Chapter 23Chapter 23

Electromagnetic Waves

Formed from an electric field and magnetic field orthonormal to each other, propagating at the speed of light (in a vacuum).

• The fundamental sources of all electromagnetic radiation are electric charges in accelerated motion.

• All objects emit electromagnetic radiation as a result of thermal motion of their molecules; this radiation, called thermal radiation, is a mixture of different wavelengths.

24.1 The Nature of Electromagnetic Waves

The speed of an electromagnetic wave in a vacuum is:

sm1000.3 8c

1. The wave is transverse: Both and are perpendicular to the direction of propagation of the wave and to each other.

2. There is a definite ratio between magnitudes of and : E= cB.

3. The wave travels in vacuum with a definite and unchanging speed c (c = 3.00 x 108 m/s).

4. Unlike mechanical waves, which need the oscillating particles of a medium such as water or air to be transmitted, electromagnetic waves require no medium. What’s “waving” in an electromagnetic wave are the electric and magnetic fields.

E

B

Characteristics of electromagnetic waves in vacuum

E

B

The electromagnetic Spectrum

All these electromagnetic waves have the general characteristics, including the common propagation speed c = 3.00 x 108 m/s (in vacuum). All are the same in principle; they differ in frequency f and wavelength , but the relation holds for all.fc

• A special light source that has attained prominence in the last 50 years is the laser, which can produce a very narrow beam of enormously intense radiation.

• A significant characteristic of laser light is that it is much more nearly monochromatic, or single frequency, than light from any other source.

The Energy Carried by Electromagnetic Waves

Electromagnetic waves, like water waves or sound waves, carry energy.

The energy is carried by the electric and magnetic fields that comprise the wave.

The total energy density u of an electromagnetic Wave:

22

2

1

2

1

Volume

energy TotalBEu

o

o

Electric energy density

Magnetic energy density

In an electromagnetic wave propagating through a vacuum or air, the electric field and the magnetic field carry equal amounts of energy per unit volume of space.

It is possible to rewrite the equation for total energy density, , in two additional, but equivalent, forms:

22

2

1

2

1BE

o

o

2

2

1Bu

Eu

o

o

22

2

1

2

1BEu

o

o

The fact that the two energy densities are equal implies that the electric and magnetic fields are related. To see how, we set the electric energy density equal to the magnetic energy density and obtain

In 1865, Maxwell determined theoretically that electromagnetic waves propagate through a vacuum at a speed given by

Hence, from equation (1) it follows that

22

2

1

2

1BE

o

o

11

or 22 BEoo

.1

oo

c

222 BcE

cBEor

As an electromagnetic wave moves through space, it carries energy from one region to another. This energy transport is characterized by the intensity of the wave. For an electromagnetic wave, the intensity is the electromagnetic power divided by the area of the surface

A

PS

At

energy Total

24.4 The Energy Carried by Electromagnetic Waves

cutA

uctA

AtA

PS

energy Total

Thus, the intensity and the energy density are related by the speed of light, c.

2

0

2

0

2

0

2

0 22

1

Bc

S

EcS

Bc

EccuS

Intensity of an electromagnetic wave depends on the electric and magnetic fields according to the following equivalent relations:

• Polarization occurs with all transverse waves (e.g., wave on a string).• When a wave has only y displacements, we say that it is linearly polarized in the y direction ; similarly, a wave with only z displacements is linearly polarized in the z direction.• For mechanical waves, we can build a polarizing filter that permits only waves with a certain polarization direction to pass.• In figure c, the string can slide vertically in the slot without friction, but no horizontal motion is possible.

Polarization

An electromagnetic wave is a transverse wave: The fluctuating electric and magnetic fields are perpendicular to the direction of propagation and to each other. We always define the direction of polarization of an electromagnetic wave to be the direction of the electric-field vector, not the magnetic-field vector, because most common electromagnetic-wave detectors (including the human eye) respond to the electric forces on electrons in materials, not the magnetic forces.

24.6 Polarization

Linearly polarized waveon a rope.

POLARIZED ELECTROMAGNETIC WAVES

24.6 Polarization

In polarized light, the electric fieldfluctuates along a single direction.

24.6 Polarization

Polarized light may be produced from unpolarized light withthe aid of polarizing material.

24.6 Polarization

MALUS’ LAW

2cosoSS

intensity beforeanalyzer

intensity afteranalyzer

24.6 Polarization

Example 7 Using Polarizers and Analyzers

What value of θ should be used so the average intensity of the polarizedlight reaching the photocell is one-tenth the average intensity of theunpolarized light?

24.6 Polarization

221

101 cosoo SS

251 cos

51cos

4.63

24.6 Polarization

Conceptual Example 8 How Can a Crossed Polarizer andAnalyzer Transmit Light?

Suppose that a third piece of polarizing material is inserted between the polarizer and analyzer. Does light now reach thephotocell?