Refraction

10 Key excerpts on "Refraction"

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  In general, we will see that the change in speed as a ray of light goes from one material to another causes the ray to deviate from its incident direc- tion. This change in direction is called Refraction. To describe the extent to which the speed of light in a material medium differs from that in a vacuum, we use a parameter called the index of Refraction (or refractive index). The index of Refraction is an important parameter because it appears in Snell’s law of Refraction, which will be discussed in the next section. This law is the basis of all the phenomena discussed in this chapter. 733 734 CHAPTER 26 The Refraction of Light: Lenses and Optical Instruments DEFINITION OF THE INDEX OF Refraction The index of Refraction n of a material is the ratio of the speed c of light in a vacuum to the speed  of light in the material: n = Speed of light in a vacuum Speed of light in the material = c υ (26.1) Table 26.1 lists the refractive indices for some common substances. The values of n are greater than unity because the speed of light in a material medium is less than it is in a vacuum. For example, the index of Refraction for diamond is n = 2.419, so the speed of light in diamond is  = c/n = (3.00 × 10 8 m/s)/2.419 = 1.24 × 10 8 m/s. In contrast, the index of Refraction for air (and also for other gases) is so close to unity that n air = 1 for most purposes. The index of refrac- tion depends slightly on the wavelength of the light, and the values in Table 26.1 correspond to a wavelength of  = 589 nm in a vacuum. 26.2 Snell’s Law and the Refraction of Light Snell’s Law When light strikes the interface between two transparent materials, such as air and water, the light generally divides into two parts, as Figure 26.1a illustrates. Part of the light is reflected, with the angle of reflection equaling the angle of incidence.

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  Gemmology

  • P. G. Read(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  The Refraction of a light ray is slightly more complicated, at least mathematically, and for many years it was not fully understood. Then in 1621 Snell discovered the underlying relationship between incident rays and refracted rays and laid the foundation for the subsequent rapid advances in applied optics. He expressed this relationship in his two laws of Refraction: 1. When a light ray passes from one medium into another there exists a definite ratio between the sines of the angle of incidence and the angle of Refraction. This ratio is dependent only on the two media and the wavelength of the light. 2. The incident ray, the refracted ray and the normal (at the point of incidence) are all in the same plane. 85 86 Reflection and Refraction NORMAL N Figure 9.1 Snell's first law of reflection states that the angle of incidence equals the angle of reflection (ION = NOR) Figure 9.2 (a) The incident light entering a gemstone (at an angle other than 90° to the surface) is refracted towards the normal. Light leaving a gemstone (other than at 90°) will be refracted away from the normal, (b) If air is the less dense medium, the RI of the denser medium is the ratio of the sines of the angles ION and MOR The word Refraction simply means angular deflection. When a ray of light passes from one medium (such as air) into an optically denser medium (such as a gemstone), at an angle other than 90°, the ray is refracted or bent towards the normal (see Figure 9.2(a)). Conversely, when the ray leaves the gemstone and passes into the air, it is refracted away from the normal. The greater the difference between the optical densities of the two mediums (or, in the case of a gemstone surrounded by air, the greater the optical density of the gem), the greater will be the amount of Refraction.

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  When light moves from one medium into another, its direction of travel changes, and this change in direction is called Refraction. The human eye is an incredible optical instrument, and, as we will see, Refraction plays a major role in the way it works to produce clear vision. 26 | The Refraction of Light: Lenses and Optical Instruments 721 Design Pics/SuperStock Chapter | 26 26.1 | The Index of Refraction As Section 24.3 discusses, light travels through a vacuum at a speed of c 5 3.00 3 10 8 m/s. It can also travel through many materials, such as air, water, and glass. Atoms in the material absorb, reemit, and scatter the light, however. Therefore, light travels through the material at a speed that is less than c, the actual speed depending on the nature of the material. In general, we will see that the change in speed as a ray of light goes from one material to an- other causes the ray to deviate from its incident direction. This change in direction is called Refraction. To describe the extent to which the speed of light in a material medium differs from that in a vacuum, we use a parameter called the index of Refraction (or refractive index). The index of Refraction is an important parameter because it appears in Snell’s law of Refraction, which will be discussed in the next section. This law is the basis of all the phenomena discussed in this chapter. Definition of the Index of Refraction The index of Refraction n of a material is the ratio of the speed c of light in a vacuum to the speed v of light in the material: n 5 Speed of light in a vacuum Speed of light in the material 5 c v (26.1) Table 26.1 lists the refractive indices for some common substances. The values of n are greater than unity because the speed of light in a material medium is less than it is in a vacuum. For example, the index of Refraction for diamond is n 5 2.419, so the speed of light in diamond is v 5 c/n 5 (3.00 3 10 8 m/s)/2.419 5 1.24 3 10 8 m/s.

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  Let There Be Light: The Story Of Light From Atoms To Galaxies (2nd Edition)

  The Story of Light from Atoms to Galaxies

  • Alex Montwill, Ann Breslin(Authors)
  • 2013(Publication Date)
  • ICP

    (Publisher)

  39 Chapter 3 Light as a Ray: Refraction Providing more than one quickest route When light crosses the boundary between two media, it changes direction. This phenomenon is called Refraction. In this chapter we study the rules and applications of Refraction . The basic rule is the same as always: it is Fermat’s principle of least time. We show that the principle leads to the experimentally established Snell’s law of Refraction. Lenses are the most common example of the application of the laws of Refraction . In making a lens, the trick is to make the shape such that all routes from a source A to a destination B on the other side of the lens take the same time, despite the fact that light traverses different thicknesses of glass on differ-ent routes. We spend the remainder of this section dealing with the geom-etry of the paths, and derive some simple formulae for lenses. Making visible things we cannot see We describe the effect of various combinations of lenses which make up optical systems. One fascinating example is the optical system of the human eye. We discuss some common eye defects and how these may be corrected using suitable lenses. Finally, we describe optical systems which enable us to look at things which are either too small or too far away to be seen with the naked eye. 40 Let There Be Light 2nd Edition 3.1 Refraction The refractive index As we all know, from experience of city traffic, if the speeds along different routes are not the same, the shortest route is not necessarily the quickest. We have seen already that in vacuum the speed of light is fixed at c = 2.99792458 × 10 8 m/s, equivalent to travelling a distance of approximately 7.5 times around the earth in one second . Light can also travel through certain ‘trans-parent’ materials such as air, water, glass or quartz, and there the speed is less than c .

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  Principles of Physical Optics

  • Charles A. Bennett(Author)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  See Section 3.7. b Far-infrared. The law of Refraction, also called Snell’s law, was found experimentally by Snell early in the seventeenth century. In Figure 3.2, the light ray is incident within the incident medium and the light beam transmits into the transmitted medium. The index of Refraction of the incident medium is n i and the index of Refraction of the transmitted medium is n t . According to Snell’s law n i sin θ i = n t sin θ t (3.4) Finally, it is implicit in Figure 3.2 that the incident, reflected, and refracted rays all lie within a single plane. This plane is called the plane of incidence. We will refer to the case where n i < n t as external incidence. An example of external incidence occurs at an air-glass interface. Internal incidence occurs when n i > n t ; for example, when a light beam passes from glass to air. 62 REFLECTION AND Refraction incident ray reflected ray refracted ray incident medium transmitted medium n i n t θ i θ i θ t Figure 3.2. An interface between two media, showing the incident, reflected, and refracted rays. EXAMPLE 3.1 Show that a light beam passing through a plane slab emerges parallel to its incident direction displaced laterally by a distance d given by d = t cos θ 2 sin (θ 1 − θ 2 ) (3.5) n 1 n 1 n 2 θ 1 θ 2 θ 3 d t a γ Figure 3.3. Light rays refracting through a slab of material with parallel sides. Solution Let the slab have index of Refraction n 2 and the incident and transmitted medium OVERVIEW OF REFLECTION AND Refraction 63 have index of Refraction n 1 as shown in Figure 3.3. To show that the incident and transmitted rays are parallel, begin with Snell’s law at the first interface: sin θ 2 = n 1 n 2 sin θ 1 The beam transmitted by the first interface is incident internally on the second interface.

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  College Physics

  • Michael Tammaro(Author)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  Video 26.1.1 A popular classroom demonstration that illustrates the Refraction of light. I N T E R A C T I V E F E A T U R E 712 | Chapter 26 Moreover, the incident and refracted rays are in the same plane. The angles θ and θ ′ are measured with respect to the normal—that is, a line that is perpendicular to the boundary between the mediums. Example 26.1.1 illustrates the use of Snell’s law. Snell’s Law When a light ray traveling in a medium of index of Refraction n enters a medium whose index of Refraction is n′, the angle of incidence θ and angle of Refraction θ ′ are related as follows: n n sin sin θ θ = ′ ′ (26.1.3) Snell’s Law Refraction is described mathematically by Snell’s law: Example 26.1.1 Light Passes Through a Window Window panes are typically made of soda-lime glass, which is the most prevalent type of glass and has an index of Refraction of 1.518 (Table 26.1.1). Suppose that sunlight passes through a soda-lime glass window whose faces are vertical and parallel. If the Sun’s angle of elevation is 59.4°, what is the elevation angle of the Sun’s rays after they pass through the window? Identify The diagram shows a cross section of the window. The normal to the glass is horizontal, so the Sun’s rays make an angle of 59.4° to the normal before entering the glass. The three dashed lines are horizontal, so the two angles labeled 1 θ are equal and the two angles labeled 2 θ are equal. (The alternate interior angles are equal because the dashed lines are parallel.) 59.4° Sun Air Air Glass θ 1 θ 1 θ 2 θ 2 From the diagram, the angle 2 θ measures the elevation angle of the Sun’s rays after they pass through the glass. The index of Refraction of air is 1.000, which is why the diagram shows that 59.4 1 θ < ° (light refracts toward the normal when it passes into a medium of higher refractive index). Similarly, the diagram shows that 2 1 θ θ > (light refracts away from the normal when it passes into a medium of lower refractive index).

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  Dielectrics and Basic Concepts in Optics

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  ________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Basic Concepts in Optics 1. Refractive index Refraction of light at the interface between two media The refractive index or index of Refraction of a substance is a measure of the speed of light in that substance. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium. The velocity at which light travels in vacuum is a physical constant, and the fastest speed at which energy or information can be transferred. However, light travels slower through any given material, or medium, that is not vacuum. A simplified, mathematical description of refractive index is as follows: n = velocity of light in a vacuum / velocity of light in medium Hence, the refractive index of water is 1.33, meaning that light travels 1.33 times as fast in a vacuum than it does in water. ________________________ WORLD TECHNOLOGIES ________________________ As light exits a medium, such as air, water or glass, it may also change its propagation direction in proportion to the refractive index. By measuring the angle of incidence and angle of Refraction of the light beam, the refractive index n can be determined. Refractive index of materials varies with the frequency of radiated light. This results in a slightly different refractive index for each color. The cited values of refractive indexes, such as 1.33 for water, are taken for yellow light of a sodium source which has the wavelength of 589.3 nanometers. Definitions The refractive index, n , of a medium is defined as the ratio of the speed, c , of a wave phenomenon such as light or sound in a reference medium to the phase speed, v p , of the wave in the medium in question: It is most commonly used in the context of light with vacuum as a reference medium, although historically other reference media (e.g. air at a standardized pressure and temperature) have been common.

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  A ray bends away from the normal when it travels from a medium with a larger refractive index into a medium with a smaller refrac- tive index. When the ray leaves the prism, it again bends upward, which is toward the normal at the point of exit. A ray bends toward the normal when traveling from a smaller toward a larger refrac- tive index. Thus, thesituationin Figure26.19acouldariseifthe prismwereimmersedinafluid,suchascarbondisulfide,that hasalargerrefractiveindexthandoesglass (see Table 26.1). We have seen in Figures 26.18a and 26.19a that a glass prism can bend a ray of light either downward or upward, depend- ing on whether the surrounding fluid has a smaller or larger index of Refraction than the glass. It is logical to conclude, then, that a prismwillnotbendarayatall,neitherupnordown,ifthesur- roundingfluidhasthesameindexofRefractionastheglass—a condition known as index matching. This is exactly what is happen- ing in Figure 26.19b, where the ray proceeds straight through the prism as if the prism were not even there. If the index of Refraction of the surrounding fluid equals that of the glass prism, then n 1 = n 2 , and Snell’s law (n 1 sin θ 1 = n 2 sin θ 2 ) reduces to sin θ 1 = sin θ 2 . Therefore, the angle of Refraction equals the angle of incidence, and no bending of the light occurs. Related Homework: Check Your Understanding 16 (a) (b) FIGURE 26.19 A ray of light passes through identical prisms, each surrounded by a different fluid. The ray of light is (a) refracted upward and (b) not refracted at all. THE PHYSICS OF . . . rainbows. Another example of dispersion occurs in rain- bows, in which Refraction by water droplets gives rise to the colors. You can often see a rain- bow just as a storm is leaving, if you look at the departing rain with the sun at your back.

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  Introduction to Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  How can the situations illustrated in Figure 26.19 arise? Reasoning and Solution Snell’s law of Refraction includes the refractive indices of both ma- terials on either side of an interface. With this in mind, we note that the ray bends upward, or away from the normal, as it enters the prism in Figure 26.19a. A ray bends away from the nor- mal when it travels from a medium with a larger refractive index into a medium with a smaller refractive index. When the ray leaves the prism, it again bends upward, which is toward the normal at the point of exit. A ray bends toward the normal when traveling from a smaller toward a larger refractive index. Thus, the situation in Figure 26.19a could arise if the prism were immersed in a fluid, such as carbon disulfide, that has a larger refractive index than does glass (see Table 26.1). We have seen in Figures 26.18a and 26.19a that a glass prism can bend a ray of light either downward or upward, depending on whether the surrounding fluid has a smaller or larger index of Refraction than the glass. It is logical to conclude, then, that a prism will not bend a ray at all, neither up nor down, if the surrounding fluid has the same index of Refraction as the glass—a condition known as index matching. This is exactly what is happening in Figure 26.19b, where the ray proceeds straight through the prism as if the prism were not even there. If the index of Refraction of the surrounding fluid equals that of the glass prism, then n 1 5 n 2 , and Snell’s law (n 1 sin u 1 5 n 2 sin u 2 ) reduces to sin u 1 5 sin u 2 . Therefore, the angle of Refraction equals the angle of incidence, and no bending of the light occurs. 26.6 | Lenses 661 After reflection from the back surface of the droplet, the different colors are again refracted as they reenter the air.

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  Physics for Scientists and Engineers

  Foundations and Connections, Extended Version with Modern Physics

  • Debora Katz(Author)
  • 2016(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Some people believed color was a mixture of light and darkness. But Isaac Newton performed an experiment in 1666 showing that white light can be spread out to reveal all the colors and that all those colors can be recombined to form white light. In this section, we’ll see how such an experiment is possible. (In Problem 27, you’ll consider the details.) The speed of an electromagnetic wave in a medium depends on the medium’s index of Refraction n (Eq. 36.8). The index of Refraction depends in turn on the fre- quency, wavelength, or color of the light (Table 38.1). For many media, the index of Refraction is highest for violet light and lowest for red light. So, when white light propagates from a medium with a low index of Refraction, like air, into a medium with a high index of Refraction, like glass, the violet light slows down more than the red light. In addition, light bends or refracts when it is transferred from one medium into another because the speed of light is different in the two media. In general, violet light is refracted more than red light (Fig. 38.9A). The result is that white light is spread out into a broader beam that is separated by color. This broad beam looks something like a rainbow and is called a visible light spectrum, a color spectrum, or simply a spectrum (Fig. 38.9B). The spreading out of light by color due to differ- ences in the index of Refraction is called dispersion. DISPERSION ★ Major Concept Because the triangle in Figure 38.8 is a right triangle, we know the two acute angles add up to 90°. u c 1 u t 5 90° u t 5 90° 2 u c u t 5 90° 2 52.0° 5 38.0° The incident angle u i is related to the refracted angle u t by Snell’s law (Eq. 38.1). At the left boundary in Figure 38.8, light is incident in air, so n i 5 n air 5 1.00029 and n t 5 n fib 5 1.27.

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