Concept Summary

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Topic | Discussion | Learning Aids
Electromagnetic wave Speed of light | 24.1 THE NATURE OF ELECTROMAGNETIC WAVES An electromagnetic wave consists of mutually perpendicular and oscillating electric and magnetic fields. The wave is a transverse wave, since the fields are perpendicular to the direction in which the wave travels. Electromagnetic waves can travel through a vacuum or a material substance. All electromagnetic waves travel through a vacuum at the same speed, which is known as the speed of light . |
| 24.2 THE ELECTROMAGNETIC SPECTRUM The frequency f and wavelength of an electromagnetic wave in a vacuum are related to its speed c through the relation |
Relation between frequency, wavelength, and speed of light in a vacuum |

Electromagnetic spectrum Visible light | The series of electromagnetic waves, arranged in order of their frquencies or wavelengths, is called the electromagnetic spectrum. In increasing order of frequency (decreasing order of wavelength), the spectrum includes radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Visible light has frequencies between about and . The human eye and brain perceive different frequencies or wavelengths as different colors. |
| 24.3 THE SPEED OF LIGHT James Clerk Maxwell showed that the speed of light in a vacuum is |
Speed of light |

| (24.1)

where is the (electric) permittivity of free space and is the (magnetic) permeability of free space.
| 24.4 THE ENERGY CARRIED BY ELECTROMAGNETIC WAVES The total energy density u of an electromagnetic wave is the total energy per unit volume of the wave and, in a vacuum, is given by |
Total energy density |

| (24.2a)

| where E and B, respectively, are the magnitudes of the electric and magnetic fields of the wave. Since the electric and magnetic parts of the total energy density are equal, the following two equations are equivalent to Equation 24.2a: |

| (24.2b)

| (24.2c)

| In a vacuum, E and B are related according to |
Relation between electric and magnetic fields |

| (24.3)

| Equations 24.2a–c can be used to determine the average total energy density, if the rms average values and are used in place of the symbols E and B. The rms values are related to the peak values and in the usual way: |
Root mean square fields |

Intensity | The intensity of an electromagnetic wave is the power that the wave carries perpendicularly through a surface divided by the area of the surface. In a vacuum, the intensity S is related to the total energy density u according to |
Relation between intensity and total energy density |

| (24.4)

| 24.5 THE DOPPLER EFFECT AND ELECTROMAGNETIC WAVES When electromagnetic waves and the source and observer of the waves all travel along the same line in a vacuum, the Doppler effect is given by |
Doppler effect |

| (24.6)

| where and are, respectively, the observed and emitted wave frequencies and is the relative speed of the source and the observer. The plus sign is used when the source and the observer come together, and the minus sign is used when they move apart. |
Linear polarized electromagnetic wave Unpolarized electromagnetic wave | 24.6 POLARIZATION A linearly polarized electromagnetic wave is one in which the oscillation of the electric field occurs only along one direction, which is taken to be the direction of polarization. The magnetic field also oscillates along only one direction, which is perpendicular to the electric field direction. In an unpolarized wave such as the light from an incandescent bulb, the direction of polarization does not remain fixed, but fluctuates randomly in time. |
Transmission axis | Polarizing materials allow only the component of the wave’s electric field along one direction (and the associated magnetic field component) to pass through them. The preferred transmission direction for the electric field is called the transmission axis of the material. |
| When unpolarized light is incident on a piece of polarizing material, the transmitted polarized light has an intensity that is one-half that of the incident light. |
Polarizer and analyzer | When two pieces of polarizing material are used one after the other, the first is called the polarizer, and the second is referred to as the analyzer. If the average intensity of polarized light falling on the analyzer is , the average intensity of the light leaving the analyzer is given by Malus’ law as |
Malus’ law |

| (24.7)

Crossed polarizer and analyzer | where is the angle between the transmission axes of the polarizer and analyzer. When , the polarizer and the analyzer are said to be “crossed,” and no light passes through the analyzer. |

Use Self-Assessment Test 24.1 to evaluate your understanding of Sections 24.1, 24.2, 24.3, 24.4, 24.5 and 24.6 .

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