Physics
Path of Light
The "Path of Light" refers to the trajectory followed by light as it travels through a medium or space. In physics, this concept is fundamental to understanding the behavior of light, including phenomena such as reflection, refraction, and dispersion. The path of light can be described using principles of optics and wave theory.
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10 Key excerpts on "Path of Light"
eBook - PDF- Robert Splinter, Brett A. Hooper(Authors)
- 2006(Publication Date)
- CRC Press(Publisher)
The maximal path length will be achieved under gravita-tional lensing; for the conditions pertaining to the material in this book the propagation will strive to satisfy a minimal path length. 3.1.4 Ray Optics Ray optics is the branch of geometrical optics that describes light as rays. The rays emanate from a source and are perpendicular to the wavefronts 1.22 D D 78 An Introduction to Biomedical Optics described in Section 2.2 in Chapter 2. The rays can illustrate the Laws of Rectilinear propagation, reflection, and refraction with great accuracy and ease. Examples of geometrical optics are presented in image formation with lenses and mirrors in the subsequent chapters. By definition, the light ray at a given point in space is along the gradient of the optical path function. The optical path function L ( r ) is defined as the optical path length from a conve-niently chosen reference wave surface 0 to an arbitrary point P . The point P is identified by the vector r , and this point can be reached by a ray emanat-ing from the wave surface 0, and a point P 0 designates a location on the sur-face 0, with the vector r 0 as position vector for P 0 . The optical path function L, traveling from point A to point B in three-dimensional space can be defined in a medium with speed of light v and index of refraction n as (3.13) or in vector notation (3.14) When there is a disturbance in optical space occurring at time t 0 , the wave-front 0 is affected. At time t , when t t 0 , the wavefront will be at the two-dimensional surface , consisting of all points that reach from 0 after the time interval ( t t 0 ), where the distance to the surface can be defined as (3.15) To obtain the path function L ( r ), when r moves a distance d r toward the loca-tion, P 1 the ray P 0 P P 1 will construct the new wave surface 1 originating from 0 at position P 1 .
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Its wave characteristics are not pronounced in such situations. Since the wavelength of visible light is less than a micron (a thousandth of a millimeter), it acts like a ray in the many common situations in which it encounters objects larger than a micron. For example, when visible light encounters anything large enough that we can observe it with unaided eyes, such as a coin, it acts like a ray, with generally negligible wave characteristics. In all of these cases, we can model the Path of Light as straight lines. Light may change direction when it encounters objects (such as a mirror) or in passing from one material to another (such as in passing from air to glass), but it then continues in a straight line or as a ray. The word “ray” comes from mathematics and here means a straight line that originates at some Chapter 1 | The Nature of Light 11 point. It is acceptable to visualize light rays as laser rays. The ray model of light describes the Path of Light as straight lines. Since light moves in straight lines, changing directions when it interacts with materials, its path is described by geometry and simple trigonometry. This part of optics, where the ray aspect of light dominates, is therefore called geometric optics. Two laws govern how light changes direction when it interacts with matter. These are the law of reflection, for situations in which light bounces off matter, and the law of refraction, for situations in which light passes through matter. We will examine more about each of these laws in upcoming sections of this chapter. 1.2 | The Law of Reflection Learning Objectives By the end of this section, you will be able to: • Explain the reflection of light from polished and rough surfaces • Describe the principle and applications of corner reflectors Whenever we look into a mirror, or squint at sunlight glinting from a lake, we are seeing a reflection. When you look at a piece of white paper, you are seeing light scattered from it.
eBook - PDF- Andrea Cusano, Francisco J. Arregui, Michele Giordano, Antonello Cutolo(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
The different models are founded in some basic postulates and have certain limits of application. Ray optics explains the cinematic of the propagation. Wave optics explains the diffraction and the interference phenomena. Electromagnetic optics makes it possible to have an exact analysis of the phenomena of classic optics, including the effect of energy at the interfaces. The propagation of light in any medium, including optical waveguides, is governed by Maxwell’s equations and can be described by specifying the evolution of the associated electric and magnetic field vectors in space and time. Finally, quantum optics (the most com-plex one) explains all the optical phenomena that we know, including the interaction of light with matter. 1.2.1 Basic Properties of Light 1.2.1.1 Optical Spectrum Up to a century ago, light was understood as the visible phenomena for the human eye and only the waves included from 380 to 750 nm band were associated with light. However, after Maxwell’s discoveries the electromagnetic spectrum of light goes from the deep ultraviolet (100 nm) to the very far infrared (1 mm) and, hence, the visible part of the light is only a very narrow band included inside it. Wave optics Beam optics Electromagnetic optics Quantum optics FIGURE 1.2 Illustration of the theories for the treatment of the light ordered (left to right) following their historical development: ray optics, wave optics, electromagnetic optics, and quantum optics, being the later the more complex. 7 Fundamentals of Photonics The infrared (0.75 μ m–1 mm) band is usually subdivided into four regions: near infrared (750 nm–3 μ m), middle infrared (3–6 μ m), far infrared (6–15 μ m), and extreme infrared (15 μ m–1 mm). Inside this band, the very interesting band of the terahertz is included.
eBook - ePub- L D Landau(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
optical systems .Because of the analogy mentioned in § 53 , between the propagation of rays and the motion of particles, the same general laws are valid for the change in direction of motion of a particle, initially moving in a straight line in vacuum, then passing through some electromagnetic field, and once more emerging into vacuum. For definiteness, we shall, however, always speak later of the propagation of light rays.We saw in a previous section that the eikonal equation, describing the propagation of the rays, can be written in the form (53.11) (for light of a definite frequency). From now on we shall, for convenience, designate by ψ the eikonal ψ0 divided by the constant ω/c . Then the basic equation of geometrical optics has the form:(55.1)= 1.(2∇ ψ)(55.1)Each solution of this equation describes a definite beam of rays, in which the direction of the rays passing through a given point in space is determined by the gradient of ψ at that point. However, for our purposes this description is insufficient, since we are seeking general relations determining the passage through an optical system not of a single definite bundle of rays, but of arbitrary rays. Therefore we must use an eikonal expressed in such a form that it describes all the generally possible rays of light, i.e. rays passing through any pair of points in space. In its usual form the eikonal ψ (r) is the phase of the rays in a certain bundle passing through the point r. Now we must introduce the eikonal as a function ψ (r, r′) of the coordinates of two points (r, r′ are the radius vectors of the initial and end points of the ray). A ray can pass through each pair of points r, r′, and ψ (r, r′) is the phase difference (or, as it is called, the optical path length ) of this ray between the points r and r′. From now on we shall always understand by r and r′
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
897 P A R T 5 Light and Optics The light rays coming from the leaves in the background of this scene did not form a focused image in the camera that took this photograph. Consequently, the background appears very blurry. Light rays passing though the raindrop, however, have been altered so as to form a focused image of the background leaves for the camera. The optical principles we study in this part of the book will explain phenomena such as this one. (Don Hammond Photography ) Light is basic to almost all life on the Earth. For example, plants convert the energy transferred by sunlight to chemical energy through photosynthesis. In addition, light is the principal means by which we are able to transmit and receive information to and from objects around us and throughout the Universe. Light is a form of electromagnetic radiation and represents energy transfer from the source to the observer. It is rep- resented by T ER in Equation 8.2. Many phenomena in our everyday life depend on the properties of light. When you watch a television or view photos on a computer moni- tor, you are seeing millions of colors formed from combinations of only three colors that are physically on the screen: red, blue, and green. The blue color of the daytime sky is a result of the optical phenomenon of scattering of light by air molecules, as are the red and orange colors of sunrises and sunsets. You see your image in your bathroom mirror in the morning or the images of other cars in your rearview mirror when you are driving. These images result from reflection of light. If you wear glasses or contact lenses, you are depending on refraction of light for clear vision. The colors of a rainbow result from dispersion of light as it passes through raindrops hovering in the sky after a rainstorm. If you have ever seen the colored circles of the glory surrounding the shadow of your airplane on clouds as you fly above them, you are seeing an effect that results from interference of light.
eBook - ePub- Cesar A. Sciammarella, Federico M. Sciammarella(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
We have to return to the wave-particle duality principle. A photon is the elementary particle, associated with the electromagnetic field and it can be thought of as the basic “unit” of light with regards to visible radiation. However in general a photon is associated with all other forms of electromagnetic radiation. It is also a force carrier for electromagnetic radiation. The effects of this force are observed both at the microscopic and macroscopic levels. The photon is a mass-less particle, meaning that it does not have mass at rest. The photon has a momentum defined by(6.5)In classical mechanics momentum is the product of the mass of a particle and the velocity of the particle. The photon as a quantum particle has another property that is of fundamental importance, “spin”, envision the photon as a small sphere that rotates around its axis. The spin is related to the state of polarization of the photon. In many areas of optics we can set aside the particle nature of light. However in some cases it is necessary to resort to the particulate nature of light. For example when we are dealing with the interaction of light with matter one has to bring back the concept of light as a particle; this is the case of the photoelectric effect. Many developments in the field of Optics in the second half of the twentieth century that cannot be explained by classical Optics arguments need to utilize the particle nature of the photon. For example it is possible to produce light interference, a typical phenomenon of the wave nature of light by detecting one photon in time. To explain this phenomenon one has to utilize the quantum theory of light since it has no explanation in Classical Optics.6.3 The Electromagnetic Theory of LightWe have introduced the main variables that help describe the light propagation phenomenon; we now must analyze the mathematical structure that supports these basic notions. The mathematical support is given by the Maxwell equations. The fundamental idea introduced by Maxwell is the classical field theory. A physical field is defined by the fact that at each point in space at a given time (usually in a continuous manner), can be defined by a physical quantity. In the case of electromagnetic fields, two vectors are present at each point in space, the electrical field E and the magnetic field B . As such, they are often written as E (x, y, x, t), electric field and B
eBook - PDF- Dieter Schu??cker(Author)
- 1999(Publication Date)
- WSPC(Publisher)
1 Light and Matter 1.1 The Nature and Properties ofLight 1.1.1 Introduction Since the actual book is devoted to lasers that generate light with very specific properties, it is of ultimate importance to understand the nature and the properties of light, therefore this first chapter deals with that topic. Since many, many centuries, even millenniums, mankind regarded light as some specific and unknown kind of energy, that moves along straight trajectories, the 'light rays' with a certain speed, the 'speed of light c. With this historical approach called 'geometrical optics' all the useful devices, that provide imaging, as eye-glasses, microscopes and telescopes, can be treated, if it is considered, that the speed of light c has different values in different materials, a phenomenon described by the 'index of refraction' n > 1, where Co is the speed of light in vacuum. With this knowledge 'reflection' and 'refraction', the latter being used for enlarging or diminishing of images, can be explained. A more detailed investigation of the optical instruments designed after the rules of geometrical optics in the last century showed, that several phenomena could not be explained by geometrical optics. One important example is the behavior of a very narrow slot exposed to the irradiation with light /l .1/, /l .2/ whereas not only an image of the slot is obtained, but also additional and somewhat weaker copies of the main image, that are arranged in a regular pattern to the right and to the left of the main image (see Fig. 1.1.). The latter experimental result can be explained first by the consideration of 'Huygen's Law' /l.l/, /1.27 that means that each point hit by light emits light in all directions of the space, what explains first, that light does not only move in the direction of the incident light behind the slot, but can be bent by the slot and move in all directions behind the slot - a phenomenon called 'diffraction'.
eBook - PDFLight Sources
Basics of Lighting Technologies and Applications
- Spiros Kitsinelis, Spyridon Kitsinelis(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
Visible light is part of the electromagnetic spectrum and consists of a series of waves with lengths from 380 to 780 nanometers that humans perceive as color. Wavelength Mag netic field M E Electric field Figure 1.2. Electromagnetic wave propagation. 1.1 Properties of Light 3 a few Angstrom (10 –10 m). The relationship between energy and the wavelength or frequency is given by the formula E = h · v = (h · c)/ λ where E = energy (joule) v = frequency (Hz) h = Planck constant (6.626 × 10–34 J·sec) c = speed of light in vacuum (2.998 × 10 8 m/sec) λ = wavelength (m) Spectrometers analyze light and other radiation by making use of the wave prop-erties of light such as refraction or the interference that comes from diffraction. The principle of refraction is a change of direction following a change in the speed of the waves that happens when a wave passes from one medium to another with a different optical density, which is called a different refractive index . Figure 1.3 depicts this change of direction when the medium changes. The angle of incidence and the angle of refraction are related to the refractive indices of the media and this relation is described by Snell’s law n 1 sin θ 1 = n 2 sin θ 2 where n is the refractive index of each medium and sin θ is the sine of each angle (for example, air has a refractive index of 1.0003; for water it is 1.33; and for glass it is 1.5–1.9, depending on the type of glass). If the angle of incidence exceeds a specific value, then the wave is totally reflected without refraction taking place. This effect, which can be observed only n 2 θ 2 θ 1 θ 1 θ 2 n 1 Figure 1.3. Wave refraction. 4 Basic Principles of Light and Vision for waves traveling from a medium of a higher refractive index to a medium of lower refractive index (glass to air, not vice versa), is known as total internal reflection and it is the principle upon which optical fibers work (Figure 1.4). Refraction is behind the optical properties of lenses.
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 - PDF- Tom Cornsweet(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
However, a line correctly representing laser light on this horizontal scale would be too narrow to print. LENSES AND All quanta of electromagnetic radiation, regardless of their wave-REFRACTION lengths, travel in straight lines and at the same velocity (186,000 miles per second) through empty space. However, their velocities are re-duced when they pass through any medium, the reduction in velocity depending upon the nature of the medium and the wavelengths of the quanta. The velocity of light in air is so close to its velocity in a vac-uum that the effect of air on light may be ignored for the present pur-poses. The velocity of a quantum in water or glass, however, may be reduced by one third or more. 32 The Physics of Light 100 (a) 500 520 540 560 580 600 620 640 Wavelength (nm) Fig. 3.3 Emission spectra of relatively new sources, (a) The spectrum of a gallium phosphide electroluminescent crystal. Note that the horizontal scale is expanded as compared with those in the preceding figures, (b) The spectrum of a helium-neon laser. 1 UU .2 8 0 '(/Ϊ <£> I 60 CD > -2 40 <υ c* 20 0 --1 1 1 1 1 1 _J (b) 500 520 540 560 580 600 620 640 Wavelength (nm) Consider a single quantum following the path labeled 1 in Fig. 3.4. As the quantum enters the glass, it continues in its original path at a reduced velocity. (There is a probability of about 0.04 that the quan-tum will be reflected from the surface and travel back along its incom-ing path. For the present discussion, only those quanta that are not re-flected will be considered.) However, if a quantum is incident on the glass at an angle other than perpendicular to the surface, as indicated by the path labeled 2, its direction of motion will be changed when it enters the glass. The amount of this change in direction depends upon the angle of incidence (angle ABN) of the quantum and its change in velocity as it enters the glass.
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