![Page 1: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/1.jpg)
Physics 2112
Topic 24
Polarization- linear
- circular
Electricity & Magnetism Lecture 24, Slide 1
![Page 2: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/2.jpg)
What you thought……
Electricity & Magnetism Lecture 24, Slide 2
• Here is a teaching tip for physics professors: When a student tries to
paraphrase something you have just taught, feed her or him the following
line: "I know you believe you understand what you think I said, but I am
not sure you realize that what you heard is not what I meant." This will
guarantee that the student will not interrupt your class again until the next
semester.
• What exactly are polarized sunglasses doing with the sun's light?
• checkpoints werent too bad but the prelecture was awful
• can you go over the right hand rule once more?
• lets do the wave in class like we're at a football game....uhh for science!
• Maybe it's because we havent gone over waves in class at all but I am
having a really hard time understanding them
• First of all, it's pretty refreshing to have a topic like this following some of
the ridiculous stuff we have been learning. Second, in "A Polarizer and a
Quarter-Wave Plate" the actual drawings say "Case 1" and "Case 2", but
in the questions, it refers to "Case A" and "Case B". It's a little
annoying...not that I'm nitpicking or anything.
• The circular polarization confused me a bit, but I feel that I will
understand after class.
![Page 3: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/3.jpg)
So far we have considered plane waves that look like this:
From now on just draw E and remember that B is still there:
Electricity & Magnetism Lecture 24, Slide 3
Ex
By
Ex
![Page 4: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/4.jpg)
“I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness)”
Linear Polarization
Electricity & Magnetism Lecture 24, Slide 4
![Page 6: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/6.jpg)
The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.
Polarizer
Electricity & Magnetism Lecture 24, Slide 8
![Page 7: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/7.jpg)
The molecular structure of a polarizer causes the component of
the E field perpendicular to the Transmission Axis to be absorbed.
Suppose we have a beam traveling in the + z direction.At t = 0 and z = 0, the electric field is aligned along the positive x axis and has a magnitude equal to Eo
z
y
Eo
What is the component of Eo along a direction in the x - y plane that makes an angle of q with respect to the x axis?
B) EocosqA) Eosinq C) 0 D) Eo/sinq E) Eo/cosq q
Eo
y
Question: Polarizer
Electricity & Magnetism Lecture 24, Slide 9
Q
![Page 8: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/8.jpg)
The molecular structure of a polarizer causes the component of
the E field perpendicular to the Transmission Axis to be absorbed.
Suppose we have a beam traveling in the + z direction.At t = 0 and z = 0, the electric field is aligned along the positive x axis and has a magnitude equal to Eo
z
y
Eo
What is the component of Eo along a direction in the x - y plane that makes an angle of q with respect to the x axis?
B) EocosqA) Eosinq C) 0 D) Eo/sinq E) Eo/cosq q
Eo
y
Question: Polarizer
Electricity & Magnetism Lecture 24, Slide 10
Q
![Page 9: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/9.jpg)
Welcome to
Physics 2112
Hit “E” on your clicker
Electricity & Magnetism Lecture 24, Slide 11
![Page 10: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/10.jpg)
The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.
Polarizer
Electricity & Magnetism Lecture 24, Slide 12
![Page 11: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/11.jpg)
“I can't believe your teaching us the law of "Malus"(Malice). I thought malice was to be avoided?”
Electricity & Magnetism Lecture 24, Slide 13
“Half Rule”
“Cosine2 Rule”
Polarization
Malus’s Law
Recall:
2EI
![Page 12: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/12.jpg)
Unpolarized light with an intensity of 1000W/m2 is incent on two polarizing lenses.
The transmission angle of the first lens is 90o to the x axis and the transmission angle of the second lens is 10o to the x axis.
Example 24.1: Two polarizers
Electricity & Magnetism Lecture 24, Slide 14
What is the intensity of the light after it passes through the second lens?
![Page 13: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/13.jpg)
The transmission angle of the first lens is 90o to the x axis and the transmission angle of the second lens is 10o to the x axis.
I1 is the intensity after the first lens and I2 is the intensity after the second lens. Malus’sLaw says: I2 = I1*cos2(Q). What is Q?
Example 24.1: Two polarizers
Electricity & Magnetism Lecture 24, Slide 15
A. 0o
B. 10o
C. 80o
D. 90o
![Page 14: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/14.jpg)
An unpolarized EM
wave is incident on two orthogonal polarizers.
CheckPoint 1: Two Polarizers
Electricity & Magnetism Lecture 24, Slide 17
What percentage of the intensity gets through both polarizers?
A. 50%
B. 25%
C. 0%
![Page 15: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/15.jpg)
What if a third
lens is place in
the middle at a 45o angle?
CheckPoint 1: Two Polarizers
Electricity & Magnetism Lecture 24, Slide 18
![Page 16: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/16.jpg)
Slide 21
Now reason X and Y components must be in phase.
I could change the phase of just one of them.
![Page 17: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/17.jpg)
Q: How can we use this to change the relative phase between Ex and Ey?
A: Birefringence
Pick right thickness to change the relative phase by exactly 90o.
quarter wave plateRight hand rule
Electricity & Magnetism Lecture 24, Slide 25
Light has different Speeds?
Speed of light is different in different materials (More about this later!)
![Page 18: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/18.jpg)
Right circularly polarizedDo right hand rule
Fingers along slow directionCross into fast direction
If thumb points in direction of propagation: RCP
“Curl fingers slow to fast”
Right or Left?
Electricity & Magnetism Lecture 24, Slide 26
![Page 19: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/19.jpg)
A B
CheckPoint 3(a)
Electricity & Magnetism Lecture 24, Slide 27
Identical linearly polarized light at
45o from the y-axis propagates
along the z-axis. In case 1 the
light is incident on a linear
polarizer with polarization along
the y-axis. In case 2 the light is
incident on a quarter wave-plate
with fast axis along the y-axis
1)Compare the intensities of the light waves after transmission.
A. I1 < I2B. I1 = I2C. I1 > I2
![Page 20: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/20.jpg)
A B
CheckPoint 3(a)
Electricity & Magnetism Lecture 24, Slide 28
Identical linearly polarized light at
45o from the y-axis propagates
along the z-axis. In case 1 the
light is incident on a linear
polarizer with polarization along
the y-axis. In case 2 the light is
incident on a quarter wave-plate
with fast axis along the y-axis
1)Compare the intensities of the light waves after transmission.
A. I1 < I2B. I1 = I2C. I1 > I2
![Page 21: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/21.jpg)
Both Ex and Ey
are still there, sointensity is the same
QW Plate
Electricity & Magnetism Lecture 24, Slide 29
Intensity:
22
0 yx EEcI +=
![Page 22: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/22.jpg)
A B
CheckPoint 3(b)
Electricity & Magnetism Lecture 24, Slide 30
Linearly polarized light at
45o from the y-axis
propagates along the z-
axis and is incident on a
quarter wave-plate with
fast axis along the y-axis
What is the polarization of the light wave in case 2 after it
passed through the quarter-wave plate?
A. linearly polarized
B. left circularly polarized
C. right circularly polarized
D. undefined
Ay
x
![Page 23: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/23.jpg)
A B
CheckPoint 3(b)
Electricity & Magnetism Lecture 24, Slide 31
Linearly polarized light at
45o from the y-axis
propagates along the z-
axis and is incident on a
quarter wave-plate with
fast axis along the y-axis
What is the polarization of the light wave in case 2 after it
passed through the quarter-wave plate?
A. linearly polarized
B. left circularly polarized
C. right circularly polarized
D. undefined
Ay
x
![Page 24: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/24.jpg)
B
CheckPoint 3(c)
Electricity & Magnetism Lecture 24, Slide 32
Linearly polarized light at
45o from the y-axis
propagates along the z-
axis and is incident on a
quarter wave-plate with
fast axis along the y-axis.
If the thickness of the quarter-wave plate in case B is
doubled, what is the polarization state of the light wave
after passing through the wave plate?
A. linearly polarized
B. left circularly polarized
C. right circularly polarized
D. undefined
Ay
x
![Page 25: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/25.jpg)
B
CheckPoint 3(c)
Electricity & Magnetism Lecture 24, Slide 33
Linearly polarized light at
45o from the y-axis
propagates along the z-
axis and is incident on a
quarter wave-plate with
fast axis along the y-axis.
If the thickness of the quarter-wave plate in case B is
doubled, what is the polarization state of the light wave
after passing through the wave plate?
A. linearly polarized
B. left circularly polarized
C. right circularly polarized
D. undefined
Ay
x
![Page 26: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/26.jpg)
Conceptual Analysis ➢ Linear Polarizers: absorbs E field component perpendicular to TA
➢ Quarter Wave Plates: Shifts phase of E field components in fast-slow directions
Strategic Analysis➢ Determine state of polarization and intensity reduction after each object➢ Multiply individual intensity reductions to get final reduction.
x
y
z
45ofast
I1
60o
I2
I3
Unpolarized light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
What is the intensity I3 in terms of I0?
Example 24.2
Electricity & Magnetism Lecture 24, Slide 35
I0
![Page 27: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/27.jpg)
How does the intensity of the light compare before and after the first polarizer?
A) I1 = I0 B) I1 = ½ I0 C) I1 = ¼ I0
Example 24.2(a)
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
x
y
z
45o fast
I1
60o
I2I3
E1
l / 4
Ex Ey
RCP
Electricity & Magnetism Lecture 24, Slide 36
E0
![Page 28: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/28.jpg)
How does the intensity of the light compare before and after the first polarizer?
A) I1 = I0 B) I1 = ½ I0 C) I1 = ¼ I0
Example 24.2(a)
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
x
y
z
45o fast
I1
60o
I2I3
E1
l / 4
Ex Ey
RCP
Electricity & Magnetism Lecture 24, Slide 37
E0
![Page 29: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/29.jpg)
How does the intensity of the light compare before and after the QWP?
A) I2 = I1 B) I2 = ½ I1 C) I2 = ¼ I1
Example 24.2(b)
x
y
z
45o fast
I1
60o
I2I3
E1
l / 4
Ex Ey
RCP E0
![Page 30: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/30.jpg)
No absorption: Just a phase change!
How does the intensity of the light compare before and after the QWP?
A) I2 = I1 B) I2 = ½ I1 C) I2 = ¼ I1
Same before & after!
Example 24.2(b)
x
y
z
45o fast
I1
60o
I2I3
E1
l / 4
Ex Ey
RCP
Electricity & Magnetism Lecture 24, Slide 39
Before:
( )tkzE
Ex -= sin2
1
( )tkzE
Ey -= sin2
1
After:
( )tkzE
Ex -= cos2
1
( )tkzE
Ey -= cos2
1
E0
![Page 31: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/31.jpg)
How does the intensity of the light compare before and after the second polarizor?
A) I3 = I2 B) I3 = ½ I2 C) I3 = I2cos2(15o) D) I3 = I2cos2(60o)
Example 24.2(c)
x
y
z
45o fast
I1
60o
I2I3
E1
l / 4
Ex Ey
RCP E0
![Page 32: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/32.jpg)
How does the intensity of the light compare before and after the second polarizor?
A) I3 = I2 B) I3 = ½ I2 C) I3 = I2cos2(15o) D) I3 = I2cos2(60o)
Example 24.2(c)
x
y
z
45o fast
I1
60o
I2I3
E1
l / 4
Ex Ey
RCP E0
![Page 33: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/33.jpg)
Conceptual Analysis ➢ Linear Polarizers: absorbs E field component perpendicular to TA
➢ Quarter Wave Plates: Shifts phase of E field components in fast-slow directions
Strategic Analysis➢ Determine state of polarization and intensity reduction after each object➢ Multiply individual intensity reductions to get final reduction.
x
y
z
45ofast
I1
60o
I2
I3
Unpolarized light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
What is the intensity I3 in terms of I0?
Electricity & Magnetism Lecture 24, Slide 42
Example 24.2
I0
![Page 34: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/34.jpg)
x
y
z
45o
I1
60o
I3
Unpolarized light is incident on two linear polarizers with no quarter wave plate as shown.
Example 24.3
Electricity & Magnetism Lecture 24, Slide 46
I0
What is the intensity I3 in terms of I0?
![Page 35: Physics 2112 Topic 24 · 2020-05-04 · Topic 24 Polarization - linear ... in the questions, it refers to "Case A" and "Case B". It's a little ... Hit “E” on your clicker Electricity](https://reader034.vdocument.in/reader034/viewer/2022042312/5edac47efa3b3a5ad21691c6/html5/thumbnails/35.jpg)
Circularly or Un-polarized LightPolarized Light
Polarizers & QW Plates:
Birefringence
0 cos( )2
=x
EE kx
0 sin( )2
y
EE kx=
RCP
Executive Summary:
Electricity & Magnetism
Lecture 24, Slide 48