physics 2112 topic 24 · 2020-05-04 · topic 24 polarization - linear ... in the questions, it...

Physics 2112

Topic 24

Polarization- linear

- circular

Electricity & Magnetism Lecture 24, Slide 1

What you thought……


• 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.

So far we have considered plane waves that look like this:

From now on just draw E and remember that B is still there:


Ex

By

Ex

“I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness)”

Linear Polarization


http://www.youtube.com/watch?v=Fu-aYnRkUgg

The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.

Polarizer


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


Q

Welcome to

Physics 2112

Hit “E” on your clicker


The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.

Polarizer


“I can't believe your teaching us the law of "Malus"(Malice). I thought malice was to be avoided?”


“Half Rule”

“Cosine2 Rule”

Polarization

Malus’s Law

Recall:

2EI

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


What is the intensity of the light after it passes through the second lens?

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


A. 0o

B. 10o

C. 80o

D. 90o

An unpolarized EM

wave is incident on two orthogonal polarizers.

CheckPoint 1: Two Polarizers


What percentage of the intensity gets through both polarizers?

A. 50%

B. 25%

C. 0%

What if a third

lens is place in

the middle at a 45o angle?

CheckPoint 1: Two Polarizers


Now reason X and Y components must be in phase.

I could change the phase of just one of them.

http://www.youtube.com/watch?v=Fu-aYnRkUgg

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


Light has different Speeds?

Speed of light is different in different materials (More about this later!)

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?


A B

CheckPoint 3(a)


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

Both Ex and Ey

are still there, sointensity is the same

QW Plate


Intensity:

22

0 yx EEcI +=

A B

CheckPoint 3(b)


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

A B

CheckPoint 3(b)



45o from the y-axis




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?




D. undefined

Ay

x

B

CheckPoint 3(c)



45o from the y-axis




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?




D. undefined

Ay

x

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


I0

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


E0

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

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


Before:

( )tkzE

Ex -= sin2

1

( )tkzE

Ey -= sin2

1

After:

( )tkzE

Ex -= cos2

1

( )tkzE

Ey -= cos2

1

E0

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

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.



Example 24.2

I0

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


I0


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

physics 2112 topic 24 · 2020-05-04 · topic 24 polarization - linear ... in the questions, it...

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