Physics
Wave Optics
Wave optics is a branch of optics that describes the behavior of light in terms of waves. It focuses on phenomena such as diffraction, interference, and polarization, which cannot be explained by geometric optics. Wave optics provides a more comprehensive understanding of light and its interactions with matter, leading to applications in various fields such as microscopy, astronomy, and telecommunications.
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6 Key excerpts on "Wave Optics"
eBook - PDF- John Matolyak, Ajawad Haija(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
385 © 2010 Taylor & Francis Group, LLC Physical (Wave) Optics 21.1 INTRODUCTION Recall that geometrical optics deals with the properties of light when it encounters objects, mirrors, lenses, and orifices that are large compared with its wavelength. Physical or Wave Optics addresses light behavior when it encounters objects that are approximately the same size or that are smaller than its wavelength. It is in this realm that light exhibits its wave nature and a wave description of light is appropriate. Under these conditions, the two main manifestations of light behavior are called interference and diffraction . These two phenomena are consequences of a very general principle called the linear superposition principle (LSP). 21.1.1 L INEAR S UPERPOSITION P RINCIPLE A wave is a periodic disturbance in a medium. The medium may be material, as in the case of sound waves traveling through air or a steel rod. Or, it may be nonmaterial as with electromagnetic waves (EMWs), where the medium consists of electric and magnetic fields. It is possible for two or more disturbances (waves) to meet at the same spatial point in a medium, at exactly the same time. Then, the question that arises is how will the medium respond, that is, what is the resultant disturbance at that spatial point and that particular time? The LSP states: The displacement (disturbance) at any point in the medium is equal to the algebraic sum of the indi-vidual displacements (disturbances). For example, consider two EMWs whose oscillations are written as E E sin k x t 1 01 1 1 1 1 = -( ) ω (21.1) and E E sin k x t 2 02 2 2 2 2 = -( ) . ω (21.2) If these two waves meet at some common point, that is, x 1 = x 2 = P, the resultant electric field at P, according to the LSP, is E E E E TOTAL i i 1 2 = = + ∑ . Figure 21.1a depicts two light rays (only the electric field components are shown for clarity) of equal wavelengths, emitted from two separate sources, propagating through air.
eBook - ePubOptical Spectroscopy
Methods and Instrumentations
- Nikolai V. Tkachenko(Author)
- 2006(Publication Date)
- Elsevier Science(Publisher)
Chapter 2Optics and Optical Devices
All optical spectroscopy instruments are optical devices in that they use light sources, manipulate the light and measure the light. Optics and optical devices have a long history going back to 17th century when the wave and corpuscular light theories were developed by two famous scientists Christian Huygens and Isaac Newton. Nowadays optics is a well developed branch of natural sciences with numerous subtopics, application fields and wide range of instruments and tools available commercially. Giving its importance for understanding the principles of the optical spectroscopy instruments this Chapter will discuss a few general topics, such as interference and interferometers, diffraction and diffraction resolution limits, monochromators, and calculation of optical systems in geometrical optics approximation. However, this is rather fragmentary selection of optics subjects and readers are advised to refer to general optics text books for more complete study of the subject.1The photon, being a quantum object, has a controversy of wave and particle presentations. Also there are unified theories, it is common to use wave theory to discuss interference or diffraction properties of the light, and to present photons as particles for ray tracing or to study their interactions with matter. Accordingly, the wave presentation of light will be discussed at first, following by its application to interference and diffraction. In the last section we shall switch to geometrical optics to discuss calculations of beam tracing in optical systems.2.1 Waves
2.1.1 Wave equationIn a simple one dimension case (1D) the wave equation is(2.1)where f = f (x, t ) is a function of coordinate x and time t , and c is a constant. For example a string vibration can be described by the wave equation, then f (x, t ) can be the string displacement at position x. A general solution of the equation is(2.2)Where u and v are any functions of a single parameter. These functions present two waves propagating in opposite directions: the wave u (ct – x ) propagates in direction of increasing x , and the wave v (ct + x ) in decreasing x
eBook - PDF- Robert Splinter, Brett A. Hooper(Authors)
- 2006(Publication Date)
- CRC Press(Publisher)
69 3 Review of Optical Principles: Classical Optics In this chapter some of the basic definitions used in optics are presented, followed by an in-depth theoretical description of the electromagnetic the-ory; how electromagnetic waves are generated, what laws they obey, and the different classifications of electromagnetic waves from television waves to gamma radiation. The general area of optics in the visible light spectrum is covered, and the sources of electromagnetic radiation are discussed. In addition, the rules that were developed over the centuries regarding the modeling of light and image formation are presented and explained. The quantum theory of light is outlined, followed by several theories regarding absorption and how to model light scattering. At the end of this chapter fol-lows a compendium of the common terms and definitions in the arena of optics principles. 3.1 Geometrical Optics Geometrical optics describes the part of optics that involves image formation and related phenomena. The principles use geometry to track the path of the electromagnetic waves. These tracks can also be seen as rays of particles, consistent with the wave-particle duality of light. In Chapter 2 the wave characteristics of electromagnetic radiation were described. Generally, wave propagation in three dimensions is quite a complicated process, especially when there are multiple waves involved. In addition, one cannot always identify the point source of each single electromagnetic wave to apply the Maxwell equations to find the final result tied into the source. The descrip-tion of the superposition of multiple waves traveling as a wavefront was formulated by Christiaan Huygens (1629–1695) in 1678, based on his obser-vations on mechanical wave propagation, and was extrapolated in the early 1900s to fit the new description of electromagnetic waves. Christiaan Huygens was a contemporary of Sir Isaac Newton (1642–1727). 69
eBook - PDF- Yoni Kahn, Adam Anderson(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
3 Optics and Waves The Optics and Waves part of the GRE weighs in at 9% of the test, and contains a mix of some very basic mate- rial and some rather advanced material. Optics is a part of any standard freshman physics course, while waves appear in all areas of physics, and their treatment can vary greatly in difficulty and sophistication. For the purposes of the GRE, “optics” refers to geometric optics (lenses, mirrors, and so on), while “waves” refers to properties such as interference and diffraction as well as some more advanced topics such as Rayleigh scattering. We’ll first discuss general properties of waves, including behavior such as diffraction and interfer- ence that can occur with any type of general wave, then we’ll go over specific examples involving light waves, finishing with geometric optics. Many of the equations required for solving optics problems arise from fairly technical calculations that are outside the scope of the exam. It is therefore worth mem- orizing the key equations in this chapter and knowing the situations where they can be applied. 3.1 Properties of Waves 3.1.1 Wave Equation Roughly speaking, a wave is a disturbance that propagates in time. More precisely, a wave (in one dimension) is any solution to the wave equation, ∂ 2 f ∂ t 2 = v 2 ∂ 2 f ∂ x 2 . (3.1) It turns out that, for any function f (x), the related func- tions f (x ± vt ) solve the wave equation. We interpret these as disturbances of fixed shape, given by the function f (x), which propagate either to the left or to the right with constant speed v. Now, the crucial property of the wave equation is its linearity in the function f , which leads to the principle of superposition: for any two solutions f (x, t ) and g (x, t ) that solve the wave equation, the function f +g also solves the wave equation. This makes analyzing wave behavior quite easy, since we can always break up any complicated wave profile into a sum of simpler pieces.
- James Stewart(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Physical Optics 2 Physical optics treats the propagation of radiation in terms of its electromagnetic wave nature. There are a number of treatments of physical optics (e.g., Jenkins and White, 1937; Born and Wolf, 1959). Geometrical optics (see Chapter 3) may be considered to be the limit of physical optics as the wavelength ap proaches zero. Some concepts from physical optics are important in geometrical optics as well. 2.1. ELECTROMAGNETIC WAVES Two vectors are associated with an electromagnetic wave, the electric field vector and the magnetic field vector. These vectors are perpendicular to each other and to the direction of propagation of the wave (Fig. 2.1). The radiant power carried by an electromagnetic wave is proportional to the Poynting vector , which is the vector cross vector product of the electric and magnetic field vectors, E x H. Because the two vectors are perpendicular to one another and the amplitude of the magnetic vector is proportional to the amp litude of the electric vector, the power carried by an electromagnetic wave may be said to be proportional to the square of the amplitude of the electric vector. The velocity of propagation of an electromagnetic wave in a vacuum is 2.9979250 x 108 meters per second. The refractive index of a medium is the velocity of radiation in the medium relative to the velocity in a vacuum. The 15 16 Chapter 2 Figure 2.1 Electric and magnetic vectors of an electro-magnetic wave. The associ ated magnetic vector is perpendicular to the electric vector and both are perpendicular to the direction of propagation of the wave. optical glass BK7 has a refractive index of 1.5168 at a wavelength of 587.56 nm. The velocity of light in BK7 is 2.9979250 x 108/1.5168 ~ 2 x 108 meters per second. As will be discussed in Chapter 3, in geometrical optics it is convenient to use the concept of a ray in describing optical phenomena. A ray is a vector that is directed in the direction of propagation of a wave.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
If not, determine the type of spacing. Also with the CD, explore the spectra of a few light sources, such as a candle flame, incandescent bulb, halogen light, and fluorescent light. Knowing the spacing of the rows of pits in the compact disc, estimate the maximum spacing that will allow the given number of megabytes of information to be stored. If you have ever looked at the reds, blues, and greens in a sunlit soap bubble and wondered how straw-colored soapy water could produce them, you have hit upon one of the many phenomena that can only be explained by the wave character of light (see Figure 27.2). The same is true for the colors seen in an oil slick or in the light reflected from a compact disc. These and other interesting phenomena, such as the dispersion of white light into a rainbow of colors when passed through a narrow slit, cannot be explained fully by geometric optics. In these cases, light interacts with small objects and exhibits its wave characteristics. The branch of optics that considers the behavior of light when it exhibits wave characteristics (particularly when it interacts with small objects) is called Wave Optics (sometimes called physical optics). It is the topic of this chapter. Figure 27.2 These soap bubbles exhibit brilliant colors when exposed to sunlight. How are the colors produced if they are not pigments in the soap? (credit: Scott Robinson, Flickr) 27.1 The Wave Aspect of Light: Interference We know that visible light is the type of electromagnetic wave to which our eyes respond. Like all other electromagnetic waves, it obeys the equation (27.1) c = f λ, where c = 3×10 8 m/s is the speed of light in vacuum, f is the frequency of the electromagnetic waves, and λ is its wavelength. The range of visible wavelengths is approximately 380 to 760 nm. As is true for all waves, light travels in straight lines and acts like a ray when it interacts with objects several times as large as its wavelength.
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