Exploring Wave Interference in Physics: Superposition, Constructive, and Destructive Interference
•
textbook sections 28-1 -- 28-3
Physics 1161:
Lecture 20
Interference
Superposition
+
Constructive
Interference
In Phase
Superposition
t
+1
-1
t
+1
-1
+
Destructive Interference
Out of Phase
180 degrees
Which type of interference results from the
superposition of the two waveforms shown?
1.
Constructive
2.
Destructive
3.
Neither
+
Different f
Which type of interference results from the
superposition of the two waveforms shown?
1.
Constructive
2.
Destructive
3.
Neither
+
Different f
Interference for Light …
•
Can’t produce coherent light from separate
sources. (f
10
14
Hz)
•
Need two waves from
single source
taking
two different paths
–
Two slits
–
Reflection (thin films)
–
Diffraction
*
Coherent & Incoherent Light
Double Slit Interference Applets
•
http://www.walter-
fendt.de/ph14e/doubleslit.htm
•
http://vsg.quasihome.com/interfer.htm
Young’s Double Slit Applet
http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/PhysicsInitiative/
Physics2000/applets/twoslitsa.html
Young’s Double Slit Layout
Interference - Wavelength
Light waves from a single source travel through
2 slits before meeting at the point shown on the
screen. The interference will be:
1.
Constructive
2.
Destructive
3.
It depends on L
Screen a distance
L
from slits
Single source of
monochromatic light
d
2 slits-separated by
d
L
Light waves from a single source travel through
2 slits before meeting at the point shown on the
screen. The interference will be:
1.
Constructive
2.
Destructive
3.
It depends on L
Screen a distance
L
from slits
Single source of
monochromatic light
d
2 slits-separated by
d
L
The rays start in phase, and
travel the same distance, so they
will arrive in phase.
Young’s Double Slit
Checkpoint
Screen a distance
L
from slits
Single source of
monochromatic light
d
2 slits-separated by
d
1)
The pattern of maxima and
minima is the same for
original and modified
experiments.
2)
Maxima and minima for
the unmodified experiment
now become minima and
maxima for the modified
experiment.
L
The experiment is modified so that one of
the waves has its phase shifted by ½
.
Now, the interference will be:
Young’s Double Slit
Checkpoint
Screen a distance
L
from slits
Single source of
monochromatic light
d
2 slits-separated by
d
1)
The pattern of maxima and
minima is the same for
original and modified
experiments.
2)
Maxima and minima for
the unmodified experiment
now become minima and
maxima for the modified
experiment.
L
The experiment is modified so that one of
the waves has its phase shifted by ½
.
Now, the interference will be:
For example at the point
shown, he rays start out of
phase and travel the same
distance, so they will arrive out
of phase.
Young’s Double Slit Concept
Screen a distance
L
from slits
Single source of
monochromatic light
d
L
At points where the
difference in path
length is
0,
,2
, …,
the screen is
bright
.
(constructive)
Young’s Double Slit Key Idea
L
Two rays travel almost exactly the same distance.
(screen must
be
very
far away: L >> d)
Bottom ray travels a little further.
Key for interference is this small extra distance.
d
Path length difference =
d
Young’s Double Slit Quantitative
d sin
Need
< d
d
Destructive
interference
Constructive
interference
where m = 0, or 1, or 2, ...
Young’s Double Slit Quantitative
sin(
)
tan(
)
=
y/L
L
A little geometry…
Young’s Double Slit Under Water
Checkpoint
When this Young’s double slit experiment is placed under water,
how does the pattern of minima and maxima change?
1) the pattern stays the same
2) the maxima and minima occur at smaller angles
3) the maxima and minima occur at larger angles
Young’s Double Slit Under Water
Checkpoint
When this Young’s double slit experiment is placed under water,
how does the pattern of minima and maxima change?
1) the pattern stays the same
2) the maxima and minima occur at smaller angles
3) the maxima and minima occur at larger angles
…wavelength is shorter under water.
Young’s Double Slit
Checkpoint
In Young’s double slit experiment, is it
possible to see interference maxima when
the distance between slits is smaller than
the wavelength of light?
1) Yes
2) No
Young’s Double Slit
Checkpoint
In Young’s double slit experiment, is it possible to see
interference maxima when the distance between
slits
is
smaller than the wavelength of light?
1) Yes
2) No
If
d then
d > 1
so
sin
> 1
Reflections at Boundaries
Free End Reflection
No phase change
Slow Medium
to
Fast Medium
Fast Medium
to
Slow Medium
Fixed End Reflection
180
o
phase change
Newton’s Rings
Iridescence
Iridescence
Soap Film Interference
•
This soap film varies in
thickness and produces a
rainbow of colors.
•
The top part is so thin it
looks black.
•
All colors destructively
interfere there.
Thin Film Interference
n
1
(thin film)
n
2
n
0
=1.0 (air)
t
Get two waves by reflection from the two different
interfaces.
Ray 2 travels approximately
2t
further than ray 1.
Reflection + Phase Shifts
Upon reflection from a boundary between two transparent
materials, the phase of the reflected light
may
change.
•
If
n
1
> n
2
-
no phase change
upon reflection.
•
If
n
1
< n
2
- phase change of
180º
upon reflection.
(equivalent to the wave shifting by
/2
.)
Thin Film Summary
n
1
(thin film)
n
2
n = 1.0 (air)
t
1
2
Ray 1:
1
= 0 or ½
Determine
number of extra wavelengths
for
each ray.
If |(
2
–
1
)| = ½ , 1 ½, 2 ½ ….
(m + ½)
destructive
If |(
2
–
1
)| = 0, 1, 2, 3 ….
(m)
constructive
Note: this is
wavelength in film!
(
film
=
o
/n
1
)
+ 2 t/
film
Ray 2:
2
= 0 or ½
Thin Film Practice
n
glass
= 1.5
n
water
= 1.3
n = 1.0 (air)
t
1
2
1
=
2
=
Blue light (
= 500 nm
) incident on a glass (
n
glass
= 1.5
) cover slip (
t = 167
nm
) floating on top of water (
n
water
= 1.3
).
Is the interference
constructive
or
destructive
or
neither
?
Phase shift =
2
–
1
=
Thin Film Practice
n
glass
= 1.5
n
water
= 1.3
n = 1.0 (air)
t
1
2
1
= ½
2
= 0 + 2t /
glass
= 2t n
glass
/
0
= 1
Blue light (
= 500 nm
) incident on a glass (
n
glass
= 1.5
) cover slip (
t = 167
nm
) floating on top of water (
n
water
= 1.3
).
Is the interference
constructive
or
destructive
or
neither
?
Phase shift =
2
–
1
= ½ wavelength
Reflection at air-film interface only
Blue light
= 500 nm incident on a thin film (
t =
167 nm
) of glass on top of plastic. The
interference is:
1
1.
Constructive
2.
Destructive
3.
Neither
Blue light
= 500 nm incident on a thin film (
t =
167 nm
) of glass on top of plastic. The
interference is:
1
1.
Constructive
2.
Destructive
3.
Neither
1
= ½
2
= ½ + 2t /
glass
= ½ + 2t n
glass
/
0
= ½ + 1
Phase shift =
2
–
1
= 1 wavelength
Thin Films
Checkpoint
The
gas
looks:
•
bright
•
dark
A thin film of gasoline (n
gas
=1.20)
and a thin film of oil (n
oil
=1.45)
are floating on water
(n
water
=1.33). When the thickness
of the two films is exactly one
wavelength…
The
oil
looks:
•
bright
•
dark
Thin Films
Checkpoint
The
gas
looks:
•
bright
•
dark
A thin film of gasoline (n
gas
=1.20)
and a thin film of oil (n
oil
=1.45)
are floating on water
(n
water
=1.33). When the thickness
of the two films is exactly one
wavelength…
1,gas
= ½
The
oil
looks:
•
bright
•
dark
2,gas
= ½ + 2
1,oil
= ½
2,oil
= 2
|
2,gas
–
1,gas
| = 2
|
2,oil
–
1,oil
| = 3/2
constructive
destructive
Delve into the fascinating world of wave interference in physics, from understanding the concept of superposition to identifying constructive and destructive interference patterns. Discover how light waves interact through different paths and sources to create coherent or incoherent light. Explore the principles of interference through double-slit experiments and applets, shedding light on the behavior of waves in various scenarios.
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Presentation Transcript
Physics 1161: Lecture 20 Interference textbook sections 28-1 -- 28-3
Superposition ConstructiveInterference +1 t -1 + +1 In Phase t -1 +2 t -2
Superposition Destructive Interference +1 t -1 + +1 Out of Phase t 180 degrees -1 +2 t -2
Which type of interference results from the superposition of the two waveforms shown? 1. Constructive 2. Destructive 3. Neither 1.5 1 0.5 0 -0.5 -1 -1.5 + 1.5 1 Different f 0.5 0 -0.5 -1 -1.5 0% 0% 0% 1 2 3
Which type of interference results from the superposition of the two waveforms shown? 1. Constructive 2. Destructive 3. Neither 1.5 1 0.5 0 -0.5 -1 -1.5 + 1.5 1 Different f 0.5 0 -0.5 -1 -1.5 2.5 2 1.5 1 0.5 0 -0.5 0% 0% 0% -1 -1.5 -2 1 2 3
Interference for Light Can t produce coherent light from separate sources. (f 1014 Hz) Need two waves from single source taking two different paths Two slits Reflection (thin films) Diffraction* Two different paths Interference possible here Single source
Double Slit Interference Applets http://www.walter- fendt.de/ph14e/doubleslit.htm http://vsg.quasihome.com/interfer.htm
Youngs Double Slit Applet youngdoubleslitapplet1 http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/PhysicsInitiative/ Physics2000/applets/twoslitsa.html
Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be: 1. Constructive 2. Destructive 3. It depends on L 2 slits-separated by d d Single source of monochromatic light L 0% 0% 0% Screen a distance L from slits 1 2 3
Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be: 1. Constructive 2. Destructive 3. It depends on L 2 slits-separated by d d Single source of monochromatic light L The rays start in phase, and travel the same distance, so they will arrive in phase. Screen a distance L from slits 0% 0% 0% 1 2 3
Youngs Double Slit Checkpoint The experiment is modified so that one of the waves has its phase shifted by . Now, the interference will be: 1) The pattern of maxima and minima is the same for original and modified experiments. shift 2) Maxima and minima for the unmodified experiment now become minima and maxima for the modified experiment. d Single source of monochromatic light L 2 slits-separated by d Screen a distance L from slits
Youngs Double Slit Checkpoint The experiment is modified so that one of the waves has its phase shifted by . Now, the interference will be: 1) The pattern of maxima and minima is the same for original and modified experiments. 2) Maxima and minima for the unmodified experiment now become minima and maxima for the modified experiment. shift d For example at the point shown, he rays start out of phase and travel the same distance, so they will arrive out of phase. Single source of monochromatic light L 2 slits-separated by d Screen a distance L from slits
Youngs Double Slit Concept At points where the difference in path length is 0, ,2 , , the screen is bright. (constructive) d At points where the difference in path 3 5 Single source of monochromatic light , , length is 2 2 2 L the screen is dark. (destructive) 2 slits-separated by d Screen a distance L from slits
Youngs Double Slit Key Idea L Two rays travel almost exactly the same distance. (screen must be very far away: L >> d) Bottom ray travels a little further. Key for interference is this small extra distance.
Youngs Double Slit Quantitative d d d sin Path length difference = dsin = m Constructive interference dsin = (m +1 2) Destructive interference Need < d where m = 0, or 1, or 2, ...
Youngs Double Slit Quantitative L y d A little geometry sin( ) tan( ) = y/L m L = y d dsin = m Constructive interference 1 dsin = (m +1 + m L 2) Destructive interference 2 = y where m = 0, or 1, or 2, ... d
Youngs Double Slit Under Water Checkpoint L y d When this Young s double slit experiment is placed under water, how does the pattern of minima and maxima change? 1) the pattern stays the same 2) the maxima and minima occur at smaller angles 3) the maxima and minima occur at larger angles
Youngs Double Slit Under Water Checkpoint L y d When this Young s double slit experiment is placed under water, how does the pattern of minima and maxima change? 1) the pattern stays the same 2) the maxima and minima occur at smaller angles 3) the maxima and minima occur at larger angles wavelength is shorter under water.
Youngs Double Slit Checkpoint In Young s double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light? 1) Yes 2) No
Youngs Double Slit Checkpoint In Young s double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light? 1) Yes 2) No Need: d sin = m => sin = m d If d then d > 1 so sin > 1 Not possible!
Reflections at Boundaries Slow Medium to Fast Medium Fast Medium to Slow Medium Fixed End Reflection 180o phase change Free End Reflection No phase change
Soap Film Interference This soap film varies in thickness and produces a rainbow of colors. The top part is so thin it looks black. All colors destructively interfere there.
Thin Film Interference 1 2 n0=1.0 (air) n1 (thin film) t n2 Get two waves by reflection from the two different interfaces. Ray 2 travels approximately 2t further than ray 1.
Reflection + Phase Shifts Reflected wave Incident wave n1 n2 Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. If n1 > n2 - no phase change upon reflection. If n1 < n2 - phase change of 180 upon reflection. (equivalent to the wave shifting by /2.)
Thin Film Summary Determine number of extra wavelengths for each ray. 1 2 n = 1.0 (air) n1 (thin film) t n2 This is important! Note: this is wavelength in film! ( film= o/n1) Reflection Distance Ray 1: 1 = 0 or Ray 2: 2 = 0 or + 2 t/ film If |( 2 1)| = 0, 1, 2, 3 . (m) constructive If |( 2 1)| = , 1 , 2 . (m + ) destructive
Example Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? 1 = 2 = Phase shift = 2 1 =
Example Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light ( = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? 1 = Reflection at air-film interface only 2 = 0 + 2t / glass = 2t nglass/ 0= 1 Phase shift = 2 1 = wavelength
Blue light = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: 1 2 n=1 (air) nglass =1.5 t nplastic=1.8 1. Constructive 2. Destructive 3. Neither 0% 0% 0% 1 2 3
Blue light = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: 1. Constructive 2. Destructive 3. Neither 1 2 n=1 (air) nglass =1.5 t nplastic=1.8 1 = 2 = + 2t / glass = + 2t nglass/ 0= + 1 Phase shift = 2 1 = 1 wavelength 0% 0% 0% 1 2 3
Thin Films Checkpoint A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength nair=1.0 t = noil=1.45 ngas=1.20 nwater=1.3 The oil looks: bright dark The gas looks: bright dark
Thin Films Checkpoint A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength nair=1.0 t = noil=1.45 ngas=1.20 nwater=1.3 The gas looks: bright dark 1,gas = | 2,gas 1,gas | = 2 The oil looks: bright dark 1,oil = | 2,oil 1,oil | = 3/2 2,gas = + 2 2,oil = 2 constructive destructive
