5/6/2019

1

AP PHYSICS 2

UNIT 7

Quantum Physics,

atomic, and nuclear

physics

CHAPTER 24

Electromagnetic

Waves

MECHANICAL WAVES

MECHANICAL WAVES

MECHANICAL WAVES Polarization of waves

Polarization is a property of waves that describes

the orientation of the oscillations of the wave.

Transverse waves can

be polarized

Longitudinal waves

cannot be polarized

5/6/2019

2

Testing the polarization of light waves

Polarization shows that light phenomena can be better explained

by a transverse wave model

ELECTROMAGNETIC WAVES

A wave that DOES NOTrequire a medium through

which to travel.

Models that tried to explain how light

propagate through air

(outdated models)

1. Light is a mechanical vibration that travels

through an elastic medium. This medium is

completely transparent and has exactly zero

mass. This medium is called ether.

2. A light wave is some new type of vibration that

does not involve physical particles vibrating

around equilibrium positions due to restoring

forces being exerted on them.

Discovery of electromagnetic waves

In 1865, Maxwell suggested a new field

relationship: a changing electric field can

produce a magnetic field.

This magnetic field was first detected in 1929,

but was not measured precisely until 1985 due

to its extremely tiny magnitude.

5/6/2019

3

Maxwell's equations

1. Stationary electric charges produce a

constant electric field.

2. There are no magnetic charges (no

magnetic monopoles).

3. A magnetic field is produced either

by electric currents or by a changing

electric field.

4. A changing magnetic field produces

an electric field.

D = v

B = 0

x E =

x H = + J

Maxwell's equations

Maxwell's equations CONSEQUENCES OF MAXWELLS EQUATIONS

Producing an electromagnetic wave

A changing electric field can produce a changing

magnetic field, which in turn can produce a

changing electric field, and so on.

This feedback loop does not require the

presence of any electric charges or currents.

WHITEBOARD

μo = 4 x10-7 N/A2

εo = 8.85 x10-12 C2/Nm2

WHITEBOARD

Show magnitude of ?

Show unit analysis? =

1

𝜀0 ∙ 𝜇0 The constant εo is the vacuum permittivity:

The constant μo is the vacuum permeability.

CONSEQUENCES OF MAXWELLS EQUATIONS

Vacuum permittivity and the speed of light

𝑐 =1

𝜀0 ∙ 𝜇0

5/6/2019

4

Testing Maxwell’s Equations

Henry Hertz (1857 – 1894)

Switch connects a charged capacitor to a the

primary coil of a transformer (transmitter).

Capacitor discharges, potential difference across the

primary coil induces a huge potential difference

across the secondary coil.

Metal spheres charged and generated a spark

Testing Maxwell’s Equations

Henry Hertz (1857 – 1894)

The spark would indicate a large electric field

between the spheres of the transmitter.

The changing electric field produces an

electromagnetic wave.

When the wake reaches the receiver, it induces and

electric current causing a weak spark.

Henry Hertz: Testing the hypothesis that light

can be modeled as an electromagnetic wave

Hertz characterized the wave nature of

electromagnetic disturbances by performing

experiments similar to those used to determine the

wave nature of visible light. For example, he

observed reflection, refraction, and diffraction.

He also performed a double-slit experiment and

observed interference.

He observed polarization and measured their speed

to be the same as the speed of light (3×108 m/s).

Antennas are used to start electromagnetic

waves

An antenna is commonly

used to produce

electromagnetic waves.

A simple type of antenna

can be made from a pair

of electrical conductors,

one connected to each

terminal of a power supply

that is producing an

alternating emf.

The alternating emf leads

to the continuous charging

and discharging of the two

ends of the antenna

Antennas are used to start electromagnetic

waves

Antennas are used to start electromagnetic

waves

5/6/2019

5

Antennas are used to start electromagnetic

waves

Antennas are used to start electromagnetic

waves

Crossed, oscillating electric and magnetic fields

will propagate indefinitely and without loss of

energy at speed c through a vacuum.

Radar

Radar is a way of determining the distance to a

faraway object by reflecting radio wave pulses

off the object.

Global Positioning System

The GPS receiver detects signals from at least three

satellites to determine your position on the ground.

Using the known positions of the satellites, the GPS

unit is able to calculate your position by a process

called trilateration.

Microwave cooking

Water is a polar molecule and is a permanent

electric dipole.

Water, fat, and other substances in food

absorb energy from microwaves in a process

called dielectric heating.

Hearing FM radio waves

The high-frequency EM waves used by FM radio

stations are known as carrier waves.

FM stands for “Frequency Modulation“

AM stands for “Amplitude Modulation”

The information converted into the sounds we

hear is encoded as tiny variations in the

frequency/amplitude of the carrier wave.

A receiver decodes the variations and

converts them into an electric signal that a

speaker can then convert into sound.

5/6/2019

6

The electromagnetic spectrum

The range of frequencies and wavelengths of

electromagnetic waves is called the

electromagnetic spectrum.

• Radio Waves– AM Radio– Shortwave radio– FM Radio– Television– Radar

• Microwaves

• Infrared

• Visible light

• Ultraviolet

• X-rays

• Gamma rays

The Electromagnetic Spectrum!

All of these frequencies of light travel at speed c in a vacuum (3 x 108 m/s).

A mnemonic to help you remember the spectrum!

(in order of increasing frequency)

Rattlesnakes May Inject Venom Upon eXtreme aGitation

Radio Microwave Infrared Visible Ultraviolet X-ray Gamma

Human eyes are only able to detect light of

wavelength 480-720 nm.

That is why this is called the visible range of the spectrum.

The wavelength that we perceive as red is about 480 nm.

The wavelength that we perceive as violet is about 720 nm.

Different animals are able to detect

different ranges of EM waves!

The image on the right shows the

ultraviolet light given off by a dandelion.

Bees and other insects have eyes that are

capable of detecting UV light!

The electromagnetic spectrum

5/6/2019

7

Why are we able to detect 480 – 720 nm

electromagnetic waves with our eyes?

That is the peak range of wavelengths

emitted by our Sun!!!

Mathematical description of EM waves and

EM wave energy

Maxwell's equations

predict that the

amplitudes of the

changing electric

and magnetic field

vectors are related:

Mathematical description of EM waves

The wave equation tells us:

Producing unpolarized light

Light emitted by a lightbulb

consists of many waves that

originate at random times with

random polarizations.

If we could observe the

many separate EM waves

as a beam of unpolarized

light moving directly toward

our eyes, the oscillations of

both the electric and

magnetic fields would look

something like a porcupine

Light polarizers

A polarizer absorbs one component of the E field

of the EM wave passing through it, allowing the

perpendicular component to pass.

How polarized glasses work

The lenses of polarized glasses are coated with

a polarizing film that only transmits light whose

electric field oscillates in the vertical direction.

5/6/2019

8

Brewster's law

Light is traveling from medium 1

when reflects off medium 2.

The reflected light is totally

polarized an axis in the plane

parallel to the surface when the

tangent of the incident polarizing

angle P equals the ratio of the

indexes of refraction of the two

media

𝑡𝑎𝑛𝜃𝑃 =𝑛2𝑛1

Example 24.4

You are facing the Sun and looking at the light

reflected off the ocean. At which angle above the

horizon should the Sun be so that you get the

most benefit from your polarizing sunglasses?

= 36.94

Polarization by scattering

If you look through polarized sunglasses at the

clear sky in an arbitrary direction and rotate the

glasses, the intensity of the light passing through

the glasses changes.

Polarization by scattering

Polarization by scattering

© 2014 Pearson Education, Inc.

5/6/2019

9

Polarization by reflection

Consider light produced by the LCD screen of a

calculator, cell phone, or laptop computer, or

reflected off a body of water.

If you look at this light through a polarizer, the

intensity of reflected light varies depending on

the orientation of the polarizer relative to the

surfaces.

This indicates that the light is partially

polarized.

Polarized LCDs

Nearly all computer, TV, calculator, and cell phone

screens are LCDs—liquid crystal displays.

Polarized LCDs

1. Unpolarized light shines on the back.

2. A horizontal polarizing filter in front of the light blocks out all

light waves except those vibrating horizontally.

3. Only light waves vibrating horizontally can get through.

4. A transistor switches on/off this pixel by switching on/off the

electric current flowing through its liquid crystal. That makes

the crystal twist. The twisted crystal rotates (or not) light

waves by 90° as they travel through it.

5. Light waves that entered the liquid crystal vibrating

horizontally emerge from it vibrating horizontally/vertically

6. The vertical polarizing filter in front of the liquid crystal

blocks out all light waves except those vibrating vertically.

The vertically vibrating light that emerged from the liquid

crystal can now get through the vertical filter.

7. The pixel is lit up. A red, blue, or green filter gives the pixel

its color

3D movies

The 3D projector produces two distinct images

on the screen.

Each image consists of polarized light.

The two images have their polarizing axes

rotated by 90° relative to each other.

3D movies

The film is recorded using two camera lenses sat side by side.

But in the cinema, the two reels of film are projected through

different polarized filters. So images destined for viewers' left

eyes are polarized on a horizontal plane, whereas images

destined for their right eyes are polarized on a vertical plane.

Cinema goers’ glasses use the same polarizing filters to

separate out the two images again, giving each eye sees a

slightly different perspective and fooling the brain into 'seeing'

Avatar's planet Pandora as though they were actually there.

“Light is a wave” or “light behaves like a wave”?

Saying that “light is a wave”, claims to know the

absolute nature of light, which is not possible.

Saying that “light behaves like a wave”, claims

to know how to describe light, which is

possible.

The second statement is more accurate because

it reflects the capacity of science to continually

fine tune itself.

5/6/2019

10

Light behaves like a wave:

The Wave Model of Light

Light is a transverse electromagnetic wave!

It is composed of perpendicular electric and

magnetic fields that propagate one another.

Light waves can constructively and destructively

interfere with one another.

Light waves obey c = 𝝀𝒇 Light waves propagate according to Huygens’

Principle.

Frequency and wavelength of

electromagnetic waves

All electromagnetic waves travel at the speed of

light c in a vacuum.

In media other than a vacuum, the speed of

electromagnetic waves is 𝒗 =𝒄

𝒏.

The speed, frequency, and wavelength are

related by 𝝀 =𝒗

𝒇:

Frequency of a wave does not change upon entering a new medium!

The frequency of an EM wave governs how much energy it carries.

Frequency is a property of the wave, and is set once the wave is produced.

Wave speed and wavelength will change inversely upon entering a new medium!

Wave properties

Reflection involves a change in direction of

waves when they bounce off a barrier.

Refraction of waves involves a change in the

direction of waves as they pass from one

medium to another.

Diffraction involves a change in direction of

waves as they pass through an opening or

around a barrier in their path

Models of Light

Particle Model

• Reflection

• Shadows and semi-shadows

• Light travels in a straight line

Wave Model

• Reflection

• Refraction

• Shadows and semi-shadows

• Light travels in a straight line

• Interference (Double slit -

small openings)

• Diffraction (Single slit - small

openings)

• Polarization

• Doppler Effect

What happens to the speed and the wavelength of light as it crosses the boundary in going from air into water?

Speed Wavelength

(A) Increases Remains the same(B) Remains the same Decreases (C) Remains the same Remains the same(D) Decreases Increases(E) Decreases Decreases

Conceptual Whiteboard

(E)