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Electromagnetic Waves
The Nature of Light: Wave or Particle
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The nature of light has been debated for
thousands of years.
In the 1600's, Newton argued that light was a
stream of particles.
Huygens argued it was a wave.
Both had good arguments, but neither could
prove their case.
1
The wave theory of light is
attributed to
A
Christian Huygens.
B
C
Isaac Newton.
D
Albert Einstein.
Max Planck.
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2
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The particle theory of light
is attributed to
A
Christian Huygens.
B
C
Isaac Newton.
D
Albert Einstein.
Max Planck.
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Young's Double Slit Experiment
In 1801, Thomas Young settled the argument
(apparently) with his Double Slit Experiment.
First, let's use what we know about sound and
particles to see one way to tell the difference
between particles and waves.
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Young's Double Slit Experiment
If two speakers are
playing a sound with
the same wavelength,
the will constructively
interfere if they travel
the same distance to a
screen.
loud
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Young's Double Slit Experiment
Or, if the extra distance
one sound has to
travel is exactly one
wavelength longer.
loud
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Young's Double Slit Experiment
But they will
destructively interfere
if one sound travels
half a wavelength
longer than the other.
quiet
Young's Double Slit Experiment
So for sounds waves,
we expect to get a
pattern of maxima and
minima like this.
But this would be the
case for all waves, not
just sound waves.
loud
quiet
loud
quiet
loud
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Young's Double Slit Experiment
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Would we expect a
pattern like that if two
machine gunners were
firing randomly at a
wall, or would we
expect an even
distribution of bullets?
Young's Double Slit Experiment
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Young tested to see if
light was a wave by
seeing if it created an
interference pattern
when it went through
two slits, like a wave
would.
Young's Double Slit Experiment
Young tested to see if
light was a wave by
seeing if it created an
interference pattern
when it went through
two slits, like a wave
would.
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Young's Double Slit Experiment
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This photo is of light (of
one color) striking a
distant screen after
passing through 2 slits.
This only makes sense if
light is a wave.
If Light is a Wave, what's waving?
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If light is a wave, what's waving.
In sound, we know its the pressure in the air.
In any simple harmonic motion, including waves,
there has to be two forms, or levels, of energy
and a means to move between them...what was
that for light?
If Light is a Wave, what's waving?
In the late 1800's James Maxwell, combined
together the known equations of electricity and
magnetism, and added one, to create:
Maxwell's Equations
Gauss's Law
Gauss's Law for Magnetism
Faraday's Law of Induction
Ampere's Law
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If Light is a Wave, what's waving?
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He found they predicted that energy could move
between two forms (electric and magnetic) and that
disturbance must travel through space at a speed of
3.0 x 108 m/s.
This very much agreed with the known speed of light.
3.0 x 108 m/s is the speed of light in a vacuum.
Creating Electromagnetic Waves
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We already learned that a changing magnetic field
produces an electric field (E = -DfB/Dt).
Maxwell showed that a changing electric field produces a
magnetic field as well.
Once these changing fields are first started up, they keep
creating each other...and travel on their own.
These traveling fields are called electromagnetic waves.
Accelerating Charges create E-M waves
A great way to start this up is to make a charge, like
an electron accelerate.
That creates a changing electric field,
which creates a changing magnetic field,
which creates a changing electric field,
which creates a changing magnetic field
which creates a changing electric field,
which creates a changing magnetic field......
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Accelerating Charges create E-M waves
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For instance, in a broadcast radio or TV antenna
electrons are accelerated up and down by a changing
voltage from an amplifier. As they accelerate they
radiate E-M waves which travel away from the antenna.
3
An electric field is
produced by a
A
constant magnetic field.
B
C
changing magnetic field.
D
4
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either a constant or a changing
magnetic field.
none of the given answers
A changing electric field
will produce a
A
current.
B
C
gravitational field.
D
none of the given answers
magnetic field.
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Electromagnetic Waves
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The electric and magnetic waves are perpendicular to each
other, and to the direction of propagation.
Light is an Electromagnetic Wave
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Young showed that light is a wave.
Maxwell showed that electromagnetic waves exist and
travel at the speed of light.
Light was shown to be an electromagnetic wave.
The frequency of an electromagnetic wave is related to
its wavelength. For electromagnetic waves (including
light), in a vacuum:
c = lf
Light is an Electromagnetic Wave
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Electromagnetic Radiation
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· All electromagnetic radiation travels at the same velocity:
the speed of light (c), c = 3.00 ´ 108 m/s.
· For all waves, velocity = wavelength x frequency: v = #f
· Therefore for light, c = lf
5
All electromagnetic waves
travel through a vacuum at
A
the same speed.
B
speeds that are proportional to their
frequency.
C
speeds that are inversely
proportional to their frequency.
D
none of the given answers
6
In a vacuum, the velocity
of all electromagnetic
waves
A
is zero.
B
C
is 3.0 × 108 m/s.
D
depends on their amplitude.
depends on the frequency.
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7
Of the following, which is
not electromagnetic in
nature?
A
microwaves
B
C
sound waves
D
radio waves
8
gamma rays
Which of the following
correctly lists
electromagnetic waves in
order from longest to
shortest wavelength?
A
gamma rays, ultraviolet,
infrared, microwaves
B
microwaves, ultraviolet, visible
light, gamma rays
C
radio waves, infrared, gamma
rays, ultraviolet
D
television, infrared, visible
light, X-rays
9
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For a wave, the frequency
times the wavelength is the
wave's
A
speed.
B
C
amplitude.
D
power.
intensity.
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10 What color of light has the
shortest wavelength?
A
Green
B
Red
C
Yellow
D
Blue
11 What color of light has the
longest wavelength?
A
Green
B
Red
C
Yellow
D
Blue
12 Electromagnetic radiation
travels through vacuum at
a speed of
A
186,000 m/s
B
125 m/s
C
3.00 x 10 m/s
D
It depends on wavelength
8
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13 The wavelength of light that
has a frequency of 1.20 x
1013s is
A
25 m
B
2.5 x 10 m
C
0.040 m
D
2.5 m
-5
c = lf
c = 3.00 ´ 108 m/s
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14 What is the frequency of
light whose wavelength is
600 nm?
A
5.0 x 10
14
B
1.0 x 10
15
Hz
C
1.5 x 10
15
Hz
D
2.0 x 10
15
Hz
Hz
c = lf
c = 3.00 ´ 108 m/s
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The Visible Spectrum
Wavelengths of visible light: 400 nm to 750 nm
Shorter wavelengths are ultraviolet; longer
wavelengths are infrared
UV
IR
λ
f
400 nm
7.5 x 1014 Hz
500 nm
14
6 x 10 Hz
600 nm
14
5 x 10 Hz
700 nm
14
4 x 10 Hz
15 Visible light ranges in
wavelength from
A
400 μm to 750 μm.
B
C
400 nm to 750 nm.
D
500 nm to 850 nm.
500 μm to 850 μm.
16 White light is
A
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light of wavelength 550 nm, in the
middle of the visible spectrum.
B
a mixture of all frequencies.
C
a mixture of red, green, and blue
light.
D
the term used to describe very bright
light.
E
the opposite (or complementary
color) of black light.
17 Light with wavelength
slightly longer than 750 nm
is called
A
ultraviolet light.
B
C
infrared light.
D
none of the given answers
visible light.
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Interference – Young’s Double-Slit
Experiment
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The double slit experiment relies on two properties of
waves (including light): diffraction and interference.
Each slit generates a new wave due to diffraction.
Those waves then either constructively or
destructively interfere on a faraway screen.
by France s co
Franco
by Patrick Edwin Moran
Waves Versus Particles:
Huygens’ Principle
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Every point on a wave
front acts as a point
source; the wavefront
as it develops is
tangent to their
envelope
Diffraction
When waves encounter an obstacle, they bend around it,
leaving a “shadow region.” This is called diffraction.
© Exploratorium, www.e xploratorium.e du. S ome rights re s e rve d. Unle s s othe rwis e note d, this
work is lice ns e d unde r cre ative commons .org/lice ns e s /by-nc-s a/3.0/us /
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Diffraction
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When waves, including light, meets an obstacle it bends
around it to some extent.
When it meets a small opening, the opening generates a
new wave on the other side.
18 What principle is
responsible for light
spreading as it passes
through a narrow slit?
A
refraction
B
C
polarization
diffraction
D
interference
19 What principle is
responsible for alternating
light and dark bands when
light passes through two or
more narrow slits?
A
refraction
B
C
polarization
D
interference
dispersion
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20 If a wave from one slit of a
Young's double slit
experiment arrives at a
point on the screen onehalf wavelength behind the
wave from the other slit,
which is observed at that
point?
A
bright fringe
B
C
gray fringe
D
multi-colored fringe
dark fringe
Double-Slit Maxima and Minima
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Interference occurs because each point on the screen is not
the same distance from both slits. Depending on the path
length difference, the wave can interfere constructively
(bright spot) or destructively (dark spot).
by France s co Franco
Double-Slit Maxima and Minima
The bright lines that
appear on the screen are
called maxima.
L
x
The dark lines are called
minima.
Maxima are evenly spaced,
and a minimum occurs
between each pair of
maxima.
d
Extra distance = #
The distance to the first
maxima can be found by
using similar triangles.
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Interference of Light Waves
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L
bright spot
bright spot
θ1 θ2
d
bright spot
bright spot
bright spot
dark spot
dark spot
dark spot
dark spot
A constructive interference pattern is given by: d sin# = m#
A destructive interference pattern is given by:
d sin# = (m + ½)#
Where m is called the order of the interference fringe.
Interference of Light Waves
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L
bright spot
d
θ1 θ2
x
bright spot
bright spot
bright spot
bright spot
For small angles, θ<10°, tan θ = sin θ.
Since tanθ = x/L, sinθ = x/L....
d sinθ = mλ becomes:
dx/L = mλ
Double-Slit Maxima and Minima
x # mlL
d
x # (m + 1/2)l L
d
The maxima and minima spread out as the distance
between the slits gets smaller.
As d gets smaller...x gets larger.
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Double-Slit Maxima and Minima
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Brightness versus distance (x) from the central
maximum is plotted below. Between the maxima and
the minima, the interference varies smoothly.
Constructive
interference
Destructive
interference
Interference - Young's Double Slit Experiment
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Since the position of the maxima (except for the central one)
depends on wavelength, the first and high-order fringes
contain a spectrum of colors.
Diffraction Grating
A diffraction grating consists of a large number of equally
spaced narrow slits or lines. They produce maxima and
minima, just like in the Double Slit experiment, but the pattern
is much sharper because there
are thousands of slits, not just
two. The more lines or slits there
are, the narrower the peaks.
Also, shining white light on the
grating produces spectra of
colors since the location of
maxima depends on wavelength.
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Diffraction Grating
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The maxima of the diffraction pattern on a far away
screen is the same as it was for two slits, the lines
are just brighter and sharper.
x # mlL
d
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21 What happens to a diffraction pattern if the
wavelength of the light is decreased?
A
Interference fringes move closer to the central
maximum.
B
Interference fringes move away from the central
maximum.
C
There is no change in the interference.
D
Bright fringes are replanced with dark fringes.
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22 What happens to a diffraction pattern if the space
between the slits is decreased?
A
Interference fringes move closer to the central
maximum.
B
Interference fringes move away from the central
maximum.
C
There is no change in the interference.
D
Bright fringes are replanced with dark fringes.
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Single Slit Interference
When light strikes even a single slit, interference
occurs between light at the center of the slit with light
at the bottom...and top.
D
D
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Single Slit Interference
In this case, d (from the equation for single slit
interference) becomes 1/2D (the distance from the top
of the slit to its center. So the equation for the first
minimum (m=0) becomes:
x # (m + 1/2)l L
d
x#
D
m = 0, 1, 2, ...
1/2l L
1/2D
x# lL
D
Single Slit Interference
The resulting pattern of light and dark stripes is called a
diffraction pattern.
The width of the central maximum is 2l/D. As D gets smaller,
the central maximum becomes wider. As D gets larger, the
central maximum gets smaller.
-3lL
D
-2lL
D
-lL
D
0
lL
D
2lL
D
3lL
D
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Single Slit Interference
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The width of the central maximum is important for
optical instruments (including our eyes) as it limits
how clearly we see.
The wider the central maximum is, the more smeared
out objects appear...the less we can resolve one
object from another.
That's why an eagle's eye is so large. Why large
lenses on cameras give better pictures...why
telescopes have to be large, etc.
As D gets very large the more clear the image we see.
Diffraction Interference Around an Object
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Light also bends around objects, creating a bright
spot where it would be least expected.
23 What principle is
responsible for alternating
light and dark bands when
light passes through two or
more narrow slits?
A
refraction
B
C
polarization
dispersion
D
interference
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24 If a wave from one slit of a
Young's double slit
experiment arrives at a
point on the screen onehalf wavelength behind the
wave from the other slit,
which is observed at that
point?
A
bright fringe
B
C
gray fringe
D
multi-colored fringe
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dark fringe
25 The separation between
adjacent maxima in a
double-slit interference
pattern using
monochromatic light is
A
greatest for red light.
B
C
greatest for green light.
greatest for blue light.
D
the same for all colors of light.
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Light slows when
traveling through a
medium. The index of
refraction (n) of the
medium is the ratio of the
speed of light in vacuum
to the speed of light in
the medium:
26 Light travels fastest
A
in a vacuum.
B
C
through water.
D
through diamond.
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through glass.
27 For all transparent material
substances, the index of
refraction
A
is less than 1.
B
C
is greater than 1.
D
could be any of the given answers; it
all depends on optical density.
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is equal to 1.
28 The index of refraction of
diamond is 2.42. This
means that a given type of
light travels
A
2.42 times faster in air than it does in
diamond.
B
2.42 times faster in diamond than it
does in air.
C
2.42 times faster in vacuum than it
does in diamond.
D
2.42 times faster in diamond than it
does in vacuum.
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The frequency of the light does not change, but the
wavelength does as it travels into a new medium.
where "n" is the index of refraction.
Wavelengths get shorter when light enters a slower medium.
29 When a light wave enters
into a medium of different
optical density,
A
B
C
D
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its speed and frequency change.
its speed and wavelength change.
its frequency and wavelength
change.
its speed, frequency, and wavelength
change.
30 When a beam of light
(wavelength = 590 nm),
originally traveling in air,
enters a piece of glass
(index of refraction 1.50),
its frequency
A
increases by a factor of 1.50.
B
C
is reduced to 2/3 its original value.
is unaffected.
D
none of the given answers
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31 When a beam of light
(wavelength = 590 nm),
originally traveling in air,
enters a piece of glass
(index of refraction 1.50),
its wavelength
A
increases by a factor of 1.50.
B
C
is reduced to 2/3 its original value.
is unaffected.
D
none of the given answers
32 When a light wave enters
into a medium of different
optical density,
A
B
C
D
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its speed and frequency change.
its speed and wavelength change.
its frequency and wavelength
change.
its speed, frequency, and wavelength
change.
33 When a beam of light
(wavelength = 590 nm),
originally traveling in air,
enters a piece of glass
(index of refraction 1.50),
its frequency
A
increases by a factor of 1.50.
B
C
is reduced to 2/3 its original value.
is unaffected.
D
none of the given answers
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34 When a beam of light
(wavelength = 590 nm),
originally traveling in air,
enters a piece of glass
(index of refraction 1.50),
its wavelength
A
increases by a factor of 1.50.
B
C
is reduced to 2/3 its original value.
is unaffected.
D
none of the given answers
Dispersion
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The index of refraction of a material varies somewhat
with the wavelength of the light.
Dispersion
This variation in refractive index is why a prism will split
white light (which contains all the colors) into a rainbow of
colors.
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35 White light is
A
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light of wavelength 550 nm, in the
middle of the visible spectrum.
B
a mixture of all frequencies.
C
a mixture of red, green, and blue
light.
D
the term used to describe very bright
light.
E
the opposite (or complementary
color) of black light.
36 The principle which
explains why a prism
separates white light into
different colors is
A
refraction.
B
C
polarization.
D
total internal reflection.
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dispersion.
37 Which color of light
undergoes the smallest
refraction when passing
from air to glass?
A
red
B
C
yellow
green
D
violet
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The Visible Spectrum and Dispersion
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Actual rainbows are created by dispersion in
tiny drops of water.
© Copyright RichTe a and lice ns e d for re us e
unde r this Cre ative Commons Lice nce .
© Copyright Be yonde r and lice ns e d for
re us e unde r this Cre ative Commons
Lice nce .
38 The principle which allows
a rainbow to form is
A
refraction.
B
C
polarization.
D
total internal reflection.
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dispersion.
39 Light with wavelength
slightly shorter than 400
nm is called
A
ultraviolet light.
B
C
infrared light.
D
none of the given answers
visible light.
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40 Which color of light
undergoes the greatest
refraction when passing
from air to glass?
A
red
B
C
yellow
green
D
violet
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Interference by Thin Films
The colors on the soap bubble are created by interference
by thin films.
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Interference by Thin Films
Consider a smooth surface of water with a thin film of oil
on top of it. The oil's index of refraction is less than that of
water.
Part of the incident light is
reflected at point A, and part of
it is reflected at point B.
The part reflected at the lower
surface must travel the extra
distance ABC in the oil.
If t is the thickness of the film
then ABC is equal to 2t.
A
C
B
Air
Oil
Water
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Interference by Thin Films
If that distance is equal to λ, 2λ, 3λ,
and so on then the waves will
interfere constructively.
2t = mλ, where m = 1, 2, 3...
If that distance is equal to λ/2, 3λ/2,
5λ/2, and so on then the waves will
interfere destructively.
2t = (m+½) λ, where m = 1, 2, 3...
A
Air
C
B
Oil
Water
nair < noil< nwater
The wavelength, λ, is the wavelength
in the film of oil and t is the thickness
of the film.
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Interference by Thin Films
If that distance is equal to λ, 2λ, 3λ,
and so on then the waves will
interfere constructively.
2t = (m+½)λ, where m = 1, 2, 3...
If that distance is equal to λ/2, 3λ/2,
5λ/2, and so on then the waves will
interfere destructively.
2t = mλ, where m = 1, 2, 3...
A
C
Air
Film
B
Air
nair < nwater > nair
The wavelength, λ, is the wavelength
in the film of oil and t is the
thickness of the film.
41 The colors on an oil slick
are caused by reflection
and
A
diffraction.
B
C
interference.
D
polarization.
refraction.
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42 A light with a wavelength of 500nm shines on a
glass block that is covered by a thin film n = 1.2.
What must be the minimum thickness of the film in
order to minimize the intensity of the reflected light?
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43 A light with a wavelength of 500nm shines on a
glass block that is covered by a thin film n = 1.2.
What must be the minimum thickness of the film in
order to maximize the intensity of the reflected
light?
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44 Electromagnetic waves are
A
longitudinal.
B
C
both longitudinal and transverse.
D
neither longitudinal or transverse.
transverse.
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Polarization
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Because the intensity of a light beam is proportional to the
square of the amplitude, the intensity of a plane-polarized beam
transmitted by a polarizer is:
I = I0 cos2 θ
where θ is the angle between the polarizer axis and the plane of
polarization and I0 is the incoming intensity.
Note that the incoming light in this equation is already polarized.
When light travels through only one polarizer then intensity is
reduced to one-half the original.
45 What principle is
responsible for the fact
that certain sunglasses
can reduce glare from
reflected surfaces?
A
refraction
B
C
polarization
diffraction
D
total internal reflection
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46 Unpolarized light passes through two polarizers
the axis of one is vertical and the axis of the other
is tilted 30 degrees from the vertical. If the
incomming intensity is I0, what is the intensity of
the transmitted light?
A
I0/4
B
I0/4
C
3I0/8
D
3I0/4