin  = m 
If instead d is increased and
 does not change, then
 must decrease, so the
pattern shrinks together.
Phys 2: Chap. 24, Pg 27
Double-slit interference
1

Light of wavelength 680 nm falls on two slits and produces
an interference pattern in which the fourth-order maximum
is 48 mm from the central fringe on a screen 1.5 m away.
What is the separation between the two slits?
See Problem 24-7
Phys 2: Chap. 24, Pg 28
Double-Slit Interference
Calculate the distance of the
bright fringes from the axis:
Note that tan  = y/L.
By hypothesis, L >> y, so then
tan and thus  are both << 1.
Then tan   sin  to a good
approximation.
So the bright fringes will be at:
therefore:
mL
y bright 
d
m
y
sin  
 tan  
d
L
So the bright fringes are evenly spaced a distance L/d apart.
Phys 2: Chap. 24, Pg 29
Problem
Light of wavelength 680 nm falls on two slits and produces an
interference pattern in which the fourth-order maximum is 48 mm
from the central fringe on a screen 1.5 m away. What is the
separation between the two slits?
Constructive or
Destructive Interference?
“maximum”  Constructive
Equation for fringes?
Constructive  d sin = m
What is sin?
sin  tan = y/L

y
L
Algebra
Plug in numbers
d = m / sin
= mL / y
m

L
y
=4
= 680 nm = 680  10–9 m
= 1.5 m
= 0.048 m
d = 0.085 mm
Phys 2: Chap. 24, Pg 30
ConcepTest 10(Post) Interference


An interference pattern is seen
from two slits.
Now cover one slit with glass,
introducing a phase difference
of 180° (½ wavelength) at the
slits. How is the pattern altered?
(1) pattern vanishes
(2) pattern expands
(3) bright and dark spots
are interchanged
(4) pattern shrinks
(5) no change at all
Double slit
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Phys 2: Chap. 24, Pg 31
ConcepTest 10(ans) Interference


An interference pattern is seen
from two slits.
Now cover one slit with glass,
introducing a phase difference
of 180° (½ wavelength) at the
slits. How is the pattern altered?
If the waves originating from the two
(1) pattern vanishes
(2) pattern expands
(3) bright and dark spots
are interchanged
(4) pattern shrinks
(5) no change at all
Double slit
Interference pattern
slits have a phase difference of
180° when they start off, the
wave
central spot will now be dark.
To the left and the right, there will
be bright spots. Thus, bright and
dark spots are interchanged.
Phys 2: Chap. 24, Pg 32
What is Diffraction?
Waves can bend around corners!
This is a characteristic of all waves:
EM waves
sound waves
water waves
Phys 2: Chap. 24, Pg 33
Diffraction
What is actually seen, close to the edge of the shadow, is
incident light
screen
Phys 2: Chap. 24, Pg 34
Diffraction
What if we shined coherent light through a single slit?

But instead you would see many lines on the wall:

Diffraction
pattern
Phys 2: Chap. 24, Pg 35
Single-slit diffraction


Light falls straight through the slit
forms a central bright line on the
screen
Now look at light falling through at angle 
such that the top and bottom waves are one
wavelength  apart.
This center wave is exactly half a
wavelength  / 2 out of phase with
this bottom wave
this gives destructive interference
Phys 2: Chap. 24, Pg 36
Single-slit diffraction

The angle corresponding
to the first minimum :
sin  =  /D

Eventually we get following
pattern:
D


Equation for all minima:
D sin = m
Phys 2: Chap. 24, Pg 37
Phys 2: Chap. 24, Pg 38
ConcepTest 7(Post) Diffraction

The diffraction pattern below
arises from a single slit. If we
would like to sharpen the pattern,
i.e. make the central bright spot
narrower, what should we do to
the slit width?
(1) narrow the slit
(2) widen the slit
(3) enlarge the screen
(4) close off the slit
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screen
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Phys 2: Chap. 24, Pg 39
ConcepTest 7(ans) Diffraction

The diffraction pattern below
arises from a single slit. If we
would like to sharpen the pattern,
i.e. make the central bright spot
narrower, what should we do to
the slit width?
(1) narrow the slit
(2) widen the slit
(3) enlarge the screen
(4) close off the slit
The angle at which the first minimum
occurs is:
sin  =  /D
The central bright spot can be made
narrower by having a smaller angle,
D


which can be accomplished by
widening the slit (increasing D).
Phys 2: Chap. 24, Pg 40
ConcepTest 8(Post) Diffraction

Blue light of wavelength  passes
through a single slit of width d and
forms a diffraction pattern on a screen.
If the blue light is replaced by red light
of wavelength 2, the original diffraction
pattern can be reproduced if the slit
width is changed to:
(1) d/4
(2) d/2
(3) no change needed
(4) 2 d
(5) 4 d
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Phys 2: Chap. 24, Pg 41
ConcepTest 8(ans) Diffraction

Blue light of wavelength  passes
through a single slit of width d and
forms a diffraction pattern on a screen.
If the blue light is replaced by red light
of wavelength 2, the original diffraction
pattern can be reproduced if the slit
width is changed to:
(1) d/4
(2) d/2
(3) no change needed
(4) 2 d
(5) 4 d
d sin = m (minima)
If   2 then we must have
d  2d for sin  to remain
unchanged (and thus give the
same diffraction pattern).
d


Phys 2: Chap. 24, Pg 42
Diffraction
1

How wide is the central diffraction peak on a screen
2.50 m behind a 0.0348 mm wide slit illuminated by
589 nm light?
D
See Problem 24-22


Phys 2: Chap. 24, Pg 43
Diffraction + Interference
Wait a minute! If we have two slits, don’t we also get
a diffraction pattern from each slit, in addition to the
interference pattern?
If laser light illuminates one slit:
If another slit is opened adjacent to the first,
the pattern now has an interference pattern:
interference
minimum
diffraction
minimum
Phys 2: Chap. 24, Pg 44
Intensity of Fringes
Constructive
Interference
m= 3
2
1
0
1
2
3
Light
Intensity
Destructive
Interference
m= 3
2
1
0
0
1
2
3
Phys 2: Chap. 24, Pg 45
Diffraction Grating

A large number of equally spaced
slits (up to 10,000 !) is called a
diffraction grating
useful for measuring
wavelengths
what does the interference
pattern look like?

Similar to the 2-slit
situation, but peaks are
much narrower.
Phys 2: Chap. 24, Pg 46
The Visible Spectrum

Assume that the light striking a diffraction grating has
several wavelengths (it is not monochromatic).

Remember that white light contains all the colors of the
spectrum
each color in the spectrum has a different wavelength
Phys 2: Chap. 24, Pg 47
Diffraction grating with different colors

If the light has two wavelengths, we get two sets of maxima:

If it is white light (all colors, therefore all wavelengths):
Phys 2: Chap. 24, Pg 48
Interference by Thin Films

Example -- thin oil film on water:
Part of the incoming light is reflected
off the top surface (point A), part at
the lower surface (point B).
Light traveling through oil travels
extra distance (from A to B to C).
If this distance is ,2,3,4,…
» constructive interference!
If this distance is /2,3/2,5/2,…
» destructive interference!
Phys 2: Chap. 24, Pg 49
Newton’s Rings

More interference: air gap between two pieces of glass.
Path difference increases for the wave reflected at
bottom surface (point C).
If the extra path length is ,2,3,4,…
» constructive interference!
If the extra path length is /2,3/2,5/2,…
» destructive interference!
Phys 2: Chap. 24, Pg 50
ConcepTest 11(Pre) Interference

A laser shines on a pair of identical
glass microscope slides that form
a very narrow edge. The waves
reflected from the top and the
bottom slide interfere. What is the
interference pattern from top view?
(1)
(2)
edge
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Phys 2: Chap. 24, Pg 51
ConcepTest 11(ans) Interference

A laser shines on a pair of identical
glass microscope slides that form
a very narrow edge. The waves
reflected from the top and the
bottom slide interfere. What is the
interference pattern from top view?
Right at the edge, the two reflected
rays have no phase difference
and therefore should interfere
constructively. However, the
light ray reflected at the lower
surface (point E) changes phase
by /2 because the index of
refraction of glass is larger than
that of air.
(1)
(2)
edge
Phys 2: Chap. 24, Pg 52
Reflection of waves on surfaces

If a light wave is reflected by a material
whose index of refraction is greater than
that of the material it is going through,
the wave changes phase by /2.
example: air and oil, oil and water,
etc.

This is similar to a wave pulse
traveling on a rope and being
reflected with the end tied down.
The pulse flips over  the
wave changes phase.
Phys 2: Chap. 24, Pg 53
And the other way around...

If a light wave is reflected by a material
whose index of refraction is less than
that of the material it is going through,
there is no phase change.

This is similar to a wave pulse
traveling on a rope and being
reflected with the end loose.
The pulse travels back the same
way it came  no phase change.
Phys 2: Chap. 24, Pg 54
ConcepTest 12(post) Interference

Consider two identical microscopic
slides in air illuminated with light
from a laser. The bottom slide is
rotated upwards so that the wedge
angle gets a bit smaller. What
happens to the interference
fringes?
(1) Spaced farther apart
(2) Spaced closer together
(3) No change
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Phys 2: Chap. 24, Pg 55
ConcepTest 12(ans) Interference

Consider two identical microscopic
slides in air illuminated with light
from a laser. The bottom slide is
rotated upwards so that the wedge
angle gets a bit smaller. What
happens to the interference
fringes?
The path difference between Ray #2 and
Ray #3 is 2t. Ray #3 also experiences
a phase change of 180°. Thus, the dark
fringes will occur for:
2t = m
m = 0,1,2,…
If t gets smaller, Ray #2 and Ray #3 have
to be further apart before they can
interfere. Thus, the fringes move apart.
(1) Spaced farther apart
(2) Spaced closer together
(3) No change
ray 2
ray 1
ray 3
t
Phys 2: Chap. 24, Pg 56
Polarization
The E field in an EM wave is perpendicular to the direction of travel
But there are many possible orientations for the E field!
polarized light
unpolarized light
1 electron E field oscillates
in one direction
millions of E field oscillates
electrons in all directions
3-D view:
3-D view:
In polarized light, all of the electric fields
in the wave oscillate in the same direction
Phys 2: Chap. 24, Pg 57
Polarization by Absorption
Three ways to polarize light
E field
of wave
Wave
absorbed
Polarization by absorption:
1) scattering
2) reflection
3) absorption
E field
of wave
Wave passes
through
long thin molecules (light)
wires (radio waves)
Vertical components of wave are
absorbed by antenna
Horizontal components pass
through
polarized
unpolarized
polaroid Phys 2: Chap. 24, Pg 58
How much light gets through?
E field:
Eo
Intensity: Io
Intensity of the outgoing polarized light:
E field:
?
Intensity: ?
I = I0 cos2 
Phys 2: Chap. 24, Pg 59
Polarization

First polaroid allows only
one orientation of the electric
field to pass, thus polarizing
the light.

Second polaroid is oriented
perpendicular to the first
one, so no light can pass
through it.
No light
Phys 2: Chap. 24, Pg 60
ConcepTest 14(post) Polarization

If unpolarized light is incident
from the left, in which case
will some light get through?
(1) only case 1
(2) only case 2
(3) only case 3
(4) cases 1 and 3
(5) all three cases
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Phys 2: Chap. 24, Pg 61
ConcepTest 14(ans) Polarization

If unpolarized light is incident
from the left, in which case
will some light get through?
(1) only case 1
(2) only case 2
(3) only case 3
(4) cases 1 and 3
(5) all three cases
In cases 1 and 3, light is
blocked by the adjacent
horizontal and vertical
polarizers. In case 2, the
intermediate 45° polarizer
allows some light to get
through the last vertical
polarizer.
Phys 2: Chap. 24, Pg 62
Polarization

1
Two polarizers are oriented at 58° to one another.
Light polarized at a 29° angle to each polarizer
passes through both.
What reduction in intensity takes place ?
See Problem 24-61
Phys 2: Chap. 24, Pg 63