Dispersion of Light

9 Key excerpts on "Dispersion of Light"

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  eBook - ePub

  Physics for O.N.C. Courses

  • R.A. Edwards(Author)
  • 2014(Publication Date)
  • Pergamon

    (Publisher)

  Chapter 21 .

  If a beam of white light such as that from the sun or from an ordinary electric filament lamp is refracted through a glass prism dispersion occurs and the different colour components of the light emerge from the prism travelling in slightly different directions from each other. It was in this way that Newton discovered in the seventeenth century that white light consisted of a spectrum of colours. He made a small hole in a window blind through which sunlight passed producing a bright, illuminated circular patch on a screen placed in its path. When a prism was placed between the hole and the screen, in the path of the light, deviation of the light occurred but also the patch of light was considerably elongated and there was a variation in colour from one end to the other, the least deviated light being red and the most deviated being violet, as shown in Fig 23.1 . Newton distinguished seven colours—the colours of the rainbow—red, orange, yellow, green, blue, indigo and violet. A spectrum obtained in this simple manner is not a “pure” spectrum since the various colours overlap. Figure 23.2 shows an arrangement in which a pure spectrum may be obtained on a screen so that there is minimum overlapping of colours and as one progresses from the red to the violet there is a continuous decrease in the wavelength of the light incident at any point. A suitable source of light is an ordinary electrically heated filament lamp and this is used to illuminate a narrow slit. The slit is situated in the focal plane of a converging lens L which, for reasons to be explained later, should preferably be a combination of a converging lens and a diverging lens of different refractive indices and in contact with each other, such a combination being known as an achromatic lens or achromatic doublet , designed so as to produce no dispersion. The light from each point of the slit thus emerges as a parallel beam. The light is said to be collimated and the lens acts as a collimator . This light then falls on one face of the prism where dispersion occurs and the emergent light consists of sets of parallel beams of light travelling in different directions and of different colours, i.e. wavelengths, from each point of the slit. A second converging achromatic lens L′

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  Spectroscopy for Amateur Astronomers

  Recording, Processing, Analysis and Interpretation

  • Marc F. M. Trypsteen, Richard Walker(Authors)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  The mechanism of dispersion by refraction finds its origin in the interaction of light with matter, in this case water drop- lets. The different beams of light interact with the electrons of the water molecules. The electron configuration of two hydro- gen atoms (1s 1 ) with one oxygen atom (1s 2 2s 2 2p 4 ) to form one water molecule mounts up to a total of 10 electrons. Blue light with a wavelength of 4500 Å causes a push/pull on those 10 electrons resulting in 200 trillion vibrations per second (Hz) more than red light does with its wavelength of 6670 Å. After this absorption and re-emission process the speed through the water droplets of the blue light is slower than that of red light. As a result blue light is more refracted than red light, hence the change of their individual direction. Θ 2 Θ 1 n 2 n 1 Figure 4.2 Snell’s law of refraction 1 2 3 β β β β α α f Figure 4.3 Pathway of a beam of light in an (idealized) water droplet, generating a rainbow Types and Function of Dispersive Elements 25 4.1.3 Dispersion by Diffraction Another way to shift wavelengths is to get dispersion by diffraction. It was discovered by the English physician Thomas Young (1773–1829) who carried out the famous double slit experiment. Therein a monochromatic light beam goes through a screen with two slits. The expected result was to see two lines on the viewing screen. But instead multiple lines were observed. In fact the light spreads out and the only possibility to understand what happened is to consider light as a wave instead of a particle. This phenomenon is called diffraction and the dark and bright fringes with specific spacing, is called an interference pattern. Historically it was the first experiment to show the wave nature of light. In Figure 4.4 light goes through a double slit and is pro- jected on a screen. The difference in the pathway between R1 and R2 is indicated as Δλ. The projection point on the screen is P. When R1 – R2 = Δλ then Δλ ¼ d sin θ.

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  Specific Fields of Physics

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

    (Publisher)

  A small proportion of light scattering from atoms or molecules may undergo Raman scattering, wherein the frequency changes due to excitation of the atoms ________________________ WORLD TECHNOLOGIES ________________________ and molecules. Brillouin scattering occurs when the frequency of light changes due to local changes with time and movements of a dense material. Dispersion occurs when different frequencies of light have different phase velocities, due either to material properties ( material dispersion ) or to the geometry of an optical waveguide ( waveguide dispersion ). The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called normal dispersion. It occurs in all dielectric materials, in wavelength ranges where the material does not absorb light. In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called anomalous dispersion. The separation of colors by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(sin (θ) / n ). Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known rainbow pattern. Dispersion: two sinusoids propagating at different speeds make a moving interference pattern. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure. In effect, the individual waves (which travel with the phase velocity) escape from the wave packet (which travels with the group velocity).

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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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  Introduction to Optics I

  Interaction of Light with Matter

  • Ksenia Dolgaleva(Author)
  • 2022(Publication Date)
  • Springer

    (Publisher)

  Dispersion plays a crucial role in light propagation through the optical medium and has to be considered in designing optical components and devices. Moreover, it serves as the mechanism of operation in certain optical components and devices. It is an important subject for discussion in this chapter. Material media respond differently to different colors of light. Some colors, or frequencies, can be far from the medium’s resonances. The interaction of such light with the medium is reduced to phase accumulation and slow-down acquired by the light, as well as some possible impact of dispersion. However, if the frequency of light matches one of the material’s resonances, it can be absorbed by the optical medium. Absorption represents a source of loss of optical power and can be regarded as a parasitic effect. On the other hand, it can serve as the mechanism of operation for some optoelectronic and optical devices, such as detectors of optical power or optically excited amplifiers and lasers. 42 3. INTERACTION OF LIGHT WITH MATTER Absorption 1 and dispersion are linear optical phenomena. The material parameters used to describe these phenomena are field-independent. This means that, when treating dispersion or linear absorption, the material medium responds equally to an optical field of any strength. On the other hand, not all the effects associated with the material response are linear. Some of them are nonlinear with intensity-dependent material parameters. In these cases, the outcome of light–matter interaction can strongly depend on the intensity of the applied light. A group of intensity-dependent phenomena is called nonlinear optical interactions. Depending on the mate- rial medium, there can be a wide variety of such effects. Some of them are accompanied by the change in the color of light, thereby allowing one to access new spectral ranges not attainable by conventional light sources. The field of optics describing such effects is called nonlinear optics.

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  Optics

  Principles and Applications

  • Kailash K. Sharma(Author)
  • 2006(Publication Date)
  • Academic Press

    (Publisher)

  Other colors occupy positions in between in the sequence VIBGYOR 2 . The Cauchy dispersion formula n = A + B 2 + C 4 +··· (1.87) describes the dependence of the index of refraction of such media on wavelength, where A , B , C are constants to be determined empirically for a given material. Normal dispersion (negative d n/ d ) occurs at wavelengths not too close to an atomic transition. In the close neighborhood of an atomic transition, d n/ d may become positive and dispersion in this region is called anomalous dispersion, although there is nothing anomalous about it except that it is accompanied by substantial absorption whereas much less absorption takes place in the spectral range of normal dispersion (see Fig. 1.21). A lens also disperses white light. Whereas the dispersion produced by a prism (in a prism spectrometer) and by a grating (in a grating spectrometer) is useful in determining the spectral (wavelength) composition of incident light, the dispersion in the image formed by a lens is undesirable, and is therefore called the chromatic aberration of the lens. As an application of light propagation through a prism, we show how the index of refraction of the material of the prism can be determined quite accurately from the deviation the prism produces in the path of a ray (Fig. 1.18). θ 1 θ 2 δ φ φ 1 2 A n 1 n 2 n 1 Fig. 1.18: Deviation of a monochromatic wave in passing through a prism. 2 VIBGYOR stands for violet, indigo, blue, green, yellow, orange and red colours. 46 Chapter 1: LIGHT WAVES The deviation of a ray passing through a prism is given by = 1 + 2 − 1 − 2 (1.88) where 1 and 2 are the angles of incidence and emergence, respectively, 1 the angle of refraction at the first interface, and 2 the angle of incidence at the second interface. We note that 1 + 2 + − A = or 1 + 2 = A (1.89) where A is the angle of the prism.

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  University Physics Volume 3

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  1.2 The Law of Reflection • When a light ray strikes a smooth surface, the angle of reflection equals the angle of incidence. • A mirror has a smooth surface and reflects light at specific angles. • Light is diffused when it reflects from a rough surface. 1.3 Refraction • The change of a light ray’s direction when it passes through variations in matter is called refraction. • The law of refraction, also called Snell’s law, relates the indices of refraction for two media at an interface to the change in angle of a light ray passing through that interface. 1.4 Total Internal Reflection • The incident angle that produces an angle of refraction of 90° is called the critical angle. • Total internal reflection is a phenomenon that occurs at the boundary between two media, such that if the incident angle in the first medium is greater than the critical angle, then all the light is reflected back into that medium. • Fiber optics involves the transmission of light down fibers of plastic or glass, applying the principle of total internal reflection. • Cladding prevents light from being transmitted between fibers in a bundle. • Diamonds sparkle due to total internal reflection coupled with a large index of refraction. 1.5 Dispersion • The spreading of white light into its full spectrum of wavelengths is called dispersion. • Rainbows are produced by a combination of refraction and reflection, and involve the dispersion of sunlight into a continuous distribution of colors. • Dispersion produces beautiful rainbows but also causes problems in certain optical systems. 44 Chapter 1 | The Nature of Light This OpenStax book is available for free at http://cnx.org/content/col12067/1.4 1.6 Huygens’s Principle • According to Huygens’s principle, every point on a wave front is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wave front is tangent to all of the wavelets.

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  The Principles of Physical Optics

  An Historical and Philosophical Treatment

  • Ernst Mach(Author)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  The Fraunhofer lines form an excellent means for the exact definition of different kinds of light. It is much more precise to speak of the refractive index of the D line, or of the light emitted by glowing sodium vapour, that is to say, of the component of sunlight which is absent at the same place in the spectrum, than merely of yellow light, which comprises several kinds of light of different refrangibility. The discovery was therefore very important in connexion with the theory of. dispersion.

  A determination of the refractive index of the Fraunhofer lines in different substances very soon brought the conviction that refraction and dispersion bear no simple relation to one another. The table on p. 112 gives the refractive indices for several media.

  Denoting the refractive index of B by µ B , that of E by µ E , and that of H by µ H , µ E represents the mean refractive index, while µ H − µ B is a measure of the dispersion. We thus see that the mean refractive index and the dispersion do not run in parallel. The mean refractive indices of two substances do not in any case bear the same relation to one another as their dispersions; for example, for crown glass and oil of cassia, the mean refractive index is almost equal, whereas the dispersion of oil of cassia is about three times that of crown glass. Oil of cassia refracts the red rays less and the violet more than crown glass. The distribution of the colours in the spectrum with different substances, also, is not geometrically similar; flint glasses, for example, draw out the violet part of the spectrum proportionally more than the other parts. Let the different kinds of light corresponding to the lines A, B, C, . . . H be represented by a succession of points marked off as abscissæ along an axis. If lengths proportionate to the refractive indices are marked off as ordinates from each of these points, then their extremities form a curve, which is called a “dispersion curve.” It follows from the above that such dispersion curves have different shapes for different substances.

  FIG. 99 .

  The refraction and dispersion through a prism of a beam of white light incident on one face can easily be followed by means of a two-fold application of Snell’s construction (Fig. 99 ). An arc of a circle of arbitrary radius r is described with the intersection of the prism faces as centre, in a plane perpendicular to them. Two other arcs of radii, r 1 and r 2 , such that r 1/ r = µ r , r 2 /r = µ v , the refractive indices for red and violet respectively, are also drawn. If SK represents an incident ray, and SUV is perpendicular to the first face and UR, VV perpendicular to the second face of the prism, then UK, KV represent the two rays in the glass, and RK, VK the rays which emerge into the air. Suppose a prism with sharp edges (Fig. 100 ) is placed on a horizontal sheet of paper, and the intersections of the edges with the paper are marked. Let a beam of sunlight be made to pass through a small slit so that it is incident on the prism and also grazes the paper. Then, by reversing the above construction, the refractive indices may be determined. In this case KA, KB, SK, RK, and VK are given. The arc r is drawn with arbitrary radius, and the intersection of the perpendiculars VV, UR, S“V give the radii r 1 and r 2

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  Theory of Reflectance and Emittance Spectroscopy

  • Bruce Hapke(Author)
  • 2012(Publication Date)
  • Cambridge University Press

    (Publisher)

  3 The absorption of light 3.1 Introduction The differential reflection and scattering of light as a function of wavelength form the basis of the science of reflectance spectroscopy. This chapter discusses the absorption of electromagnetic radiation by solids and liquids. The classical descrip- tions of absorption and dispersion are derived first, followed by a brief discussion of these processes from the point of view of quantum mechanics and modern physics. Finally, the various types of mechanisms by which light is absorbed are summarized. 3.2 Classical dispersion theory 3.2.1 Conductors: the drude model The simplest model for absorption and dispersion by a solid is that of Drude (1959). This model assumes that some of the electrons are free to move within the lattice, while the ions are assumed to remain fixed. These approximate the conditions within a metal. The average electric-charge density associated with the semifree electrons is equal to the average of that associated with the lattice ions, so that the total electric-charge density ρ e = 0. Because the quantum-mechanical wave functions of the conduction electrons are not localized in a metal, the local field E loc seen by the electrons is equal to the macroscopic field E e . Thus, the force on each electron is –e 0 E e ,where e 0 is the charge of an electron. Assume that E e is parallel to the x -axis. In addition to the electric field, there is a force due to collisions of each elec- tron with the lattice, resulting in nonradiative loss of energy. This force, which is proportional to the velocity d x/dt of the electron, but opposite in direction, may be characterized by a parameter , defined such that the average collisional force on the electron is given by −2πm e d x/dt, where m e is the mass of the electron, and x is the displacement of the electron relative to the lattice. Physically, it can be shown that  = 1/2π t, where t is the mean time between collisions of the electron 27

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