Physics
Geometrical and Physical Optics
Geometrical and Physical Optics are branches of optics that deal with the behavior of light. Geometrical optics focuses on the propagation of light as rays and the formation of images by lenses and mirrors, while Physical optics explores the wave nature of light, including phenomena such as interference, diffraction, and polarization. Both branches are essential for understanding the behavior of light in various optical systems.
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eBook - ePub- Britannica Educational Publishing, Erik Gregersen(Authors)
- 2010(Publication Date)
- Britannica Educational Publishing(Publisher)
CHAPTER 7 OPTICSO ptics is the branch of science concerned with the genesis and propagation of light, the changes that it undergoes and produces, and other phenomena closely associated with it.Originally, the term optics was used only in relation to the eye and vision. Later, as lenses and other devices for aiding vision began to be developed, these were naturally called optical instruments, and the meaning of the term optics eventually became broadened to cover any application of light, even though the ultimate receiver is not the eye but a physical detector, such as a photographic plate or a television camera. In the 20th century, optical methods came to be applied extensively to regions of the electromagnetic radiation spectrum not visible to the eye, such as X-rays, ultraviolet, infrared, and microwave radio waves, and to this extent these regions are now often included in the general field of optics.GEOMETRICAL OPTICS
There are two major branches of optics: physical and geometrical. Physical optics deals primarily with the nature and properties of light itself. Geometrical optics has to do with the principles that govern the image-forming properties of lenses, mirrors, and other devices that make use of light. It also includes optical data processing, which involves the manipulation of the information content of an image formed by coherent optical systems.THE OPTICAL IMAGEAn optical image may be regarded as the apparent reproduction of an object by a lens or mirror system, employing light as a carrier. An entire image is generally produced simultaneously, as by the lens in a camera, but images may also be generated sequentially by point-by-point scanning, as in a television system or in the radio transmission of pictures across long distances in space. Nevertheless, the final detector of all images is invariably the human eye, and, whatever means is used to transmit and control the light, the final image must either be produced simultaneously or scanned so rapidly that the observer’s persistence of vision will give him the mental impression of a complete image covering a finite field of view. For this to be effective the image must be repeated (as in motion pictures) or scanned (as in television) at least 40 times a second to eliminate flicker or any appearance of intermittency.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
Traditional optics is divided into two main branches: geometrical optics and physical optics. Geometrical optics As a light wave travels through space, it oscillates in amplitude. In this image, each maximum amplitude crest is marked with a plane to illustrate the wavefront. The ray is the arrow perpendicular to these parallel surfaces. Geometrical optics , or ray optics , describes light propagation in terms of rays. The ray in geometric optics is an abstraction, or instrument, that can be used to predict the path of light. A light ray is a ray that is perpendicular to the light's wavefronts (and therefore collinear with the wave vector). Light rays bend at the interface between two dissimilar media and may be curved in a medium in which the refractive index changes. Geometrical optics provides rules for propagating these rays through an optical system, which indicates how the actual wavefront will propagate. This is a significant simplification of optics that fails to account for optical effects such as diffraction and polarization. It is a good approximation, however, when the wavelength is very small compared with the size of structures with which the light interacts. Geometric optics can be used to describe the geometrical aspects of imaging, including optical aberrations. ____________________ WORLD TECHNOLOGIES ____________________ A slightly more rigorous definition of a light ray follows from Fermat's principle which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. Approximations Geometrical optics is often simplified by making the paraxial approximation, or small angle approximation. The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
Geometrical optics As a light wave travels through space, it oscillates in amplitude. In this image, each maximum amplitude crest is marked with a plane to illustrate the wavefront. The ray is the arrow perpendicular to these parallel surfaces. Geometrical optics , or ray optics , describes light propagation in terms of rays. The ray in geometric optics is an abstraction, or instrument, that can be used to predict the path of light. A light ray is a ray that is perpendicular to the light's wavefronts (and therefore collinear with the wave vector). Light rays bend at the interface between two dissimilar media and may be curved in a medium in which the refractive index changes. Geometrical optics provides rules for propagating these rays through an optical system, which indicates how the actual wavefront will propagate. This is a significant simplification of optics that fails to account for optical effects such as diffraction and polarization. It is a good approximation, however, when the wavelength is very small compared with the size of structures with which the light interacts. Geometric optics can be used to describe the geometrical aspects of imaging, including optical aberrations. A slightly more rigorous definition of a light ray follows from Fermat's principle which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. Approximations Geometrical optics is often simplified by making the paraxial approximation, or small angle approximation. The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques ________________________ WORLD TECHNOLOGIES ________________________ of Gaussian optics and paraxial ray tracing , which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications.
- Andrei D. Polyanin, Alexei Chernoutsan(Authors)
- 2010(Publication Date)
- CRC Press(Publisher)
Chapter P5 Optics P5.1. Geometric Optics. Radiometry P5.1.1. Geometric Optics ◮ Fundamental laws of geometric optics. Optics studies the electromagnetic radiation of optic (light) range (see Subsection P4.2.2) as well as phenomena arising in its propagation in space and under interaction with matter. Geometric optics does not consider the wave character and polarization of light radiation and deals with notions of light rays pointing out the direction of light propagation and narrow light beams formed by light rays. The fundamental laws of geometric optics are listed below. 1. Law of rectilinear light propagation . 2. Law of independence of light beams . The energy in each beam propagates indepen-dently of other beams; illumination of the surface on which several beams are incident, is equal to the sum of illuminations created by each beam separately. 3. Law of light reflection . The reflected ray lies in incidence plane , formed by the incident ray and the normal to the surface at the point of incidence; the angle of incidence is equal to the angle of reflection. All the angles are counted from the normal. 4. Law of light refraction . The refracted ray lies in the plane of incidence; the ratio of the sine of the angle of incidence α 1 to the sine of angle of refraction α 2 depends on the wavelength but is independent of the angle of incidence (Snell law): sin α 1 sin α 2 = n 21 = n 2 n 1 . (P5. 1 . 1 . 1 ) The constant quantity n 21 is called the relative index of refraction of the second medium with respect to the first one, which is equal to the ratio of ( absolute ) indices of refraction of each of the media (of indices of refraction of the medium with respect to a vacuum). From the viewpoint of wave optics, the absolute index of refraction shows by what factor the phase velocity of the light wave of a given frequency is less than the velocity of this wave in a vacuum: v = c/n , n = √ με ≈ √ ε (P5. 1 . 1 . 2 ) (see Subsection P4.2.2).
- 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 - PDFObservational Astronomy
Techniques and Instrumentation
- Edmund C. Sutton(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
8 Optics We begin our treatment of optics by first considering geometrical optics. In the limit of small wavelengths, geometrical optics describes the direction in which light travels through space as it encounters materials with different indices of refraction. Initially the refractive index will simply be assumed to be a property of a material which describes the speed at which light propagates in that material. That will be sufficient to allow us to treat the theory of aberrations and to look into some basic aspects of telescope design. Next we will look at the physical origins of the refractive index and at the Fresnel coefficients, which are important in a number of contexts including the design of various spectroscopic devices. Then we will consider physical optics, the behavior of light in the regime of finite wavelengths where diffractive effects become important. This will include a look at the Airy pattern. Finally we will introduce the concepts of the point spread function and the modulation transfer function and use them to consider some general properties of imaging. 8.1 Geometrical optics The properties of light propagation can often usefully be described by geomet- rical optics, an approximation which is valid in the limit of small wavelengths. The wavelength λ is assumed to be small compared with all relevant length scales, including the dimensions of any physical objects present. The media of propaga- tion are described by various values of the refractive index n, which in general is wavelength dependent. In this approximation it is possible to visualize the indi- vidual paths followed by narrow pencils of light, a process known as ray tracing. These rays are considered to have small cross sectional area A and small diver- gence and therefore small étendue. Ray tracing depends on two basic laws: the law of reflection and Snell’s law. 117
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 4 Optics Optics includes study of dispersion of light Optics is the branch of physics which involves the behavior and properties of light, inclu-ding its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical electromagnetic des-cription of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation. ________________________ WORLD TECHNOLOGIES ________________________ Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics. When considering light's particle-like properties, the light is modeled as a collection of particles called photons. Quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astro-nomy, various engineering fields, photography, and medicine (particularly ophthal-mology and optometry).
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 4 Optics and Photometry Optics Optics includes study of dispersion of light ________________________ WORLD TECHNOLOGIES ________________________ Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics. When considering light's particle-like properties, the light is modeled as a collection of particles called photons. Quantum optics deals with the application of quantum mechanics to optical systems.
eBook - PDF- Andri M. Gretarsson(Author)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
3 Geometric Optics 3.1 The Geometric Optics Approximation In geometric optics, we assume that the wavelength of light approaches zero. In that limit, successive wavefront normals trace out straight lines in free space, just like a stream of classical particles. For example, laser beams (Gaussian beams) spread out slowly as they travel, due to diffraction. In the limit λ → 0, this spread also becomes zero and all the light moves in a perfectly straight line. (See, for example, Eq. (4.15).) We imagine these straight line paths as “rays” of light that are affected only by the optics placed in their path. In geometric optics, the light waves are also assumed to be incoherent so they will have random phase and amplitude. The mean square field amplitude resulting from a sum of such random fields is the sum of the mean squares of the contributing fields. E 2 tot = E 2 1 + E 2 2 + . . . Just like random errors, random fields add in quadrature. Irradiance (power per unit area) is proportional to the field squared, so this implies that the total irradiance at any point in space is just the sum of the contributing irradiances: I tot = I 1 + I 2 + . . . That’s of course what our intuition tells us should happen. Since we are used to incoherent light in everyday life our intuition is attuned to that case. It is the coherent case that’s less intuitive. When diffraction is insignificant and coherence is low, geometric optics provides a good model for the behavior of light. The most important application of geometric optics is in imaging. Yet, geometric optics is applied in many other contexts such as architectural lighting design, microwave antenna design, spectroscopy, and so forth. 3.2 Refraction Refraction refers to the tendency of light to change direction when there is a change in the index of refraction of the medium in which the wave travels.
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- David A. Boas, Constantinos Pitris, Nimmi Ramanujam, David A. Boas, Constantinos Pitris, Nimmi Ramanujam(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
3 Geometrical optics .is.the.study.of.light.without.diffraction.or. interference.and.is.based.on. Fermat’s principle . .We.treat.light. as.particles.of.energy.traveling.through.space . .These.particles. follow. trajectories. that. are. called. rays . . Hence,. geometrical. optics.is.often.called. ray optics . .Fermat’s.principle.is.a.concise. statement.that.contains.all.the.physical.laws,.such.as.the. law of reflection .and.the. law of refraction ,.in.geometrical.optics.(Poon. and.Kim.2006) . 1.1 Fermat’s Principle Fermat’s.principle.states.that.the.path.of.a.light.ray.follows.is.an. extremum.in.comparison.to.nearby.paths . .The.extremum.may.be. a.minimum,.a.maximum,.or.stationary.with.respect.to.variations. in.the.ray.path . .However,.the.extremum.is.usually.a.minimum . .For. a.simple.example,.as.shown.in.Figure.1 .1, .the.shortest.distance.(the. minimum.distance).between.two.points.A.and.B.is.along.a.straight. line.(solid.line).in.a. homogeneous medium ,.i .e., .in.a.medium.with.a. constant. refractive index ,.instead.of.taking.the.nearby.dotted.line . . Since.the.speed.of.light.in.a.homogeneous.medium.is.constant,.the. time.it.takes.for.the.ray.to.traverse.the.solid.line.must.be.minimum . . Hence.Fermat’s.principle.is.often.stated.as.a. principle of least time . . Under.this.context,.the.light.ray.would.follow.that.path.for.which. the.time.taken.is.minimum . .For.a.more.complicated.example,.we. show.the.derivation.of.the.well-known.Snell’s.law.of.refraction . .In. Figure.1 .2, . θ i .and. θ t .are.the.angles.of.incidence.and.transmission,. respectively. .The.angles.are.measured.from.the.normal.NN ′ .to.the. interface.MM ′ ,.which.separated.media.1.and.2,.characterized.by. refractive.indexes. n i .and. n t ,.respectively . .The.total.time.taken.to. transit.from.point.A.to.B.is.given.by . t z v v h z v h d z v ( ) ( ) , = + = + + + -AO OB 1 2 1 2 2 1 1 2 2 2 . (1 .1) where. v 1 .and. v 2 .are.the.light.velocities.in.media.1.and.2,.respec-tively.
- Christof M. Aegerter(Author)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
5.5 Geometric Optics 5.5.1 Light Rays While we know that light is a wave from the polarization and interference effects we have described in the preceding sections, we also know that we can produce seemingly sharply defined light beams with the help of, e.g., an iris. These light rays are decisive in designing optical imaging systems such as microscopes, which is why we will be looking in more detail at geometric optics in the coming sections. Such beams are reflected on well-defined surfaces (polished glass or a calm water surface). Rays are also refracted into the other medium. We have the law of refraction, which we have established earlier from the wave properties of the light, also known as Snell’s law. We will now however formulate it generally when we consider two materials, each with a refractive index n 1 and n 2 respectively. 176 Optics, Light, and Colors k 1 k 2 k 1 ' n 1 n 2 b a a' Figure 5.27 Refracted and reflected light rays following Snell’s law. If a plane wave impinges onto a surface in the direction of k 1 with an angle α relative to the normal of said surface separating two media of different wave velocities v 1 and v 2 , it is partially reflected and partially refracted (see Figure 5.27). The law of reflection says α = α . In addition, we have Snell’s law of refraction: sin α sin β = v 1 v 2 = c n 1 n 2 c = n 2 n 1 . These laws do not make any statement about the proportions of reflected and transmitted intensity. Only in the special case of the so-called total internal reflection conservation of energy implies that the reflected intensity is equal to the incident intensity. This case can occur for the transition from the optically denser to the less dense medium (n 1 > n 2 ). From sin α = n 2 n 1 sin β ≤ n 2 n 1 < 1, we know that there is a maximum angle of incidence α T . If sin α > sin α T = n 2 /n 1 , there is no refracted part anymore and all of the incoming intensity is therefore reflected.
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