Physics
Light Wave
A light wave is a type of electromagnetic wave that travels through space and carries energy. It consists of oscillating electric and magnetic fields that propagate through a medium or vacuum. Light waves have properties such as wavelength, frequency, and amplitude, and they exhibit behaviors like reflection, refraction, and diffraction.
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eBook - PDFOptics
Principles and Applications
- Kailash K. Sharma(Author)
- 2006(Publication Date)
- Academic Press(Publisher)
C H A P T E R 1 Light Waves 1.1 INTRODUCTION Visible light constitutes a small, albeit an important, segment of the broad spec-trum of electromagnetic waves encompassing -rays on one extreme and radio waves on the other. Between these two extremes, lie X-rays, ultraviolet radiation, visible light, infrared radiation and microwaves in decreasing order of frequency (Table 1.1). At the present stage of development of the field of optics, it is really not necessary to justify the wave nature of light. Having said that, it must also be mentioned that the original controversy between the two protagonists (Sir Issac Newton and Christian Huygens) representing two schools of thought – light being corpuscular and light having wave nature – took a new twist with the develop-ment of quantum mechanics. Light, like matter, is now understood to have a dual character – the wave-like behavior as well as the particle-like (photon) behavior. Both attributes may not be revealed in a single measurement. Broadly speaking, light propagation in free space and in other media can be described in classical terms whereas light–matter interaction (absorption and emission of light) can be understood only in the quantum mechanical description. In this book, we are primarily concerned with light propagation and hence the classical description in terms of Maxwell’s equations is quite adequate. Maxwell’s equations predict the velocity of propagation of electromagnetic waves in vacuum which is in close agreement with the measured velocity of light. This observation firmly establishes light in the realm of the electromagnetic waves. 1.2 MAXWELL’S EQUATIONS All electromagnetic phenomena, including light propagation, can be fully described in terms of Maxwell’s equations (written here, in the SI units): · E = / 0 · B = 0 1 2 Chapter 1: Light WaveS Table 1.1. The electromagnetic spectrum.
eBook - PDF- Michael R Fisch(Author)
- 2004(Publication Date)
- WSPC(Publisher)
Chapter 5 An Introduction to Light Waves 5.1 Overview A wave is a traveling disturbance. Waves are important because all infor- mation that we receive via hearing and seeing is transmitted via waves. While light has both particle-like and wave-like properties, the present dis- cussion will focus on the wave-like character of light. The focus in this chapter is on the interaction of these Light Waves with “polarizers,” such as are found in some sunglasses, and material media. Some related topics will be addressed in later chapters, those needed to understand displays will be discussed in this chapter. We will address the following questions. (1) What is a wave? How is a wave represented? ( 2 ) What is light? What makes Light Waves different than waves on water (3) What is a polarizer, and how does it work? (4) How is the interaction of light with essentially transparent materials or sound waves in air? explained? 5.2 Waves Almost all of the applications of liquid crystals that we shall discuss concern how light and liquid crystals interact. To understand this phenomenon, one must understand some of the basic properties of light. We begin by noting that light has wave-like properties, and in elemen- tary discussions may be treated as a wave. A wave is characterized by a traveling disturbance in which the disturbance propagates but the me- 57 58 LIQUID CRYSTALS, LAPTOPS AND LIFE dial as a whole, does not move. Broadly, there are two different types of waves: transverse waves in which the displacement , the movement caused by the disturbance, is perpendicular to the direction the wave propagates, and longitudinal waves where the displacement is parallel to the direction of propagation. Mathematically, the simplest waves are “periodic waves” which continue unchanged for very long periods of time, ideally for all time. The simplest type of periodic wave is the sine wave.
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.
No longer available |Learn more- Mathieu Hébert(Author)
- 2022(Publication Date)
- EDP Sciences(Publisher)
Chapter 1 Light and Optical Radiations The optical or visual characterization of surfaces cannot be separated from the properties of light itself: its wavelength, polarization, angular distribution are all determining factors in the optical signal that is measured or perceived, and therefore in the way it is interpreted. The optical models used in this book will rarely refer to the wave nature of light, except for important properties which are directly related: wavelength, on which many intrinsic characteristics of matter depend, and polar- ization, which determines the amount of light reflected at the interfaces between different materials. It will therefore prove useful to introduce the wave model of light before exposing the types of light signals that will be considered throughout the following chapters for the description of the light-matter interactions that give materials their appearance. 1.1 Light According to the Commission Internationale de l’Eclairage (CIE), light is the generic name for the electromagnetic radiations visible to the human eye [39]. This notion is to be extended to infrared (IR) and ultraviolet (UV) radiations which, respectively, have longer and shorter wavelengths but similar physical properties (see figure 1.1). The limit of wavelengths for the spectral range of visible radiation may vary depending on the radiant power falling on the retina and the sensibility of the observer, but they lie generally between 360 and 400 nm for the lower limit, and between 760 and 830 nm for the upper limit. The CIE tabulates most spectral values related to the response of the standard visual system between 380 and 780 nm [42]. 1.1.1 Light Waves Electromagnetic radiations correspond to a simultaneous vibration of the electric field and the magnetic field, oscillating both perpendicularly to each other and perpendicularly to the wave propagation direction.
eBook - PDF- Pradeep Fulay, Jung-Kun Lee(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
This means that light behaves like a particle as well as a wave. To represent the particle-like prop-erty of an electromagnetic wave, physicists introduced the concept of a photon, which is an elemen-tary unit of the electromagnetic wave. The photon can be understood as a discrete wave packet that behaves like a particle. As schematically illustrated in the left of Figure 8.7, when multiple waves with slightly different wavelengths are superimposed, the wave is localized instead of uni-formly spreading out in space. Hence, the superimposition of waves creates a discrete wave pocket that looks like a particle. As more waves are added, the wave packet is more localized (i.e., Δ x in Figure 8.7 decreases). Smaller Δ x means that the wave packet gets closer to the particle, although uncertainty of the wave vector of the wave packet is increased at the same time. This is because the product of Δ x and Δ k is a constant or larger than a constant, which is predicted in quantum mechanics. As seen in the right of Figure 8.7, the particle-like photon is visualized as a wave pocket and the frequency of the wave pocket is considered the frequency of the photon. Since the photon is an elementary unit of light and the energy of light is quantized, the minimum energy unit of light is the energy of a single photon. The energy of a photon is proportional to its frequency: Energy = hv (8.19) where h is the Planck’s constant (6.62606957 × 10 − 34 m 2 kg/s) and v is the frequency of the light. When the photon travels in different media or when they come across the boundary between two media, the energy of a photon (i.e., frequency of the electromagnetic wave) is maintained. Therefore, a change in the refractive index of the medium only leads to a change in the wavelength of light; the light speed is altered without modifying the frequency of the light.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Mathilde Renard/Medical Images 704 CHAPTER 24 Electromagnetic Waves Concept Summary 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 c (c = 3.00 × 10 8 m/s). 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 c = f. The series of electromagnetic waves, arranged in order of their frequen- cies 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 colors. 24.3 The Speed of Light 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 √ε 0 μ 0 (24.1) 24.4 The Energy Carried by Electromagnetic Waves The total en- ergy 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.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
The idea that light can display both wave and particle characteristics is called wave-particle duality, which is examined in Photons and Matter Waves. In this chapter, we study the basic properties of light. In the next few chapters, we investigate the behavior of light when it interacts with optical devices such as mirrors, lenses, and apertures. Chapter 1 | The Nature of Light 7 1.1 | The Propagation of Light Learning Objectives By the end of this section, you will be able to: • Determine the index of refraction, given the speed of light in a medium • List the ways in which light travels from a source to another location The speed of light in a vacuum c is one of the fundamental constants of physics. As you will see when you reach Relativity, it is a central concept in Einstein’s theory of relativity. As the accuracy of the measurements of the speed of light improved, it was found that different observers, even those moving at large velocities with respect to each other, measure the same value for the speed of light. However, the speed of light does vary in a precise manner with the material it traverses. These facts have far-reaching implications, as we will see in later chapters. The Speed of Light: Early Measurements The first measurement of the speed of light was made by the Danish astronomer Ole Roemer (1644–1710) in 1675. He studied the orbit of Io, one of the four large moons of Jupiter, and found that it had a period of revolution of 42.5 h around Jupiter. He also discovered that this value fluctuated by a few seconds, depending on the position of Earth in its orbit around the Sun. Roemer realized that this fluctuation was due to the finite speed of light and could be used to determine c. Roemer found the period of revolution of Io by measuring the time interval between successive eclipses by Jupiter. Figure 1.2(a) shows the planetary configurations when such a measurement is made from Earth in the part of its orbit where it is receding from Jupiter.
eBook - PDFAn Introduction to Quantum Optics
Photon and Biphoton Physics
- Yanhua Shih, Yanhua Shih(Authors)
- 2018(Publication Date)
- CRC Press(Publisher)
1 Electromagnetic Wave Theory and Measurement of Light 1.1 Electromagnetic Wave Theory of Light To introduce the basic concepts on the coherence property of light, we begin with the Maxwell equations—the foundation of the classical electromag-netic (EM) wave theory of light. The set of four Maxwell equations forms the basis of the theory for classical electromagnetic phenomena and electro-magnetic wave phenomena. In free space, the Maxwell equations have the form ∇ × E = − ∂ B ∂ t , (1.1) ∇ × H = ∂ D ∂ t , (1.2) ∇ · D = 0, (1.3) ∇ · B = 0, (1.4) where E and H are the electric and magnetic field vectors D and B are the electric displacement and magnetic induction vectors, respectively We also have the relations D = 0 E , B = μ 0 H , (1.5) where 0 and μ 0 are the free-space electric permittivity and magnetic permeability, respectively. Taking the curl of Equation 1.1, using Equations 1.2, 1.3, 1.5, as well as the identity ∇ × ∇ × E = ∇ ( ∇ · E ) − ∇ 2 E , (1.6) 1 2 An Introduction to Quantum Optics: Photon and Biphoton Physics the electric field vector E ( r , t ) can be shown to satisfy the wave equation ∇ 2 E − 1 c 2 ∂ 2 E ∂ t 2 = 0. (1.7) Similarly, the magnetic field vector H ( r , t ) , or the magnetic induction vector B ( r , t ) , can be shown to satisfy the same wave equation ∇ 2 H − 1 c 2 ∂ 2 H ∂ t 2 = 0 (1.8) where c ≡ 1 / √ 0 μ 0 is the speed of light in free space. Equations 1.7 and 1.8 both contain the basic wave equation structure (for a variable v ): ∇ 2 v − 1 c 2 ∂ 2 v ∂ t 2 = 0. (1.9) Now, suppose v ( r , t ) has a Fourier integral representation v ( r , t ) = ∞ −∞ d ω v ( r , ω) e − i ω t (1.10) with the inverse transform v ( r , ω) = 1 2 π ∞ −∞ dt v ( r , t ) e i ω t . (1.11) Substituting Equation 1.10 into Equation 1.9, it is straightforward to find that the Fourier transform v ( r , ω) also satisfies the Helmholtz wave equation ∇ 2 v ( r , ω) + k 2 v ( r , ω) = 0 (1.12) where k = ω/ c is the wave number.
eBook - PDF- Graham Saxby(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
1 1 Chapter The Nature of Light Models for the Behavior of Light For thousands of years people have wondered what light really is, and have tried to construct models predicting its behavior. In the seventeenth century Sir Isaac Newton put forward the concept of “energy,” and used it as a fundamental property of objects in motion. He also ascribed it to such things as unwinding springs, burn-ing gases, sound and—important in our context—light. Not everyone agreed with him at the time. But today, when we operate switches, drill teeth, and even weld metal with light beams, there is no longer any doubt. Newton himself believed that light consisted of particles like tiny bullets, trav-elling at enormous speed. This model does predict much of the more obvious behavior of light such as reflection and the formation of shadows, and refraction too, if one makes some dodgy assumptions. Indeed, the entire system of what we now call geometrical optics is based on the idea of the rectilinear propagation of light. Newton’s contemporary Christiaan Huyghens suggested that the behavior of light, particularly with regard to refraction, could be accounted for better if light con-sisted of waves like sound waves. Newton strongly opposed this theory, and this disagreement led to a permanent antagonism between the two men. When the polarization of light was discovered, it became necessary to modify Huyghens’s model of longitudinal waves (which can’t be polarized) to transverse waves (which can) (Figure 1.1). The wave model provided a reasonably good account of diffraction and interfer-ence, as the principle assumed that each point on a wavefront was a source of “wavelets,” the envelope of which would form the new wavefront (Figure 1.2).
eBook - PDFQuips, Quotes and Quanta
An Anecdotal History of Physics
- Anton Z Capri(Author)
- 2007(Publication Date)
- WSPC(Publisher)
Chapter 8 Particles are Waves are Particles “Are not the rays of Light very small Bodies emitted from shining Sub-stances?” Isaac Newton, Philosophical transactions (1672). At the beginning of the twentieth century, physicists again learned to view optical theory in an earlier light. In the seventeenth century Newton asserted that light was corpuscular or particle-like in nature. A century and a half later the work of luminaries like Thomas Young (1773 – 1829) and Augustin Jean Fresnel (1788 – 1827) definitely showed that, contrary to Newton’s view, light was wave-like and not corpuscular, or particle-like, in nature. By passing light through a slit they demonstrated that light was diffracted just like a sound wave or water wave. It was only the very short wavelengths of visible light that had made it appear to travel like a particle in a straight line without spreading. This viewpoint was about to be reversed. In 1887, at the technological institute at Karlsruhe, Heinrich Rudolf Hertz, only thirty years old, a master of Homer and Greek tragedies, as well as economics and the history of mathematics and physics, was about to open the doors to wireless communication and radio. During the four short years between 1885 and 1889, he not only demonstrated that accelerating charges produce radiation that travels at the speed of light but that this radiation conforms in every respect to the radiation predicted by the theory of electromagnetism produced by James Clerk Maxwell twenty years earlier. After he produced the first electromagnetic (radio) waves, his students were 92 Particles are Waves are Particles 93 impressed and asked him, “What next?” he simply replied, “It’s of no use whatsoever. This is just an experiment that proves Maestro Maxwell was right — we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there.” Hertz was born in Hamburg where his father was a prominent lawyer and later senator.
eBook - PDFQuips, Quotes and Quanta
An Anecdotal History of Physics
- Anton Z Capri(Author)
- 2011(Publication Date)
- WSPC(Publisher)
Chapter 9 Particles are Waves are Particles “Are not the rays of Light very small Bodies emitted from shining Sub-stances?” Isaac Newton, Philosophical transactions (1672). At the beginning of the twentieth century, physicists again learned to view optical theory in an earlier light. In the seventeenth century Newton asserted that light was corpuscular or particle-like in nature. A century and a half later the work of luminaries like Thomas Young (1773 – 1829) and Augustin Jean Fresnel (1788 – 1827) definitely showed that, contrary to Newton’s view, light was wave-like and not corpuscular, or particle-like, in nature. By passing light through a slit they demonstrated that light was diffracted just like a sound wave or water wave. It was only the very short wavelengths of visible light that had made it appear to travel like a particle in a straight line without spreading. This viewpoint was about to be reversed. In 1887, at the technological institute at Karlsruhe, Heinrich Rudolf Hertz, only thirty years old, a master of Homer and Greek tragedies, as well as economics and the history of mathematics and physics, was about to open the doors to wireless communication and radio. During the four short years between 1885 and 1889, he not only demonstrated that accelerating charges produce radiation that travels at the speed of light but that this radiation conforms in every respect to the radiation predicted by the theory of electromagnetism produced by James Clerk Maxwell twenty years earlier. After he produced the first electromagnetic (radio) waves, his students were impressed and asked him, “What next?” he simply replied, “It’s of no use whatsoever. This is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot 107 108 Quips, Quotes, and Quanta: An Anecdotal History of Physics see with the naked eye.
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