Physics
Light Waves
Light waves are electromagnetic waves that travel through space and carry energy. They are characterized by their wavelength and frequency, with shorter wavelengths corresponding to higher frequencies and vice versa. Light waves exhibit properties of both waves and particles, and they can be described using the wave-particle duality concept in quantum mechanics.
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11 Key excerpts on "Light Waves"
eBook - PDFIntroduction to Optics I
Interaction of Light with Matter
- Ksenia Dolgaleva(Author)
- 2022(Publication Date)
- Springer(Publisher)
In essence, light is electromagnetic radiation, and it consists of electromagnetic waves where the electric and magnetic fields oscillate both in time and space and carry energy. We will further refer to the electromagnetic waves associated with light as Light Waves. Let us consider a single light wave. If we take a snapshot and assume that we can observe a wave “frozen” in time (and, consecutively, in space), we will find that it exhibits a periodic change in the strength of its electric field as we move in space along the direction of the wave’s propaga- tion (see Fig. 1.5a). Looking at this snapshot, we can identify the spatial distance between the two consecutive peaks in the field oscillation to be the wavelength of light 0 . This characteristic dictates the color that the light appears in. While the optical range typically includes a spectral window between ultraviolet (UV, 0 D 300 nm) and infrared (IR, 0 D 10 m), defined by the operation range of conventional laser sources, the spectrum that our eye is capable of perceiv- ing, which we call the visible spectrum, spans between 380 nm (purple) and 750 nm (red); see Fig. 1.6. 1 1 The latest achievements in laser sources allow us to push the optical limit to the shorter 272 nm (deep-UV ) wavelengths with the new laser diode [6] and longer terahertz (THz) wavelength of around 300 m [7]. One can also define a broader range of electromagnetic waves used in optics: from 13 nm (photolithography) to 300 m (THz frequencies for medical diagnostics, molecular spectroscopy, airport security, and other applications). 1.2. CHARACTERISTICS OF LIGHT 7 Figure 1.5: Electromagnetic light wave. (a) The variation of the electric field in space: a temporal snapshot of the wave, resulting in a wave “frozen” in space; and (b) temporal oscillations of the electric field. Figure 1.6: Colors of light and their respective wavelength ranges.
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 - ePubMaking Physics Fun
Key Concepts, Classroom Activities, and Everyday Examples, Grades K?8
- Robert Prigo(Author)
- 2015(Publication Date)
- Skyhorse(Publisher)
So the particle picture of light was back on the scene. Indeed, the nature of light turned out to be much more interesting than an either-or particle or wave reality. Both descriptions are needed for a full picture of light. This complementary picture is known as the wave-particle duality for light. The dual nature of light, propagating as an electromagnetic wave while interacting with matter through particle-like photons, sums up our present understanding of light. This wave-particle duality is now known to be a universal property of nature. Based on an analogy with the dual nature of light, Louis de Broglie (1892–1987) proposed that matter itself (electrons, atoms, etc.) might show the same duality. He proposed that particles such as electrons might have wave-like features. His ideas were soon put to the test and vindicated when experiments revealed the diffraction and superposition of electrons! All forms of light, both visible and nonvisible, share many fascinating characteristics and properties. Light does not need a medium through which to propagate. It can propagate in a vacuum. Light is made up of oscillating and self-sustaining electric and magnetic fields that interact with matter in a particle-like way (photons). Light travels at a constant speed in a vacuum (299,792,458 meters per second). In a transparent material, light travels at a slower speed, with different frequencies traveling at slightly different speeds. In a vacuum and in uniform transparent materials, light travels in straight lines. Some objects reflect light, some absorb light, and some do both. Light bends— refracts —when it propagates from one transparent medium into another. Visible light comes in a narrow but continuous spectrum of frequencies that we detect as different colors (red to violet). “White” light is composed of light of different colors (red to violet). “Black” is the absence of light
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- 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- 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.
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- Dieter Schu??cker(Author)
- 1999(Publication Date)
- WSPC(Publisher)
Since temporal changes of an electric field always give rise to magnetic fields with a direction perpendicular to the electric field, the electric wave is associated to a magnetic wave and therefore finally light can be identified as an 'electromagnetic wave' /1.2/, /l 31. Although the simple approach of geometrical optics is sufficient to describe everyday's optical instruments as mentioned above, for the description of the much more sophisticated laser devices - as far as it concerns the formation and the properties of beams and their behavior - the electromagnetic wave nature of light must be considered, as treated in the subsequent chapter. 1 Light and Matter 3 1.1.2 Lightwaves a) Electromagnetic waves It is well known, that electric currents, as they result from moving electric charges, generate a magnetic field, that surrounds the stream lines of current ('Law of Mot-Savor?) I .3/. The electric current mentioned before is fully equivalent to an alternating electric field strength, as it becomes obvious, if a condenser is regarded that is subject to the flow of an alternating current. So temporal variations of an electric field strength also generate a magnetic field, where the field lines of the latter surround the field lines of the electric field and the magnetic field varies with the same frequency as the electric field, but with a delay of 1/4 of the length of periodicity T. It is also well known, that a varying magnetic field induces an electric field, whereas also again the field lines of the electric field surround the magnetic field and there is also a delay of 1/4 of the length of periodicity (Law of Induction' /1.3/). Since now each variation of electric or magnetic fields generates magnetic and electric field lines, that are not only situated near to the initially varying field, but extend into remote regions of the space and generate there again fields of the other kind, the fields generating each other propagate in all directions of space.
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
1. Light. The visible region of the spectrum is the one most familiar to us, because as a species we have adapted receptors (eyes) that are sensitive to the most intense elec- tromagnetic radiation emitted by the Sun, the closest ex- traterrestrial source. The limits of the wavelength of the Light Waves I n this chapter we discuss the characteristics of Light Waves, including sources of visible radiation, the speed of propagation in vacuum and in matter, the change in direction that occurs when light encounters a boundary between two materials in which the speed of propagation is different, and the Doppler effect (the change in frequency due to relative motion of source and observer). Because there is nothing fundamental that distinguishes light from any other type of electromagnetic wave, you should keep in mind that the discussions in this chapter could apply equally well to other kinds of electromagnetic waves. Nevertheless, this chapter serves as a bridge from our discussion of electromag- netic waves in the previous chapter to the discussion of optics (the science of light), which will be the sub- ject of the next several chapters. CHAPTER 39 CHAPTER 39 *The word spectrum comes from a Latin word meaning “form” or “ap- pearance.” Other familiar words from the same root include “spectacle” and “species.” Newton introduced the word to describe the rainbow-like image that resulted when a beam of sunlight passed through a glass prism. Today we speak of the electromagnetic spectrum to indicate the many dif- ferent kinds of electromagnetic radiation, classified according to their fre- quency or wavelength on a scale from small to large. We also speak of the political spectrum, which similarly indicates the broad range of political views on a scale from ultraconservative to ultraliberal. visible region are from about 400 nm (violet) to about 700 nm (red).
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).
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