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TRANSCRIPT
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Electromagnetic Waves
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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.
The Nature of Light: Wave or Particle
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1 The wave theory of light is attributed to
A Christian Huygens.B Isaac Newton.C Max Planck.D Albert Einstein.
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2 The particle theory of light is attributed to
A Christian Huygens.B Isaac Newton.C Max Planck.D Albert Einstein.
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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.
Young's Double Slit Experiment
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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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Or, if the extra distance one sound has to travel is exactly one wavelength longer.
Young's Double Slit Experiment
loud
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But they will destructively interfere if one sound travels half a wavelength longer than the other.
Young's Double Slit Experiment
quiet
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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.
Young's Double Slit Experiment
quiet
loud
loud
loud
quiet
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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's Double Slit ExperimentYoung 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 ExperimentYoung 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 ExperimentThis 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.
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If Light is a Wave, what's waving?
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?
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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:
Gauss's Law
Gauss's Law for Magnetism
Faraday's Law of Induction
Ampere's Law
Maxwell's Equations
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If Light is a Wave, what's waving?
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.
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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.
Creating Electromagnetic Waves
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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......
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.
Accelerating Charges create E-M waves
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3 An electric field is produced by a
A constant magnetic field.B changing magnetic field.C either a constant or a changing
magnetic field.D none of the given answers
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4 A changing electric field will produce a
A current.B gravitational field.C magnetic field.D none of the given answers
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The electric and magnetic waves are perpendicular to each other, and to the direction of propagation.
Electromagnetic Waves
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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:
Light is an Electromagnetic Wave
c = lf
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Light is an Electromagnetic Wave
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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
Electromagnetic Radiation
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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
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6 In a vacuum, the velocity of all electromagnetic waves
A is zero.B is 3.0 × 108 m/s.C depends on the frequency.D depends on their amplitude.
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7 Of the following, which is not electromagnetic in nature?
A microwavesB gamma raysC sound wavesD radio waves
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8 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
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9 For a wave, the frequency times the wavelength is the wave's
A speed.B amplitude.C intensity.D power.
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10 What color of light has the shortest wavelength?
A Green
B Red
C Yellow
D Blue
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11 What color of light has the longest wavelength?
A Green
B Red
C Yellow
D Blue
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12 Electromagnetic radiation travels through vacuum at a speed of
A 186,000 m/s
B 125 m/s
C 3.00 x 108 m/s
D It depends on wavelength
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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 10-5 m
C 0.040 m
D 2.5 m
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 1014 Hz
B 1.0 x 1015 Hz
C 1.5 x 1015 Hz
D 2.0 x 1015 Hz
c = lf
c = 3.00 ´ 108 m/s
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Wavelengths of visible light: 400 nm to 750 nm
Shorter wavelengths are ultraviolet; longer wavelengths are infrared
UV IR
400 nm 500 nm 600 nm 700 nm
7.5 x 1014 Hz 6 x 1014 Hz 5 x 1014 Hz 4 x 1014 Hz
f
λ
The Visible Spectrum
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15 Visible light ranges in wavelength from
A 400 μm to 750 μm.B 400 nm to 750 nm.C 500 μm to 850 μm.D 500 nm to 850 nm.
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16 White light is
A 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.
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17 Light with wavelength slightly longer than 750 nm is called
A ultraviolet light.B visible light.C infrared light.D none of the given answers
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Interference – Young’s Double-Slit Experiment
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 Patrick Edwin Moran
by Francesco Franco
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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
Waves Versus Particles: Huygens’ Principle
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DiffractionWhen waves encounter an obstacle, they bend around it, leaving a “shadow region.” This is called diffraction.
© Exploratorium, www.exploratorium.edu. Some rights reserved. Unless otherwise noted, this work is licensed under creativecommons.org/licenses/by-nc-sa/3.0/us/
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Diffraction
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.
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18 What principle is responsible for light spreading as it passes through a narrow slit?
A refractionB polarizationC diffractionD interference
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19 What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits?
A refractionB polarizationC dispersionD interference
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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 one-half wavelength behind the wave from the other slit, which is observed at that point?
A bright fringeB dark fringeC gray fringeD multi-colored fringe
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Double-Slit Maxima and Minima
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 Francesco Franco
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x
L
d
Extra distance = #
The bright lines that appear on the screen are called maxima.
The dark lines are called minima.
Maxima are evenly spaced, and a minimum occurs between each pair of maxima.
The distance to the first maxima can be found by using similar triangles.
Double-Slit Maxima and Minima
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Interference of Light Waves
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.
L
d bright spotθ1θ2 dark spot
bright spot
bright spot
bright spot
bright spot
dark spot
dark spot
dark spot
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Interference of Light Waves
For small angles, θ<10°, tan θ = sin θ.
Since tanθ = x/L, sinθ = x/L....
d sinθ = mλ becomes:
dx/L = mλ
L
d bright spotθ1θ2
bright spot
bright spot
bright spot
bright spot
x
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x # mlLd
x # (m + 1/2)l Ld
Double-Slit Maxima and Minima
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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Brightness versus distance (x) from the central maximum is plotted below. Between the maxima and
the minima, the interference varies smoothly.
Double-Slit Maxima and Minima
Constructive interference
Destructive interference
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Interference - Young's Double Slit Experiment
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.
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Diffraction GratingA 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 GratingThe 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 # mlLd
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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 InterferenceWhen 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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D
Single Slit InterferenceIn 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 # 1/2l L1/2D
x # l LD
x # (m + 1/2)l Ld
m = 0, 1, 2, ...
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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.
3lLD
-3lLD
-2lLD
lLD
2lLD
-lLD 0
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.
Single Slit Interference
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Diffraction Interference Around an Object
Light also bends around objects, creating a bright spot where it would be least expected.
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23 What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits?
A refractionB polarizationC dispersionD 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 one-half wavelength behind the wave from the other slit, which is observed at that point?
A bright fringeB dark fringeC gray fringeD multi-colored fringe
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25 The separation between adjacent maxima in a double-slit interference pattern using monochromatic light is
A greatest for red light.B greatest for green light.C 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:
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26 Light travels fastest
A in a vacuum.B through water.C through glass.D through diamond.
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27 For all transparent material substances, the index of refraction
A is less than 1.B is greater than 1.C is equal to 1.D could be any of the given answers; it
all depends on optical density.
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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.
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29 When a light wave enters into a medium of different optical density,
A its speed and frequency change.B its speed and wavelength change.C its frequency and wavelength
change.D its speed, frequency, and wavelength
change.
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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 is reduced to 2/3 its original value.C 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 is reduced to 2/3 its original value.C is unaffected.D none of the given answers
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32 When a light wave enters into a medium of different optical density,
A its speed and frequency change.B its speed and wavelength change.C its frequency and wavelength
change.D its speed, frequency, and wavelength
change.
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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 is reduced to 2/3 its original value.C 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 is reduced to 2/3 its original value.C is unaffected.D none of the given answers
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Dispersion
The index of refraction of a material varies somewhat with the wavelength of the light.
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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 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.
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36 The principle which explains why a prism separates white light into different colors is
A refraction.B polarization.C dispersion.D total internal reflection.
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37 Which color of light undergoes the smallest refraction when passing from air to glass?
A redB yellowC greenD violet
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© Copyright RichTea and licensed for reuse under this Creative Commons Licence.
The Visible Spectrum and DispersionActual rainbows are created by dispersion in tiny drops of water.
© Copyright Beyonder and licensed for reuse under this Creative Commons Licence.
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38 The principle which allows a rainbow to form is
A refraction.B polarization.C dispersion.D total internal reflection.
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39 Light with wavelength slightly shorter than 400 nm is called
A ultraviolet light.B visible light.C infrared light.D none of the given answers
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40 Which color of light undergoes the greatest refraction when passing from air to glass?
A redB yellowC greenD violet
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Interference by Thin FilmsThe colors on the soap bubble are created by interference by thin films.
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Interference by Thin FilmsConsider 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.
Air
Oil
Water
A C
B
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Interference by Thin FilmsIf 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...
The wavelength, λ, is the wavelength in the film of oil and t is the thickness of the film.
Air
Oil
Water
A C
B
nair < noil< nwater
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Interference by Thin FilmsIf 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...
The wavelength, λ, is the wavelength in the film of oil and t is the thickness of the film.
Air
Film
Air
A C
B
nair < nwater > nair
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41 The colors on an oil slick are caused by reflection and
A diffraction.B interference.C refraction.D polarization.
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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 transverse.C both longitudinal and transverse.D neither longitudinal or transverse.
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Polarization
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.
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45 What principle is responsible for the fact that certain sunglasses can reduce glare from reflected surfaces?
A refractionB polarizationC diffractionD 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 I0/4B I0/4C 3I0/8D 3I0/4