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Lecture 13 Electromagnetic Waves Ch. 33

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Lecture 13 Electromagnetic Waves Ch. 33. Cartoon Opening Demo Topics Electromagnetic waves Traveling E/M wave - Induced electric and induced magnetic amplitudes Plane waves and spherical waves Energy transport snd Intensity of a wave Poynting vector Radiation Pressure produced by E/M wave

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slide1

Lecture 13 Electromagnetic Waves Ch. 33

  • Cartoon
  • Opening Demo
  • Topics
    • Electromagnetic waves
    • Traveling E/M wave - Induced electric and induced magnetic amplitudes
    • Plane waves and spherical waves
    • Energy transport snd Intensity of a wave Poynting vector
    • Radiation Pressure produced by E/M wave
    • Polarization
    • Reflection, refraction,Snell’s Law, Internal reflection
    • Prisms and chromatic dispersion
    • Polarization by reflection-Brewsters angle
    • Elmo
    • Polling
slide6

To investigate further the properties of

electromagnetic waves we consider

the simplest situation of a plane wave.

A single wire with variable current

generates propagating electric and

magnetic fields with cylindrical symmetry

around the wire.

If we now stack several wires parallel

to each other, and make this stack

wide enough (and the wires very close

together), we will have a (plane) wave

propagating in the z direction, with

E-field oriented along x, E = Ex

(the current direction) and B-field

along y B=By(Transverse waves)

electromagnetic wave self generation
Faraday’s Law of Induction

Maxwell’s Law of Induction

Changing electric field induces a magnetic field

Changing magnetic field induces a electric field

Electromagnetic Wave Self Generation
slide12

Magnitude of S is like the intensity

U is the energy

carried by a wave

slide15

Relation of intensity and power for a Spherical Wave - Variation of Intensity with distance

A point source of light generates a spherical wave. Light is emitted isotropically and the intensity of it falls off as 1/r2

Let P be the power of the source

in joules per sec. Then the intensity

of light at a distance r is

Lets look at an example

slide16

(c) The power of the source is

15. The maximum electric field at a distance of 10 m from an isotropic point light source is 2.0 V/m. Calculate

(a) the maximum value of the magnetic field and

(b) the average intensity of the light there?

(c) What is the power of the source?

(a) The magnetic field amplitude of the wave is

(b) The average intensity is

nothing is known to travel faster than light in a vacuum
Nothing is known to travel faster than light in a vacuum

However, electrons can travel faster than light in water.

And when the do the electrons emit light called

Cerenkov radiation

momentum and radiation pressure
Momentum and Radiation Pressure

Momentum = p

What is the change in momentum of the paper over some time interval?

Light beam

c

paper

p=U/c

p=0

1) Black paper absorbs all the light

2) Suppose light is 100% reflected

From this we define the pressure

radiation pressure p r
Radiation Pressure Pr

Want to relate the pressure Pr felt by the paper to the

intensity of light

For 100% absorption of light on the paper

For 100% reflection of light

polarization of light
Polarization of Light
  • All we mean by polarization is which direction is the electric vector vibrating.
  • If there is no preferred direction the wave is unpolarized
  • If the preferred direction is vertical, then we say the wave is vertically polarized
slide25

A polarizing sheet or polaroid filter is special

material made up of rows of

molecules that only allow light

to pass when the electric

vector is in one direction.

Pass though a polarizing sheet

aligned to pass only the y-component

slide26

Unpolarized light

Resolved into its y and z-components

The sum of the y-components and

z components are equal

slide27

Intensity I0

Pass though a

polarizing sheet

aligned to pass

only the y-component

Malus’s Law

One Half Rule

Half the intensity out

slide28

Malus’s Law

Light comes

from here

Intensity is proportional to

square of amplitude

y

slide29

Sunglasses are polarized vertically. Light reflected from sky is partially polarized and light reflected from car hoods is polarized in the plane of the hood

Sunglass 1

Sunglass 2

Rotate sun glass 2 90 deg and no light gets through

because cos 90 = 0

polaroid material
Polaroid Material

Transmits

Light

Yes

Light

No

slide31

Chapter 33 Problem 33

In the figure, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles of 1 = 40o, 2 = 20o, and 3 = 40o with the direction of the y axis. What percentage of the light’s initial intensity is transmitted by the system? (Hint: Be careful with the angles.)

The polarizing direction of the third sheet is 3= 40o counterclockwise from the y axis. Consequently, the angle between the direction of polarization of the light incident on that sheet and the polarizing direction of the sheet is 20o + 40o = 60o. The transmitted intensity is

slide32

Chapter 33 Properties of Light Continued

  • Law of Reflection
  • Law of Refraction or Snell’s Law
  • Chromatic Dispersion
  • Brewsters Angle
slide33

Lab06

Lab07

Lab06

Lab08

slide35

Dispersion: Different wavelengths have different velocities and therefore different indices of refraction. This leads to differentrefractive angles for different wavelengths. Thus the light is dispersed.The frequency does not change when n changes.

snells law

n2=1.33

Snells Law

Red

θ1

n1=1.00

θ2

chapter 33 problem 49
Chapter 33 Problem 49

In Figure 33-51, a 2.00 m long vertical pole extends from the bottom of a swimming pool to a point 90.0 cm above the water. Sunlight is incident at angle θ = 55.0°. What is the length of the shadow of the pole on the level bottom of the pool?

slide38

1

l1

air

water

2

l2

shadow

L

x

Chapter 33

47. In the figure, a 2.00-m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. What is the length of the shadow of the pole on the level bottom of the pool?

slide39

1

l1

air

water

2

l2

shadow

L

x

Consider a ray that grazes the top of the pole, as shown in the diagram below. Here 1 = 35o, l1 = 0.50 m, and l2 = 1.50 m.

The length of the shadow is x + L.

x is given by

x = l1tan1 = (0.50m)tan35o = 0.35 m.

L is given by

L=l2tan 

Use Snells Law to find 

slide40

1

l1

air

water

L is given by

2

l2

shadow

L

x

Calculation of L

According to the law of refraction, n2sin2 = n1sin1. We take n1 = 1 and n2 = 1.33

The length of the shadow is L+x.

L+x = 0.35m + 0.72 m = 1.07 m.

slide45

Equilateral prism

dispersing sunlight

late afternoon.

Sin θrefr= 0.7nλ

slide46

How much light is polarized when reflected from a surface?

Polarization by Reflection: Brewsters Law

slide47

What causes a Mirage

eye

sky

1.09

1.09

1.08

1.08

1.07

1.07

Index of refraction

1.06

Hot road causes gradient in the index of refraction that increases

as you increase the distance from the road