Physics
Electromagnetic Waves in a Vacuum
Electromagnetic waves in a vacuum are transverse waves that consist of oscillating electric and magnetic fields. They do not require a medium to propagate and travel at the speed of light. These waves have a wide range of frequencies, from radio waves to gamma rays, and play a fundamental role in various phenomena, including light, radiation, and wireless communication.
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12 Key excerpts on "Electromagnetic Waves in a Vacuum"
eBook - PDFOptics
Principles and Applications
- Kailash K. Sharma(Author)
- 2006(Publication Date)
- Academic Press(Publisher)
Aether has no place in the special theory of relativity developed by Albert Einstein. 8 Chapter 1: LIGHT WAVES Electromagnetic waves including the light waves can propagate in absolutely empty space. They do not require matter to facilitate propagation. The chang-ing electric and magnetic fields associated with an electromagnetic wave are capable of sustaining each other. A comparison of the wave equation with its counterpart for mechanical waves suggests that the product must represent the inverse of the square of the speed of propagation of electromagnetic waves. A medium is not necessary for the propagation of electromagnetic waves. How-ever, the velocity of propagation of electromagnetic waves in a given medium is determined by its permeability and permittivity. The vacuum with permeabil-ity 0 = 4 × 10 − 7 N s 2 C − 2 and permittivity 0 = 8 85 × 10 − 12 C 2 N − 1 m − 2 has velocity c = 2 99 × 10 8 m s − 1 for the propagation of electromagnetic waves. This value agrees very closely with the velocity of light measured in the laboratory. This brings light within the domain of applicability of Maxwell’s equations. The wave equation (1.11) is a linear, homogeneous, second-order differential equation. The linearity of the wave equation leads to the superposition principle which states that if E j ( j = 1 2 3 n ) are solutions of the wave equation, then ∑ j a j E j is also a solution of the wave equation, where a j are arbitrary constants (real or complex). The wave equation admits a variety of solutions – some extremely simple in form, others sufficiently intricate. The implication of this statement needs to be appreciated. All light fields in a homogeneous medium must be solutions of the wave equation. However, external conditions must be accurately controlled to generate light fields to correspond to a particular solution of the wave equation. Some solutions may be mathematically easy to handle, but difficult to realize in practice.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Figure 24.3 shows the electromagnetic wave of the radiation field far from the antenna. The picture shows only the part of the wave traveling along the 1x axis. The parts traveling in the other directions have been omitted for clarity. It should be clear from the drawing that an electromagnetic wave is a transverse wave because the electric and magnetic fields are both perpendicular to the direction in which the wave travels. Moreover, an electromagnetic wave, unlike a wave on a string or a sound wave, does not require a medium in which to propagate. Electromagnetic waves can travel through a vacuum or a material substance, since electric and magnetic fields can exist in either one. Electromagnetic waves can be produced in situations that do not involve a wire antenna. In general, any electric charge that is accelerating emits an electromagnetic wave, whether the charge is inside a wire or not. In an alternating current, an electron oscillates in simple harmonic motion along the length of the wire and is one example of an accelerating charge. B I P I Figure 24.2 The oscillating current I in the antenna wires creates a magnetic field B B at point P that is tangent to a circle centered on the wires. The field is directed as shown when the current is upward and is directed in the opposite direction when the current is downward. y z x B E Direction of wave travel Figure 24.3 This picture shows the wave of the radiation field far from the antenna. Observe that E B and B B are perpendicular to each other, and both are perpendicular to the direction of travel. 24.1 | The Nature of Electromagnetic Waves 675 All electromagnetic waves move through a vacuum at the same speed, and the sym- bol c is used to denote its value. This speed is called the speed of light in a vacuum and is c 5 3.00 3 10 8 m/s.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Figure 24.3 shows the electromagnetic wave of the radiation field far from the antenna. The picture shows only the part of the wave traveling along the 1x axis. The parts traveling in the other directions have been omitted for clarity. It should be clear from the drawing that an electromagnetic wave is a transverse wave because the electric and magnetic fields are both perpendicular to the direction in which the wave travels. Moreover, an electromagnetic wave, unlike a wave on a string or a sound wave, does not require a medium in which to propagate. Electromagnetic waves can travel through a vacuum or a material substance, since electric and magnetic fields can exist in either one. Electromagnetic waves can be produced in situations that do not involve a wire antenna. In general, any electric charge that is accelerating emits an electromagnetic wave, whether the charge is inside a wire or not. In an alternating current, an electron oscillates in simple harmonic motion along the length of the wire and is one example of an accelerating charge. B I P I Figure 24.2 The oscillating current I in the antenna wires creates a magnetic field B B at point P that is tangent to a circle centered on the wires. The field is directed as shown when the current is upward and is directed in the opposite direction when the current is downward. y z x B E Direction of wave travel Figure 24.3 This picture shows the wave of the radiation field far from the antenna. Observe that E B and B B are perpendicular to each other, and both are perpendicular to the direction of travel. 24.1 | The Nature of Electromagnetic Waves 605 All electromagnetic waves move through a vacuum at the same speed, and the sym- bol c is used to denote its value. This speed is called the speed of light in a vacuum and is c 5 3.00 3 10 8 m/s.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 5 Electromagnetic Radiation Electromagnetic radiation (often abbreviated E-M radiation or EMR ) is a pheno-menon that takes the form of self-propagating waves in a vacuum or in matter. It comprises electric and magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according to the frequency of its wave; these types include (in order of increasing frequency and decreasing wavelength): radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. A small and somewhat variable window of frequencies is sensed by the eyes of various organisms; this is what is called the visible spectrum. The photon is the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation and is also the force carrier for the electromagnetic force. EM radiation carries energy and momentum that may be imparted to matter with which it interacts. ________________________ WORLD TECHNOLOGIES ________________________ Physics Theory Shows three electromagnetic modes (blue, green and red) with a distance scale in micrometres along the x-axis. Electromagnetic waves were first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. According to Maxwell's equations, a spatially-varying electric field generates a time-varying magnetic field and vice versa .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as retarded time (as opposed to advanced time, which is unphysical in light of causality), which adds to the expressions for the electrodynamic electric field and magnetic field. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. At the quantum level, electromagnetic radiation is produced when the wavepacket of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in oscillation, which is responsible for the phenomenon of radiative transition between quantum states of a charged particle. Depending on the circumstances, electromagnetic radiation may behave as a wave or as particles. As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν , where E is the energy of the photon, h = 6.626 × 10 −34 J·s is Planck's constant, and ν is the frequency of the wave. One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer , regardless of the observer's velocity. (This observation led to Albert Einstein's development of the theory of special relativity.) In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
These relations are illustrated by the following equations: where: • c = 299,792,458 m/s is the speed of light in vacuum and • h = 6.62606896(33)×10 −34 J s = 4.13566733(10)×10 −15 eV s is Planck's constant. Whenever electromagnetic waves exist in a medium with matter, their wavelength is decreased. Wavelengths of electromagnetic radiation, no matter what medium they are traveling through, are usually quoted in terms of the vacuum wavelength , although this is not always explicitly stated. Generally, EM radiation is classified by wavelength into radio wave, microwave, infrared, the visible region we perceive as light, ultraviolet, X-rays and gamma rays. The behavior of EM radiation depends on its wavelength. When EM radiation interacts with single atoms and molecules, its behavior also depends on the amount of energy per quantum (photon) it carries. Spectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. Detailed information about the physical properties of objects, gases, or even stars can be obtained from this type of device. Spectroscopes are widely used in astrophysics. For example, many hydrogen atoms emit a radio wave photon which has a wavelength of 21.12 cm. Also, frequencies of 30 Hz and below can be produced by and are important in the study of certain stellar nebulae and frequencies as high as 2.9×10 27 Hz have been detected from astrophysical sources. Rationale Electromagnetic radiation interacts with matter in different ways in different parts of the spectrum. The types of interaction can be so different that it seems to be justified to refer to different types of radiation. At the same time, there is a continuum containing all these ________________________ WORLD TECHNOLOGIES ________________________ different kinds of electromagnetic radiation.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 5 Electromagnetic Radiation Electromagnetic radiation (often abbreviated E-M radiation or EMR ) is a phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It comprises electric and magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according to the frequency of its wave; these types include (in order of increasing frequency and decreasing wavelength): radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. A small and somewhat variable window of frequencies is sensed by the eyes of various organisms; this is what is called the visible spectrum. The photon is the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation and is also the force carrier for the electromagnetic force. EM radiation carries energy and momentum that may be imparted to matter with which it interacts. ________________________ WORLD TECHNOLOGIES ________________________ Physics Theory Shows three electromagnetic modes (blue, green and red) with a distance scale in micrometres along the x-axis. Electromagnetic waves were first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. According to Maxwell's equations, a spatially-varying electric field generates a time-varying magnetic field and vice versa .
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
24.2 Calculate speed, frequency, and wavelength for electromagnetic waves. The frequency f and wavelength of an electromagnetic wave in a vacuum are related to its speed c through the relation c = f. The series of electromagnetic waves, arranged in order of their frequencies 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 4.0 × 10 14 and 7.9 × 10 14 Hz. The human eye and brain perceive different frequencies or wavelengths as different colours. 24.3 Relate the speed of light to electromagnetic quantities. James Clerk Maxwell showed that the speed of light in a vacuum is given by equation 24.1, where 0 is the (electric) permittivity of free space and 0 is the (magnetic) permeability of free space. c = 1 √ 0 0 (24.1) 24.4 Calculate energy, power, and intensity for 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 equation 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, equations 24.2b and 24.2c are equivalent to equation 24.2a. In a vacuum, E and B are related according to equation 24.3. u = 1 2 0 E 2 + 1 2 0 B 2 (24.2a) u = 0 E 2 (24.2b) u = 1 0 B 2 (24.2c) E = cB (24.3) Equations 24.2a–24.2c can be used to determine the average total energy density, if the rms average values E rms and B rms are used in place of the symbols E and B. The rms values are related to the peak values E 0 and B 0 in the usual way, as shown in equations 1 and 2. The intensity of an electromagnetic wave is the power that the wave carries perpendicularly through a surface divided by the area of the surface.
eBook - PDF- Jean-pierre Fillard(Author)
- 1996(Publication Date)
- World Scientific(Publisher)
7 CHAPTER 1 ELECTROMAGNETIC WAVES To begin dealing with Near Field (NF) optics and related applications in Nanoscopy it is worth gathering together some basic knowledge about light wave propagation in a vacuum and in the materials in the first part of this chapter. A second part is be devoted to the interaction of light with interfaces which introduces the fundamental base for the study of evanescent waves. The third and fourth parts deal with diffraction in the Far Field (FF) and in the NF. Of course most of this material has already been largely developed in all the classical treatises on Optics or Electromagnetics 9 * 10 > ll and naturally in the still dazzling volumes of the Feynman lectures 12 . 1.1 Theory of light in vacuum and matter The electrical action obviously originates in the presence of electric charges which induce a local perturbation in space by creating a force field. When the distance between the charges and the observation point is large enough a delay of propagation must be taken into account for the field to be established if any change is introduced in the charge arrangement. This propagating field change is to be observed in any case where an electric charge is accelerated and the propagation speed is known to be equal to the speed of the light wave packets (celerity c) carrying the quantum energy hv of the photon. 8 Near Field Optics and Nanoscopy 1.1.1 Maxwell-Helmholtz propagation From the initial tutorial experiments with electric charges which have evidenced the electrostatic and electromagnetic force fields it has appeared that these are regulated through rather simple laws which have been attributed to Maxwell: £o V A £ = -— VAB = 1(J+Z 0 I 0 — (1.1.1) where E and B are respectively the e.s. and e.m. fields, p is the local charge density and £o, MO two dimensional constants referring to the vacuum.
eBook - PDF- Charles A. Bennett(Author)
- 2015(Publication Date)
- Wiley(Publisher)
CHAPTER 2 ELECTROMAGNETIC WAVES AND PHOTONS When I am judging a theory, I ask myself whether, if I were God, I would have arranged the world in such a way. —Einstein Now, let’s look at the first basic action — a photon goes from [A to B]. I will draw this action as a wiggly line from A to B for no good reason. —Feynman Contents 2.1 Introduction 25 2.2 Electromagnetism 26 2.3 Electromagnetic Wave Equations 32 2.4 Photons 42 2.5 The Electromagnetic Spectrum 48 Appendix: Maxwell’s Equations in Differential Form 53 2.1 INTRODUCTION In this chapter, we attempt to answer the question: "What is light?" Interestingly, there seems to be more than one answer. The bedrock of our description will be the theory of 25 26 ELECTROMAGNETIC WAVES AND PHOTONS electromagnetism, as summarized by Maxwell’s equations. From this perspective, light is most certainly a wave — a transverse electromagnetic wave — with properties that we will obtain from Maxwell’s equations. We will use the "wave picture" of electromagnetic radiation extensively in subsequent chapters to develop many optical concepts and appli- cations. Examples include effects due to interference and diffraction, coherence, optical imaging and resolution, and many of the concepts relating to laser design. However, it will often be necessary to utilize the concept of a light particle, or photon. Thus, electromagnetic radiation presents complementary aspects that are determined by the type of observation being made. From a fundamental point of view, the particle-wave dualism of electromagnetic radiation (and, as it turns out, of matter as well) offers many fascinating mysteries that still await resolution. From a practical perspective, both pictures will be useful as we develop the many aspects of modern optical technology discussed within this text. 2.2 ELECTROMAGNETISM All known observations of classical electromagnetism can be explained with the set of equations collectively known as Maxwell’s equations 1 .
eBook - PDF- Charles A. Bennett(Author)
- 2022(Publication Date)
- Wiley(Publisher)
23 2 Electromagnetic Waves and Photons When I am judging a theory, I ask myself whether, if I were God, I would have arranged the world in such a way. Einstein Now, let’s look at the first basic action — a photon goes from [A to B]. I will draw this action as a wiggly line from A to B for no good reason. Feynman And God said, Let there be light: and there was light. Moses 2.1 Introduction In this chapter, we attempt to answer the question: “What is light?” Interestingly, there seems to be more than one answer. The bedrock of our description will be the theory of electro- magnetism, as summarized by Maxwell’s equations. From this perspective, light is most cer- tainly a wave — a transverse electromagnetic wave — with properties that we will obtain from Maxwell’s equations. We will use the “wave picture” of electromagnetic radiation extensively throughout the rest of the text to develop many optical concepts and applications. Examples include effects due to interference and diffraction, coherence, optical imaging and resolution, and many of the concepts relating to laser design. However, it will often be necessary to utilize the concept of a light particle, or photon. Thus, electromagnetic radiation presents complementary aspects that are determined by the type of observation being made. From a fundamental point of view, the particle-wave dualism of electromagnetic radiation (and, as it turns out, of matter as well) offers many fascinating mysteries that still await resolution. From a practical perspective, both pictures will be useful as we develop the many aspects of modern optical technology discussed within this text. 2.2 Electromagnetism All known observations of classical electromagnetism can be explained with the set of equations collectively known as Maxwell’s equations. 1 These equations are expressed using 1 James Clerk Maxwell: 1831–1879. Scottish mathematician and physicist. Principles of Physical Optics, Second Edition.
eBook - PDF- David J. Griffiths(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
C H A P T E R 9 Electromagnetic Waves 9.1 WAVES IN ONE DIMENSION 9.1.1 The Wave Equation What is a “wave”? I don’t think I can give you an entirely satisfactory answer—the concept is intrinsically somewhat vague—but here’s a start: A wave is a distur- bance of a continuous medium that propagates with a fixed shape at constant ve- locity. Immediately I must add qualifiers: In the presence of absorption, the wave will diminish in size as it moves; if the medium is dispersive, different frequencies travel at different speeds; in two or three dimensions, as the wave spreads out, its amplitude will decrease; and of course standing waves don’t propagate at all. But these are refinements; let’s start with the simple case: fixed shape, constant speed (Fig. 9.1). How would you represent such an object mathematically? In the figure, I have drawn the wave at two different times, once at t = 0, and again at some later time t —each point on the wave form simply shifts to the right by an amount vt , where v is the velocity. Maybe the wave is generated by shaking one end of a taut string; f (z , t ) represents the displacement of the string at the point z , at time t . Given the initial shape of the string, g(z ) ≡ f (z , 0), what is the subsequent form, f (z , t )? Well, the displacement at point z , at the later time t , is the same as the displacement a distance vt to the left (i.e. at z − vt ), back at time t = 0: f (z , t ) = f (z − vt , 0) = g(z − vt ). (9.1) That statement captures (mathematically) the essence of wave motion. It tells us that the function f (z , t ), which might have depended on z and t in any old way, in fact depends on them only in the very special combination z − vt ; when that vt f v z f(z, 0) f(z, t) FIGURE 9.1 382 9.1 Waves in One Dimension 383 θ′ z z T T f z + Δz θ FIGURE 9.2 is true, the function f (z , t ) represents a wave of fixed shape traveling in the z direction at speed v.
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