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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  Physical Methods in Modern Chemical Analysis V2

  • Theodore Kuwana(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  All rights of reproduction in any form reserved. ISBN 0-12-430802-3 338 Thomas M. Niemczyk reduction is dependent on the wavelength of the light passing through the substance and on the temperature, pressure, chemical composition, homo-geneity, purity, etc. of the substance. Thus the Refractive Index is an important parameter in many measurements concerned with the testing or control of products. For example, the purity of a substance may be estimated on the basis of a Refractive Index determination. Refractive Index measurements have long been used in many situations and many instruments have been developed that can be used to make the measurements simple and reliable. It is the purpose of this chapter to review the means by which Refractive Index measurements can be made and discuss some of the applications. The fundamental basis of Refractive Index measurements is the phenom-enon of refraction. When light of a given wavelength passes from one isotropic medium, j in Fig. 1, into a second optically denser medium J, it undergoes a change in wave velocity (vj -* Vj) and its direction also changes unless the ray is perpendicular (N) to the surface boundary. The relation between the angle of incidence i and the angle of refraction r is expressed in Snell's law of refraction (Jenkins and White, 1957). The refracted ray lies in the plane of incidence, and the sine of the angle of refraction bears a constant ratio to the sine of the angle of incidence. The second part of this law states sinz/sinr = const (1) The constant in Eq. (1) is defined as the Refractive Index η of the medium J relative to the medium j and is equal to the characteristic ratio Vj /vj. By experimentally measuring the angles i and r one can determine the values of the Refractive Index for various transparent media. Fig. 1 Refraction of a beam of light upon inci-dence, at angle i, on a plane interface between medium j and a second optically denser medium J.

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  Physics

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

    (Publisher)

  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 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 refrac- tive 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 sec- tion. 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  υof light in the material:  n = Speed of light in a vacuum ____________________ Speed of light in the material = c  __ υ  (26.1) 814 CHAPTER 26 The Refraction of Light: Lenses and Optical Instruments 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 υ = 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 refraction depends slightly on the wavelength of the light, and the values in Table 26.1 correspond to a wavelength of λ = 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.

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  College Physics Essentials, Eighth Edition

  Electricity and Magnetism, Optics, Modern Physics (Volume Two)

  • Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  This change in direction is caused by the fact that light travels with different speeds in different media. Intuitively, you might expect the passage of light to take longer through a medium with more atoms per volume, and the speed of light is, in fact, generally less in denser media. For example, the speed of light in water is about 75% of that in air or a vacuum.

  The change in the direction of wave propagation is described by the angle of refraction . In ▼ Figure 22.11 , refraction of light at a medium boundary, θ 1 is the angle of incidence and θ 2 is the angle of refraction. The symbols θ 1 and θ 2 are used for the angles of incidence and refraction so as to avoid confusion with θ i and θ r , the angles of incidence and reflection. Willebrord Snell (1580–1626), a Dutch physicist, discovered a relationship between the angles (θ ) and the speeds (v ) of light in two media:

  sin   θ 1 sin   θ 2 = v 1 v 2   ( Snell ' s   law )	(22.2)

  ▲ Figure 22.11 Refraction Light changes direction on entering a different medium. The angle of refraction θ 2 , describing the direction of the refracted ray, is different from the angle of incidence θ 1 . (Both angles are measured from the normal.)

  This expression is known as Snell’s law or the law of refraction . Note that θ 1 and θ 2 are always taken with respect to the normal.

  Thus, light is refracted when passing from one medium into another because the speed of light is different in the two media. The speed of light is greatest in a vacuum, and it is therefore convenient to compare the speed of light in other media with this constant value (c ). This is done by defining a ratio called the index of refraction ( n ) :

  n = c v   ( speed   of   light   in   a   vacuum speed   of   light   in   a   medium )     ( index   of   refraction )	(22.3)

  As a ratio of speeds, the index of refraction is a unitless quantity. The indices of refraction of several substances are given in ▶

  Ta ble 22.1

  . Note that these values are for a specific wavelength of light. The wavelength is specified because v , and consequently n , are slightly different for different wavelengths within a particular medium. (This is the cause of dispersion, to be discussed in Section 22.5.) The values of n given in the table will be used in Examples and Exercises in this chapter for all wavelengths of light in the visible region, unless otherwise noted. Observe that n is always greater than 1, because the speed of light in a vacuum is always greater than the speed of light in any material (c > v

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  Physical Properties of Textile Fibres

  • J. W. S. Hearle, W E Morton(Authors)
  • 2008(Publication Date)
  • Woodhead Publishing

    (Publisher)

  One particular result is that the direction of travel of light is refracted or bent on passing from one medium to another. This leads to an alternative definition: Refractive Index n = sine of angle of incidence/sine of angle of refraction. The lower velocity of the waves means that the light waves are retarded on passing through a medium of high Refractive Index. If they are then combined with a beam that has passed through a different medium, various interference phenomena occur, and these may be utilised in the measurement of Refractive Index. In general, the Refractive Index of a material varies with the temperature and with the wavelength of the light being transmitted. The usual standard conditions of measurement involve the use of monochromatic sodium light, with a wavelength of 589 nm, at 20 °C. Light is composed of electromagnetic waves, and the change in velocity is associated with the electric polarisation that occurs under the influence of the electric field. The frequency of the waves is very high, so that only the polarisation of the electron distribution round the nuclei of atoms (i.e. the relative displacement of positive and negative charge) is important. Larger-scale effects, such as the rotation of permanent dipoles, cannot take place rapidly enough. The outer electrons, which are taking part in covalent bonds, are those affected, since electrons in the inner complete shells are not easily displaced: this is illustrated in Fig. 24.1. It is therefore possible to assign a polarisability to each chemical bond, although this is influenced to some extent by other atoms nearby. For example, there will be a small difference between the behaviour of a C—H bond in a —CH 2 — group in a chain and that of a C—H bond in a terminal —CH 3 group. The polarisability will also vary with the direction of the electric field, as illustrated in Fig. 24.1(b) and (c) : it is usually greatest when the field is directed along the line joining the atoms

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  Optical System Design

  • Rudolf Kingslake(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  This law underlies all considerations of optical systems based on ray paths. As already mentioned, a ray is a purely mathematical concept, and it represents the path along which a light wave will travel. The rays are everywhere perpendicular to the wave fronts, and because of the symmetry of the law of refraction, we can assume that light can travel in either direction along a ray. A. TOTAL INTERNAL REFLECTION It is clear from Fig. 2.3 that if a ray in a denser medium of Refractive Index n is refracted at a surface into a medium of lower Refractive Index n the angle of refraction /' will be greater than the angle of incidence /, and when / reaches the limiting value of sin / = n/n', the angle of refraction /' will be just equal to 90° and the refracted ray will lie along the surface. This particular value of the angle of incidence in the denser medium is called the critical angle φ. At angles of incidence smaller than φ the ray is refracted out in the ordinary way, but if/in the denser medium is greater than φ, there will be no refracted ray, and the whole of the light will be reflected back into the denser medium, as indicated 12 2. LIGHT AND IMAGES O ε I / Air n'=/.0 . G/oss n= 1.523 FIG. 2.3. Refraction and the critical angle. by the dashed ray in Fig. 2.3. This subject is discussed much more fully in Chapter VII, Section HIA. B. INTERPOLATION OF REFRACTIVE INDICES Optical glass catalogs give Refractive Index data for a large number of wavelengths, from 0.365 μτη in the near ultraviolet to 1.014 μτη in the infrared. However, it is sometimes necessary to interpolate between the given wavelengths, and for this purpose a formula connecting Refractive Index with wavelength is needed. In the catalog of the Schott Optical Glass Company, a six-term formula is used of the form n 2 = A 0 + Α λ λ 2 + Α 2 /λ 2 + Α 3 /λ 4 + Α 4 /λ 6 + Α 5 /λ*. (1) AU six coefficients A 0 to A 5 are given explicitly to eight significant figures for each type of glass.

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  Optoelectronics and Fiber Optic Technology

  • Ray Tricker(Author)
  • 2002(Publication Date)
  • Newnes

    (Publisher)

  Note: One everyday effect of refraction is that objects seen under water always appear to be at a shallower depth than they really are. This is because the observer sees an underwater object in a higher position, as the eye cannot tell that the light has been refracted on its path from the object. 38 Optoelectronics and Fiber Optic Technology 111111111111111111, :;;;2:Z:::Z Red Orange Yellow Green Blue Violet Figure 2.1 The speed of different wavelengths of light through the same medium 2.1 Reflection and refraction When light travelling in a transparent material meets the surface of another transparent material, two things happen: 9 some of the light will be reflected; and 9 some of the light will be transmitted into the second transparent material. Angle of Incident incidence r a y ~ ~ Angle of refraction J Reflected .... -- ~ ray s .. ,...,.. s n9 (air) n 2 (glass) Refracted ray Figure 2.2 Showing how light is refracted when passing from one medium into a denser medium Theory 39 The transmitted light usually changes direction when it enters the second material. This bending of light is called refraction and depends on the fact that whilst light travels at one speed in one material it will travel at a different speed in a different material. As a result, each material has its own Refractive Index and this is used to calculate the amount of bending that takes place. 2.2 Refractive Index The optical density of a material is referred to as its Refractive Index and is a direct proportion between the velocity of light in a vacuum to the velocity of light in the material: Velocity of light in a vacuum Refractive Index - = n Velocity of light in a medium As shown in Table 2.1, the Refractive Index of glass varies between the limits of pure crown glass and pure flint glass with a typical value of 1.6.

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  Beginner's Guide to Gemmology

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

    (Publisher)

  6 Refractive Index and Double Refraction For identification purposes, the most important single item of information about a gemstone is its refrac five index. The reason for this is that the Refractive Index (RI) of most gemstones is a constant which can be measured with precision to four signifi- cant figures (i.e. to three decimal places). Because of this precision and constancy, most gems can be distinguished with ease even when their RIs differ only very slightly (e.g. natural and synthetic spinel; pink topaz and tourmaline). The Refractive Index of a material is a measure of the degree by which it bends or refracts light rays passing through it. When a ray of light passes from one medium (such as air) into another medium of greater optical density (such as a gemstone), the ray is refracted, or bent, towards the normal (i.e. towards an imaginary line drawn at right-angles to the surface - see Figure 6.1). Conversely, when the ray leaves the gemstone and passes into air, it is refracted away from the normal. (Note: for optical work all ray angles are given relative to the normal.) Perhaps the most commonplace example of refraction is the apparent bending of a rod when it is partially immersed in water. The Refractive Index of a material can, in fact, be ex- pressed as the ratio of the optical density of the material, to that of air (the standard for all practical gemmological purposes): Optical density of material R I = Optical density of air 78 Refractive Index AND DOUBLE REFRACTION 79 The greater the difference in the optical densities of the two media, the greater will be the amount of refraction of light passing through them. As the velocity of light is decreased in an optically dense material (and is inversely porportional to the optical density), the RI of the material can also be expressed as the ratio of the velocity of light in air to the velocity of light in the medium.

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  The Characterization of Chemical Purity

  Organic Compounds

  • L. A. K. Staveley(Author)
  • 2016(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Refractive Indexj CHARLES PROFFER SAYLOR The National Bureau of Standards, Washington D.C. 20234, U.S.A. INTRODUCTION Refractive Index is not particularly valuable in the measurement of purity because the effects of impurities upon the property are indeterminate. A given impurity may raise, lower, or leave the Refractive Index unchanged. Those impurities that will most probably be present are, ordinarily, least certain to affect the Refractive Index. Still, a sample that has exactly the same Refractive Index as the perfectly pure material can usually be presumed to have high purity, since contaminants are unlikely to compensate precisely, and the more accurately the property is measured the more valid is the presumption. The methods of determination using liquid samples and the limits of accuracy to which the measurements of Refractive Index can be pressed will be discussed. The situation with solids is different. In most cases, an impurity influences the Refractive Index of a solid very little if at all. Refractive Index differences can be used to recognize isolated pockets of impurity, however, and by estima-tion and summation of the volumes of such outcroppings useful clues to the degree of contamination that are not otherwise available can be secured. 1. LIQUIDS No physical property can be measured with equal accuracy more easily than the Refractive Index of a liquid. The ratio of the probable error of a single determination to the broad range within which most materials cluster is favourable. The conditions that modify the measured values in signifi-cant degree are few and tractable. Indeed, only the necessary temperature control provides a continuing source of trouble. At every level of required accuracy, the necessary apparatus is hardy, and is not particularly expensive. For these reasons Refractive Index, like boiling-point, has had extensive use for monitoring separations or purifications and has even been used as a criterion of purity.

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  Polymer Characterization

  Physical Techniques, 2nd Edition

  • Dan Campbell, Richard A. Pethrick, Jim R. White(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  The specimen, in the form of a film of Refractive Index n, is placed between the two prisms and illuminated with monochromatic light from below. The critical angle for extinction is determined at the exit face of the upper crystal, and is indicated in terms of the angle of refraction (ϕ′ c) in Fig. 11.2. If the prism has Refractive Index n′ and the prism angle indicated in Fig. 11.2 is a, then Fig. 11.1 Refraction at a boundary between materials of different Refractive Index (n, n′) where n′ > n. The ray with the double arrowhead travels parallel to the interface in the upper material (angle of incidence = π /2) and passes into the lower material with angle of refraction ϕ c. n = n ′ sin ⁡ ϕ c ′ n ′ sin ⁡ ϕ = sin ⁡ ϕ ′ c and ϕ c = α − ϕ By eliminating first ϕ c, then ϕ, it can be shown that n = sin ⁡ α (n ′ 2 − sin 2 ϕ ′ c ⁡) 1 / 2 − cos ⁡ α ⁢ sin ϕ ′ c ⁡ (11.1) In a. typical commercial instrument the angle ϕ′ c is converted into the corresponding Refractive Index. The alignment of the instrument is usually checked with liquids of standard Refractive Index. If sodium light is used, this technique is capable of measuring n to about 0.1%. A typical commercial instrument has a small prism which allows compensation for the effect of dispersion when a white light source is used. Fig. 11.2 Abbé refractometer. 11.3 Birefringence If processing causes molecular orientation and/or moulding stresses to be present, the Refractive Index varies according to the direction of light propagation and the orientation of the plane of polarization. Birefringence is defined as the difference between the Refractive Index in two orthogonal directions. It is normally easier and more accurate to measure it directly, as described below, than to measure the two relevant refractive indices separately. 11.3.1 Birefringence Measurement Figure 11.3 is a schematic representation of an apparatus for measuring birefringence

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  Principles of Optical Fiber Measurements

  • Dietrich Marcuse(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  However, once a computer is employed as part of the mea-suring apparatus, the mathematical complexity of profile evaluation ceases to be of concern. For computer evaluation it hardly matters if a simple arithmetic expression or an integral has to be processed; the dif-ference is only one of time and, perhaps, of required computer size. 119 120 4 Refractive Index Profiling Methods 4.1 The Reflection Method Conceptually, one of the simplest methods for refractive-index pro-filing is the reflection method whose physical principle of operation is based on the fact that the reflectivity of a dielectric surface depends on the difference of the refractive indices of the surrounding medium, for ex-ample, air, and the glass of the fiber. Principle of Operation Figure 4.1.1 shows the principle of operation. Collimated light im-pinges at right angles on the end face of a fiber. The intensity of the re-flected light can be observed in the image plane of the same microscope that provides the illumination. Variations in the reflected light intensity can then be used to compute the refractive-index distribution. The method for measuring the light intensity distribution is not im-portant for the principle of operation. Photographic film could be used. The light intensity measurement would then consist of densitometer traces of the developed film using proper calibration. Direct electrical methods for measuring light intensities are preferable because they are much faster. A photodiode mounted behind a pinhole can physically be moved in the image plane of the microscope parallel to the image of the fiber end face and its output can be registered by a chart recorder. If more speed is required, an electronically scanned array of photodiodes may be used. Finally, a television camera (vidicon) can be employed to observe the microscopic image of the end face of the fiber and its output can be suitably sampled to obtain the desired intensity information.

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