chapter 25 lecture 12 april 28, 2005. electromagnetic waves are transverse ^ ^ y
TRANSCRIPT
![Page 1: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/1.jpg)
Chapter 25
Lecture 12April 28, 2005
![Page 2: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/2.jpg)
Electromagnetic waves are transverse
0
0
0 0
0 0 0
cos( )
cos( )
B
P S
E kx t
B kx t
d dd d
dt dt
kE B
E B cBk
E x
B z
E s B A
^
^y
![Page 3: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/3.jpg)
PoyntingVector
0
1S E B
S
2
0 0
~ / : E=cBEB E
Power area notec
S
Poynting Vector and Intensity
• Points in the direction of the wave• the magnitude is the rate of
energy transfer per unit area carried by the wave
20
02avg
EPowerI S
Area c
Average{ [cos(kx-wt)]2 } = 1/2
![Page 4: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/4.jpg)
Traveling Waves
![Page 5: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/5.jpg)
Traveling Waves
![Page 6: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/6.jpg)
Standing Waves between two flat mirrors
EB
![Page 7: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/7.jpg)
My total energy output per unit time is constant
My energy output per unit time and area drops as the
distance2
RNear Earth:P~0.00001 N/m2
Radiation pressureThe theory of relativity: anything moving at the speed of light will carry momentum p=E/c
Light can push stuff!
2
( ) 1
4Sun
Sail Sail Sail Sail
PowerI RF PA A A
c c R
c
I
A
Power
ct
cE
At
p
AArea
Force
1/11
Pressure
![Page 8: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/8.jpg)
Polarization
When E points in one direction the wave is
linearly polarized
There are materials that absorb waves when E points in one direction
E
… but not in the other
●
E
Points out of the screen
There are also other polarizations for which
E changes direction
![Page 9: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/9.jpg)
Polarizers at angles reduce the intensity
Selects one polarization
Only the projection onto the transmission
axis gets through I=I1 cos2
I=I1=I0/2
I=I0
![Page 10: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/10.jpg)
Crossed polarizers transmit approximately what fraction of an electromagnetic wave?
1. 0%
2. 25%
3. 50%
4. 75%
5. 100%
![Page 11: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/11.jpg)
What is light? I believe light is a stream of fast moving particles. This explains why and how light
reflects and refracts.
I can also understand how and why light reflects and refracts if I assume
it is a wave.HUYGENS’ PRINCIPLE
If light is a wave it can should be able to go around small obstacles…and it
does!YOUNG’S INTERFERENCE EXPT.
My equations predicted that light is a high frequency electromagnetic wave in1865.
![Page 12: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/12.jpg)
So, is light a wave or a particle?
Since it sometimes behaves like one and sometimes like the other it is neither.
Instead of trying to force it into some label convenient to us we should find out its
properties.
In many cases light behaves like a wave, but sometimes (when quantum effects are
important) it behaves like a particle.
![Page 13: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/13.jpg)
The ray approximation
When light propagates its wave nature is hidden if
• We never look at distances of the order of (or smaller)• All obstacles have typical sizes much larger than
d
The wave nature of light is not important
for d >>
Light behaves as a ray. In uniform media it travels in a straight
line
![Page 14: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/14.jpg)
The ray approximation
d ~d d
For smaller distances (d ~ ) the wave nature begins to show
up
For d << the wave nature is central in
understanding light’s behavior
When looking at features smaller than the interference of
light waves shows up
![Page 15: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/15.jpg)
The shortest time principle – FERMAT’S PRINCIPLE
When light behaves as a ray and travels from point A to point B it follows the path that gets it to B in the shortest time possible
In a uniform medium where the light speed is c1 …
A
B
This path is longer
This is the shortest path
… for constant speed the shortest path takes the least amount of time
In uniform media light rays travel in straight lines
![Page 16: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/16.jpg)
A B
L
When light behaves as a ray and travels from point A to point B it follows the path that gets it to B in the shortest time possible
Let us look at a reflected ray
mirror
h
x
L - x
x is such that it takes the least amount of time to go from A to B
22 hx 22 hxL
2222 11)( :time hx
vhxL
vxt
110 0
2222 hx
x
vhxL
xL
vdx
dt(x)
'
sin sin
sin1
sin1
0
'
'
'vv
Speed of light in the medium
![Page 17: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/17.jpg)
I. The law of reflection
II. The path of a light ray is reversible.
III. The path of a light ray in vacuum defines what is meant by “a straight line”.
1
![Page 18: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/18.jpg)
25.17
• The reflecting surfaces of two intersecting flat mirrors are at an angle of θ. If a light ray strikes the horizontal mirror, show that the emerging ray will intersect the incident ray at an angle of β=180º-2
![Page 19: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/19.jpg)
Exercise 25.17
This looks like an application to the reflection formula and a bit of geometry
![Page 20: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/20.jpg)
When light behaves as a ray and travels from point A to point B it follows the path that gets it to B in the shortest time possible
Look at a ray going form one medium with v1 to another with v2
v1
v2
h
h
A
B
x
L - x
22 hx
22 hxL
22
2
22
1
11)( hxL
vhx
vxt
22
11
222
221
sin1
sin1
1
1
: 0
vv
hxL
xL
vhx
x
v
dx
dt(x)
1
2
![Page 21: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/21.jpg)
Define the index of refraction:
v
cn
mediumin light of speed
in vacuumlight of speed
2211
22
11
sin sin
sin sin
nn
v
c
v
c
v1
v2
A
B
1
2
Then under refraction,
Index of Refraction
![Page 22: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/22.jpg)
Snell’s law of refraction
n2 sinn1sin1
n2
n1
![Page 23: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/23.jpg)
Given two slabs of transparent material of equal thickness, Fermat’s principle means that the part of a ray passing through the medium with the higher index of refraction is ______ the part passing through the lower index medium.
1. longer than
2. equal to
3. shorter than
4. perpendicular to
5. parallel to
![Page 24: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/24.jpg)
25.13
• When the light in the figure passes through the glass block, it is shifted laterally by the distance d. If n = 1.76, find the value of d.
![Page 25: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/25.jpg)
Exercise 25.13
This looks like an application to the refraction formula and a bit of geometry
2
21
2
21
212
cos
sin
cos
sin
sin cos
θ
θθhd
h
dL
d
L
h
h
L
1122 sin sin nn
d
cm 39.09428.0
1827.02
34.0
5.01sin 5.1
6/ ,51 ,1
2
2
121
d
.nn
![Page 26: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/26.jpg)
Larger than 1
When light goes from medium 1 to medium 2 with n1 > n2
12
12 sin sin
n
n
If we increase 1 the right hand side grows
Eventually, when sin1 = n2/n1 we get sin2=1
If we increase 1 beyond that the wave in medium 2 disappears
The ray suffers total internal reflection
θc is when sinθ2=1 i.e. n1/n2 sin θc =1
Total internal reflection
![Page 27: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/27.jpg)
Find the critical angle for a ray of light in glass
Critical Anglen1 sin1 n1 sinC
n2 sin2 n2 sin(90o)
sinc n2
n1
for n1 n2
Air: n2 = 1 Glass: n1 = 1.5 --> c = 42o
Two Rt Angle PrismsNo Loss of Light; use inoptical instruments
Fiber Optics
core, n1
clad, n2 < n1
n1
n2
![Page 28: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/28.jpg)
Huygen’s principle (1678)
Each point on a wave front is a source of secondary spherical wavelets.
Constructive interference creates the new wave front.
![Page 29: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/29.jpg)
Endoscope
"Foreign Body" in the Stomach Swallowed QuarterHere is a quarter which a young man swallowed and which is lying in the stomach. These are easily removed with a wire snare or device for grasping a coin.
![Page 30: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/30.jpg)
Why is the sky blue?
![Page 31: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/31.jpg)
why are sunsets red?
![Page 32: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/32.jpg)
If n depends on we get dispersion
Dispersion
blue bent more than red
![Page 33: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/33.jpg)
Iscattered=λ-4
longer wavelengthless scattered more scattered
![Page 34: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/34.jpg)
Rainbows
400
420
Primary
520
Secondary
Colors Reversed
![Page 35: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/35.jpg)
Examples
![Page 36: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/36.jpg)
24.22
• At what distance from a 100W electromagnetic wave point source does Emax=15V/m
![Page 37: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/37.jpg)
24.22
![Page 38: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/38.jpg)
24.26
• A possible means of space flight is to place an absorbing sheet into orbit around the Earth and then use the light from the Sun to push this “solar sail.” Suppose a sail of area 6105 m2 and mass 6000kg is placed in orbit facing the Sun.
a) what is the force exerted on the sail? b) What is the sail’s acceleration?c) How long does it take the sail to reach the Moon,
3.84108 m away? Ignore all gravitational effects, assume that the acceleration calculated in part b) remains constant, and assume a solar intensity of 1340 W/m2
![Page 39: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/39.jpg)
24.26
![Page 40: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/40.jpg)
24.35
• An important news announcement is transmitted by radio waves to people sitting next to their radios, 100 km from the station, and by sound waves to people sitting across the news room, 3M from the newscaster. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s.
![Page 41: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/41.jpg)
Exercise 24.35
• the sound and radio waves start at the same time• sound covers a distance d in a time d/v• radio waves cover a distance L in a time L/c
3sound
34
light 8
3 m s 8.75 10 s
343 m/s
100 103.33 10 s
3 10 /
t
mt
m s
Light wins
![Page 42: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/42.jpg)
24.41
In the figure, suppose that the transmission axes of the left and right polarizing disks are perpendicular to each other.
Also, let the center disk be rotated on a the common axis with angular speed . Show that if unpolarized light is incident on the left disk with an intensity Imax, the intensity of the beam emerging from the right disk is
This means that the intensity of the emerging beam is modulated at a rate four times the rate of rotation of the center disk. Hint: Use the trig. identities
cos2=(1+ cos2)/2 and sin2=(1- cos2)/2
max
1(1 cos 4 )
16I I t
![Page 43: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/43.jpg)
Exercise 24.41
• c is so large that the polarizers appear frozen to a “bit” of light ... At time t the rotation angle will bet• the intensity is decreased by (cos )2
Polarization after the 1st polarizer
Polarization after the 2nd polarizer
Polarization after the 3rd polarizer
0 max
1
2I I 2
01 cos II
Imax
2
2 1
2
0
cos / 2
cos cos / 2
I I
I
![Page 44: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/44.jpg)
24.21
![Page 45: Chapter 25 Lecture 12 April 28, 2005. Electromagnetic waves are transverse ^ ^ y](https://reader031.vdocuments.mx/reader031/viewer/2022020716/5516f7fe550346fe558b4cfd/html5/thumbnails/45.jpg)
2
12
F=-kx x=Acos( t+ )
1
2spring
f fT
kSHO
m
gPendulum
L
PE kx Energy PE KE
total 0
0
2 2 2 20
2 20
sin( )
/
( / ) ( )
/tan
ma F kx bv F t
F mA
b m
b m
2
)2/(
2
)cos(
m
b
m
k
tAex tmb
/0
t mE E e where
b
( , ) sin( )
2
D x t A kx t
k vk
dampled SHO
driven and damped SHO
traveling waves
2 2
2 2 2
1d d
dt c dx
E E 8
0 0
13 10 m/sc
0
0
0 0
cos( )
cos( )
E kx t
B kx t
E cB
E x
B z
^
^2
av 0 0
1
2u E
0
1S E B
2
0 0
~ /EB E
Power areac
S2
0
02avg
EPowerI S
Area c
p=E/c
1 1 / 1 PowerP
F p E c I
A A t A t A c c
I=I0 cos2
LL S
S
v vf f
v v
positive is from L to Spositive v will use (+), negative v (-)
sin(a+a) + sin(a-a)=2 sin(a) cos(a)
string
Tv